what is an example of ad hoc hypothesis

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Prediction versus Accommodation

In early philosophical literature, a ‘prediction’ was considered to be an empirical consequence of a theory that had not yet been verified at the time the theory was constructed—an ‘accommodation’ was one that had. The view that predictions are superior to accommodations in the assessment of scientific theories is known as ‘predictivism’. Commonly, however, predictivism is understood more precisely as entailing that evidence confirms theory more strongly when predicted than when accommodated. Much ink has been spilled modifying the concept of ‘prediction’ and explaining why predictivism is or is not true, and whether the history of science and, more recently, logic (Martin and Hjortland 2021) reveals that scientists are predictivist in their assessment of theories. The debate over predictivism also figures importantly in the debate about scientific realism.

1. Historical Introduction

2. ad hoc hypotheses, 3. early characterizations of novelty, 4. a predictivist taxonomy, 5. the null support thesis, 6.1 reliable discovery methods, 6.2 the fudging explanation, 6.3 arbitrary and non-arbitrary conjunctions, 6.4 severe tests, 6.5 conditional and unconditional confirmation, 6.6 the archer analogy, 6.7 the akaike approach, 6.8 endorsement novelty and the confirmation of background beliefs, 7. anti-predictivism, 8 the realist/anti-realist debate, other internet resources, related entries.

There was in the eighteenth and nineteenth centuries a passionate debate about scientific method—at stake was the ‘method of hypothesis’ which postulated hypotheses about unobservable entities which ‘saved the phenomena’ and thus were arguably true (see Laudan 1981a). Critics of this method pointed out that hypotheses could always be adjusted artificially to accommodate any amount of data. But it was noted that some such theories had the further virtue of generating specific predictions of heretofore unobserved phenomena—thus scientists like John Herschel and William Whewell argued that hypotheses that saved phenomena could be justified when they were confirmed by such ‘novel’ phenomena. Whewell maintained that predictions carry special weight because a theory that correctly predicts a surprising result cannot have done so by chance, and thus must be true (Whewell 1849 [1968: 294]). It thus appeared that predicted evidence confirmed theory more strongly than accommodated evidence. But John Stuart Mill (in his debate with Whewell) categorically denied this claim, affirming that

(s)uch predictions and their fulfilment are, indeed, well calculated to impress the ignorant vulgar, whose faith in science rests solely upon similar coincidences between its prophecies and what comes to pass. But it is strange that any considerable stress should be laid upon such a coincidence by scientific thinkers. (1843, Vol. 2, 23)

John Maynard Keynes provides a simple account of why predictivism has a misleading appearance of truth in a brief passage in his book A Treatise on Probability :

The peculiar virtue of prediction or predesignation is altogether imaginary… The plausibility of the argument [for predictivism] is derived from a different source. If a hypothesis is proposed a priori , this commonly means that there is some ground for it, arising out of our previous knowledge, apart from the purely inductive ground, and if such is the case the hypothesis is clearly stronger than one which reposes on inductive grounds only. But if it is merely a guess, the lucky fact of its preceding some or all of the cases which verify it adds nothing whatever to its value. It is the union of prior knowledge, with the inductive grounds which arise out of the immediate instances, that lends weight to any hypothesis, and not the occasion on which the hypothesis is first proposed. (1921: 305–306) [ 1 ]

By ‘the inductive ground’ for a hypothesis Keynes clearly means the data that the hypothesis fits. Keynes means that when some theorist who undertakes to test a hypothesis first proposes it, typically some other (presumably theoretical) form of support prompted the proposal. Thus hypotheses which are proposed without being built to fit the empirical data (which they are subsequently shown to entail) are typically better supported than hypotheses which are proposed merely to fit the data—for the latter lack the independent support possessed by the former. The appearance of plausibility to predictivism arises because the role of the preliminary hypothesis-inducing evidence is being suppressed.

Karl Popper is probably the most famous proponent of prediction in the history of philosophy. In his lecture “Science: Conjectures and Refutations” Popper recounts his boyhood attempt to grapple with the question “When should a theory be ranked as scientific?” (Popper 1963: 33–65). Popper had become convinced that certain popular theories of his day, including Marx’s theory of history and Freudian psychoanalysis, were pseudosciences. Popper deemed the problem of distinguishing scientific from pseudoscientific theories ‘the demarcation problem’. His solution to the demarcation problem, as is well known, was to identify the quality of falsifiability (or ‘testability’) as the mark of the scientific theory.

The pseudosciences were marked, Popper claimed, by their vast explanatory power. They could explain not only all the relevant actual phenomena the world presented, they could explain any conceivable phenomena that might fall within their domain. This was because the explanations offered by the pseudosciences were sufficiently malleable that they could always be adjusted ex post facto to explain anything. Thus the pseudosciences never ran the risk of being inconsistent with the data. By contrast, a genuinely scientific theory made specific predictions about what should be observed and thus ran the risk of falsification. Popper emphasized that what established the scientific character of relativity theory was that it ‘stuck its neck out’ in a way that pseudosciences never did.

Like Whewell and Herschel, Popper appeals to the predictions a theory makes as a way of separating the illegitimate uses of the method of hypothesis from its legitimate uses. But while Whewell and Herschel pointed to predictive success as a necessary condition for the acceptability of a theory that had been generated by the method of hypothesis, Popper focuses in his solution to the demarcation problem not on the success of a prediction but on the fact that the theory made the prediction at all. Of course, there was for Popper an important difference between scientific theories whose predictions were confirmed and those whose prediction were falsified. Falsified theories were to be rejected, whereas theories that survived testing were to be ‘tentatively accepted’ until falsified. Popper did not hold, with Whewell and Hershel, that successful predictions could constitute legitimate proof of a theory—in fact Popper held that it was impossible to show that a theory was even probable based on the evidence, for he embraced Hume’s critique of inductive logic that made evidential support for the truth of theories impossible. Thus, one should ascribe to Popper a commitment to predictivism only in the broad sense that he held predictions to be superior to accommodations—he did not hold that predictions confirmed theory more strongly than accommodations. It would ultimately prove impossible for Popper to reconcile his claim that a theory which enjoyed predictive success ought to be ‘tentatively accepted’ with his anti-inductivism (see, e.g., Salmon 1981).

Imre Lakatos (1970, 1971) proposed an account of scientific method in the form of his ‘methodology of scientific research programmes’ which was a development of Popper’s approach. A scientific research program was constituted by a ‘hard core’ of propositions which were retained throughout the life of that programme together with a ‘protective belt’ which was constituted by auxiliary hypotheses that were adjusted so as to reconcile the hard core with the empirical data. The attempt on the part of the proponents of the research programme to reconcile the programme to empirical data produced a series of theories \(T_1\), \(T_2\),… \(T_n\) where, at least in some cases, \(T_{i+1}\) serves to explain some data that is anomalous for \(T_i\). Lakatos held that a research programme was ‘theoretically progressive’ insofar as each new theory predicts some novel hitherto unexpected fact. A research programme is ‘empirically progressive’ to the extent that its novel empirical content was corroborated, that is, if each new theory leads to the discovery of “some new fact” (Lakatos 1970: 118). Lakatos thus offered a new solution to the demarcation problem: a research programme was pseudoscientific to the extent that it was not theoretically progressive. Theory evaluation is construed in terms of competing research programmes: a research programme defeats a rival programme by proving more empirically progressive over the long run.

According to Merriam-Webster’s Collegiate Dictionary, [ 2 ] something is ‘ad hoc’ if it is ‘formed or used for specific or immediate problems or needs’. An ad hoc hypothesis then is one formed to address a specific problem—such as the problem of immunizing a particular theory from falsification by anomalous data (and thereby accommodating that data). Consequently what makes a hypothesis ad hoc, in the ordinary English sense of the term, has nothing to do with the content of the hypothesis but simply with the motivation of the scientist who proposes it—and it is unclear why there would be anything suspicious about such a motivation. Nonetheless, ad hoc hypotheses have long been suspect in discussions of scientific method, a suspicion that resonates with the predictivist’s skepticism about accommodation.

For Popper, a conjecture is ad hoc “if it is introduced…to explain a particular difficulty, but…cannot be tested independently” (Popper 1974: 986). Thus Popper’s conception of ad hocness added to the ordinary English meaning a further requirement—in the case of an ad hoc hypothesis that was simply introduced to explain a single phenomenon, the ad hoc hypothesis has no testable consequences other than that phenomenon. In the case of an ad hoc theory modification introduced to resolve an anomaly for a theory, the modified theory had no testable consequences other than those of the original theory.

Popper offered two explications of why ad hoc hypotheses were suspect. One was that if we offer T as an explanation of f , but then cite f as the only reason we have to believe T , Popper claims that we have engaged in reasoning that is suspicious for reasons of circularity (Popper 1972: 192–3). This was arguably fallacious on Popper’s part—a circular proof would offer one proposition, p , in support of a second proposition q , when q has already been offered in support of p . But in the above example, while f is offered as evidence for T , T is offered as an explanation of (not as evidence for) f —and thus there is no circular reasoning (Bamford 1993: 338).

Popper’s other explanation of why ad hoc hypotheses were regarded with suspicion was that they ran counter to the aim of science, which for Popper included the proposal of theories with increasing empirical content, viz., increasing falsifiability. Ad hoc hypotheses, for Popper, suffer from a lack of independent testability and thus reduce (or at least fail to increase) the testability of the theories they modify (cf. above). However, Popper’s claim that the process of modifying a theory ad hoc tends to lead to insufficient falsifiability and is ‘unscientific practice’ has been challenged (e.g., Bamford 1993: 350).

Subsequent authors argued that a hypothesis proposed for the sake of immunizing a theory from falsification could be ‘suspicious’ for various reasons, and thus could be ‘ad hoc’ in various ways. Zahar (1973) argued that a hypothesis was ad hoc 1 if it had no novel consequences as compared with its predecessor (i.e. was not independently testable), ad hoc 2 if none of its novel predictions have actually been verified (either because it has not yet been tested or has been falsified), and ad hoc 3

if it is obtained from its predecessor through a modification of the auxiliary hypotheses which does not accord with the spirit of the heuristic of the programme. (1973: 101)

Beyond Popper’s criterion of a lack of independent testability then, a hypothesis introduced to accommodate some datum could be ad hoc because it was simply unconfirmed (ad hoc 2 ) or because it failed to cohere with the basic commitments of the research programme in which it is proposed (ad hoc 3 ).

Another approach proposes that a hypothesis H introduced into a theory T in response to an experimental result E is ad hoc if it is generally unsupported and appears to be a superficial attempt to paper over deep problems with a theory that is actually in need of substantive revision. Thus to level the charge of ad hocness against a hypothesis was actually to direct serious skepticism toward the theory the hypothesis was meant to rescue. This concept of ad hocness arguably makes sense of Einstein’s critique of the Lorentz-Fitzgerald contraction hypothesis as ‘ad hoc’ as a supplementary hypothesis to the aether theory, and Pauli’s postulation of the neutrino as an ad hoc rescue of classical quantum mechanics (Leplin 1975, 1982; for further discussion see Grünbaum 1976).

It seems clearly true that the scientific community’s judgment about whether a hypothesis is ad hoc can change. Given this revisability, and the aesthetic dimension of theory evaluation (which leaves assessment to some degree ‘in the eye of the beholder’) there may be no particular point to embracing a theory of ad hocness, if by the term ‘ad hoc’ we mean ‘illegitimately proposed’ (Hunt 2012).

Popper wrote that

Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory in question, we should have expected an event which was incompatible with the theory—an event which would have refuted the theory. (1963: 36)

Popper (and subsequently Lakatos) thereby endorsed a temporal condition of novelty—a prediction counts as novel is if it is not known to be true (or is expected to prove false) at the time the theory is constructed. But it was fairly obvious that this made important questions of confirmation turn implausibly on the time at which certain facts were known.

Thus Zahar proposed that a fact is novel “if it did not belong to the problem-situation which governed the construction of the hypothesis” (1973: 103). This form of novelty has been deemed ‘problem-novelty’ (Gardner 1982: 2). But in the same paper Zahar purports to exemplify this concept of novelty by referring to the case in which Einstein did not use the known behavior of Mercury’s perihelion in constructing his theory of relativity. [ 3 ] Gardner notes that this latter conception of novelty, which he deemed ‘use-novelty’, is distinct from problem-novelty (Gardner 1982: 3). Evidence is use-novel for T if T was not built to fit that evidence (whether or not it was part of the relevant ‘problem-situation’ the theory was intended to address). In subsequent literature, the so-called heuristic conception of novelty has been identified with use-novelty—it was further articulated in Worrall 1978 and 1985. [ 4 ]

Another approach argues that a novel consequence of a theory is one that was not known to the theorist at the time she formulated the theory—this seems like a version of the temporal conception, but this point appeals implicitly to the heuristic conception: if a theorist knew of a result prior to constructing a theory which explains it, it may be difficult to determine whether that theorist somehow tailored the theory to fit the fact (e.g., she may have done so unconsciously). A knowledge-based conception is thus the best that we can do to handle this difficulty (Gardner 1982). [ 5 ]

The heuristic conception is, however, deeply controversial—because it makes the epistemic assessment of theories curiously dependent on the mental life of their constructors, specifically on the knowledge and intentions of the theorist to build a theory that accommodated certain data rather than others. Leplin’s comment is typical:

The theorist’s hopes, expectations, knowledge, intentions, or whatever, do not seem to relate to the epistemic standing of his theory in a way that can sustain a pivotal role for them…. (1997: 54)

(For similar comments see Gardner 1982: 6; Thomason 1992: 195; Schlesinger 1987: 33; Achinstein 2001: 210–230; and Collins 1994.)

Another approach notes that scientists operate with competing theories and that the role of novel confirmations is to decide between them. Thus, a consequence of a theory T is a ‘novel prediction’ if it is not a consequence of the best available theory actually present in the field other than T (e.g., the prediction of the Mercury perihelion by Einstein’s relativity theory constituted a novel prediction because it was not a (straightforward) consequence of Newtonian mechanics; Musgrave 1974: 18). Operating in a Lakatosian framework, Frankel claims a consequence was novel with respect to a theory and its research programme if it is not similar to a fact which already has been used by members of the same research program to support a theory designed to solve the same problems as the theory in question (1979: 25). Also in a Lakatosian framework, Nunan claims that a consequence is novel if it has not already been used to support, or cannot readily be explained in terms of, a theory entertained in some rival research program (1984: 279). [ 6 ]

There are clearly multiple forms of novelty and it is generally recognized that a fact could be ‘novel’ in multiple senses—as we will see, some carry more epistemic weight than others (Murphy 1989).

Global predictivism holds that predictions are always superior to accommodations, while local predictivism holds that this only holds in certain cases. Strong predictivism asserts that prediction is intrinsically superior to accommodation, whereas weak predictivism holds that predictive success is epistemically relevant because it is symptomatic of other features that have epistemic import. The distinction between strong and weak predictivism cross classifies with the distinctions between different types of novelty. For example, one could maintain that temporal predictions are intrinsically superior to temporal accommodations (strong temporal predictivism) or that temporal predictions were symptomatic of some other good-making feature of theories (weak temporal predictivism; Hitchcock and Sober 2004: 3–5). These distinctions will be further illustrated below.

A version of global strong heuristic predictivism is the null support thesis that holds that theories never receive confirmation from evidence they were built to fit—precisely because of how they were built. This thesis has been attributed to Bacon and Descartes (Howson 1990: 225). Popper and Lakatos also subscribe to this thesis, though it is important to remember that they do not recognize any form of confirmational support—even from successful predictions. But others who maintained that successful predictions do confirm theories nonetheless endorsed the null support hypothesis. Giere provides the following argument:

If the known facts were used in constructing the model and were thus built into the resulting hypothesis…then the fit between these facts and the hypothesis provides no evidence that the hypothesis is true [since] these facts had no chance of refuting the hypothesis. (1984: 161; Glymour 1980: 114 and Zahar 1983: 245 offer similar arguments)

The idea is that the way the theory was built provided an illegitimate protection against falsification by the facts—hence the facts cannot support the theory. Others however find this argument specious, noting that since the content of the hypothesis is fixed, it makes no sense to think of any facts as having a ‘chance’ to falsify the theory. The theory says what it says, and any particular fact refutes it or it doesn’t.

Giere has confused what is in effect a random variable (the experimental setup or data source E together with its set of distinct possible outcomes) with one of its values (the outcome e )…Moreover, it makes perfectly good sense to say that E might well have produced an outcome other than the one, e , it did as a matter of fact produce. (Howson 1990: 229; see also Collins 1994: 220)

Thus Giere’s argument collapses.

Howson argued in a series of papers (1984, 1988, 1990) that the null support thesis is falsified using simple examples, such as the following:

An urn contains an unknown number of black and white tickets, where the proportion p of black tickets is also unknown. The data consists simply in a report of the relative frequency \(r/k\) of black tickets in a large number k of draws with replacement from the urn. In the light of the data we propose the hypothesis that \(p = (r/k)+\epsilon\) for some suitable \(\epsilon\) depending on k . This hypothesis is, according to standard statistical lore, very well supported by the data from which it is clearly constructed. (1990: 231)

In this case there is, Howson notes, a background theory that supplies a model of the experiment (it is a sequence of Bernoulli trials, viz., a sequence of trials with two outcomes in which the probability of getting either outcome is the same on each trial; it leaves only a single parameter to be evaluated). As long as we have good reason to believe that this model applies, our inference to the high probability of the hypothesis is a matter of standard statistical methodology, and the null support thesis is refuted.

It has been argued that one of the limitations of Bayesianism is that it is fatally committed to the (clearly false) null support thesis (Glymour 1980). The standard Bayesian condition by which evidence e supports h is given by the inequality \(p(h\mid e) \gt p(h)\). But where e is known (and thus \(p(e) = 1\)), we have \(p(h\mid e) = p(h)\). This came to be known as the ‘Bayesian problem of old evidence’. Howson (1984) noted that this problem could be overcome by selecting a probability function \(p^*\) based on the assumption that e was not known—thus even if \(p(h\mid e) = p(h)\), it could still hold that \({p^*}(h\mid e) \gt {p^*}(h)\). Thus followed an extensive literature on the old evidence problem which will not be summarized here (see, e.g., Christiansen 1999; Eells & Fitelson 2000; Barnes 1999, 2008: Ch. 7; and Hartmann & Fitelson 2015).

6 Contemporary Theories of Predictivism

Patrick Maher (1988, 1990, 1993) presented a seminal thought experiment and a Bayesian analysis of its predictivist implications.

The thought experiment contained two scenarios: in the first scenario, a subject (the accommodator) is presented with E , a sequence of 99 coin flips. E forms an apparently random sequence of heads and tails. The accommodator is then instructed to tell us the outcome of the first 100 flips—he responds by reciting E and then adding the prediction that the 100 th toss will be heads—the conjunction of E and this last toss is T . In the other scenario, another subject (the predictor) is asked to predict the first 100 flip outcomes without witnessing any outcomes—the predictor endorses theory T . Thereafter the coin is flipped 99 times, E is established, and the predictor’s first 99 predictions are confirmed. The question is in which of these two scenarios is T better confirmed. It is strongly intuitive that T is better confirmed in the predictor’s scenario than in the accommodator’s scenario, suggesting that predictivism holds true in this case. If we allow ‘ O ’ to assert that evidence E was input into the construction of T , predictivism asserts:

Maher argues that the successful prediction of the initial 99 flips constitutes persuasive evidence that the predictor ‘has a reliable method’ for making predictions of coin flip outcomes. T ’s consistency with E in the case of the accommodator provides no particular evidence that the accommodator’s method of prediction is reliable—thus we have no particular reason to endorse his prediction about the 100 th flip. Allowing R to assert that the method in question is reliable, and \(M_T\) that method M generated hypothesis T , this amounts to:

Maher’s (1988) provides a rigorous proof of (2), which is shown to entail (1) on various assumptions.

Maher’s (1988) makes the simplifying assumption that any method of prediction used by a predictor is either completely reliable (this is the claim abbreviated by ‘ R ’) or is no better than a random method (\(\neg R\)). (Maher [1990] shows that this assumption can be surrendered and a continuum of degrees of reliability of scientific methods assumed; the predictivist result is still generated.) In qualitative terms, where M generates T (and thus predicts E ) without input of evidence E , we should infer that it is much more likely that the method that generated E is reliable than that E just happened to turn out true though R was no better than a random method. In other words, we judge that we are much more likely to stumble on a subject using a reliable method M of coin flip prediction than we are to stumble on a sequence of 99 true flip predictions that were merely lucky guesses—because

Maher has articulated a weak heuristic predictivism because he claims that predictive success is symptomatic of the use of a reliable discovery method. [ 7 ]

For critical discussion of Maher’s theory of predictivism see Howson and Franklin 1991 (and Maher’s 1993 reply); Barnes 1996a,b; Lange 2001; Harker 2006; and Worrall 2014. [ 8 ]

It was noted above that ad hoc hypotheses stand under suspicion for various reasons, one of which was that a hypothesis that was proposed to resolve a particular difficulty may not cohere well with the theory it purports to save or relevant background beliefs. [ 9 ] This could result from the fact that there is no obvious way to resolve the difficulty in a way that is wholly ‘natural’ from the standpoint of the theory itself or operative criteria of theory choice. For example, the phlogiston theory claimed that substances emitted phlogiston while burning. However, it was established that some substances actually gained weight while burning. To accommodate the latter phenomenon it was proposed that phlogiston had negative weight—but the latter hypothesis was clearly ad hoc in the sense of failing to cohere with the background belief that substances simply do not have negative weight, and with the knowledge that many objects lost weight when burned (Partington & McKie 1938a: 33–38).

Thus the ‘fudging explanation’ defends predictivism by pointing out that the process of accommodation lends itself to the proposal of hypotheses that do not cohere naturally with operative constraints on theory choice, while successful predictions are immune from this worry (Lipton 1990, 1991: Ch. 8). Of course, it is an important question whether scientists actually rely on the fact that evidence was predicted (or accommodated) in their assessment of theories—if a theory was fudged to accommodate some datum, couldn’t the scientist simply note that the fudged theory suffers a defect of coherence and pay no attention to whether the data was accommodated or predicted? Some argue, however that scientists are imperfect judges of such coherence—a scientist who accommodates some datum may think his accommodation is fully coherent, while his peers may have a more accurate and objective view that it is not. The scientist’s ‘assessed support’ of his proposed accommodation may thus fail to coincide with its ‘objective support’, and the scientist might rely on the fact that his evidence was accommodated as evidence that it was fudged (or conversely, that his evidence was predicted as evidence that it was not fudged; Lipton 1991: 150f).

Lange (2001) offers an alternate interpretation of the coin flip example that claims that the process of accommodation (unlike prediction) tends to generate theories that are not strongly supported by confirming data. He imagines a ‘tweaked’ version of the coin flip example in which the initial 99 outcomes form a strict alternating sequence ‘tails heads tails heads…’ (instead of forming the ‘apparently random sequence’ of outcomes provided in the original case). Again we imagine a predictor who correctly predicts 99 outcomes in advance and an accommodator who witnesses them. Both the predictor and the accommodator predict that the 100 th outcome will be tails. Now there is little or no difference in our assessed probability that the subject will correctly predicted the 100 th outcome.

This suggests that the intuitive difference between Maher’s original pair of examples does not reflect a difference between prediction and accommodation per se. (Lange 2001: 580)

Lange’s analysis appeals to what Goodman called an ‘arbitrary conjunction’—the mark of which is that

establishment of one component endows the whole statement with no credibility that is transmitted to other component statements. (1983: 68–9)

An example of an arbitrary conjunction is “The sun is made of helium and August 3 rd 2017 falls on a Thursday and 17 is a prime number”. In the original coin flip case, we judge that H is weakly supported in the accommodator’s scenario because we judge that the apparently random sequence of outcomes is probably an arbitrary conjunction—thus the fact that the initial 99 conjuncts are confirmed implies almost nothing about what the 100 th outcome will be. But the success of the predictor in predicting the initial 99 outcomes strongly implies that the sequence is not an arbitrary conjunction after all:

(w)e now believe it more likely that the agent was led to posit this particular sequence by way of something we have not noticed that ties the sequence together—that would keep it from being a coincidence that the hypothesis is accurate to the 100 th toss…. (Lange 2001: 581)

Having judged it not to be an arbitrary conjunction, we are now prepared to recognize the first 99 outcomes as strongly confirming the prediction in the 100 th case. What accounts for the difference between the two scenarios, in other words, is not primarily whether E was predicted or accommodated, but whether we judge H to be an arbitrary conjunction, and thus whether E provides support for the remaining portion of H .

Thus in Lange’s tweaked case, the non-existence of the predictivist effect is due to the fact that it is clear from the initial 99 flips that the sequence is not an arbitrary conjunction—thus E confirms H equally strongly in both scenarios.

Lange goes on to suggest that in actual science the practice of constructing a hypothesis by way of accommodating known evidence has a tendency to generate arbitrary conjunctions. Thus Lorentz’s contraction hypothesis, when appended to his electrodynamics to accommodate the failure to detect optically any motion with respect to the aether, resulted in an arbitrary conjunction (since evidence that supported the contraction hypothesis did not support the electrodynamics, or vice versa)—essentially for this reason, Lange argues, it was rejected by Einstein as ad hoc. When evidence is predicted by a theory, by contrast, this is typically because the theory is not an arbitrary conjunction. The evidential significance of prediction and accommodation for Lange is that they tend to be correlated (negatively and positively) with the construction of theories that are arbitrary conjunctions. Lange’s view might thus be classed as a weak heuristic predictivism, though Lange never takes a stand on whether scientists actually rely on such correlations in assessing theories.

For critical discussion of Lange’s theory see Worrall 2014: 59–61 and Harker 2006: 317f.

Deborah Mayo has argued (particularly in Mayo 1991, 1996, and 2014) that the intuition that predictivism is true derives from a premium on severe tests of hypotheses. A test of a hypothesis H is severe to the extent that H is unlikely to pass that test if H is false. Intuitively, if a novel consequence N is shown to follow from H , and the probability of N on the assumption \({\sim}H\) is very low (for the reason of its being novel), then testing for N would seem to count as a severe test of H , and a positive outcome should strongly support H . Here novelty and severity appear to coincide—but Mayo observes that there are cases in which they come apart. For example, it has seemed to many that if H is built to fit some body of evidence E then the fact that H fits E does not support H because this fit does not constitute H ’s having survived a severe test (or a test at all). One of Mayo’s central objectives is to expose the fallacies that this latter reasoning involves.

Giere (1984: 161, 163) affirms that evidence H was built to fit cannot support H because, given how H was built, it was destined to fit that evidence. Mayo summarizes his reasoning as follows:

• (1) If H is use-constructed, then a successful fit is assured no matter what.

But Mayo notes that ‘no matter what’ can be interpreted in two ways: (a) no matter what the data are, and (b) no matter whether H is true or false. (1) is true when interpreted as (a), but in order to establish that accommodated evidence fails to support H (as Giere intends) (1) must be interpreted as (b). However, (1) is false when so interpreted. Mayo (1996: 271) illustrates this with a simple example: let the evidence e be a list of SAT scores from students in a particular class. Use this evidence to compute the average score x , and set h = the mean SAT score for these students is x . Now of course h has been use-constructed from e . It is true that whatever mean score was computed would fit the data no matter what the data are—but hardly true that h would have fit the evidence no matter whether h was true or false. If h were false it would not fit the data, because the data will inevitably fit only a true hypothesis. Thus h has passed a maximally severe test: it is virtually impossible for h to fit the data if h is false—despite the fact that h is built to fit e .

Mayo gives an additional example of how a use-constructed hypothesis can count as having survived a severe test that pertains to the famous 1919 Eddington eclipse experiment of Einstein’s General Theory of Relativity. GTR predicted that starlight that passed by the sun would be bent to a specific degree (specifically 1.75 arcseconds). There were actually two expeditions carried out during the eclipse—one to Sobral in Northern Brazil and the other to the island of Principe in the Gulf of Guinea. Each expedition generated a result that supported GTR, but there was a third result generated by the Sobral expedition that appeared to refute GTR. This result was however disqualified because it was determined that a mirror used to acquire the images of the stars’ position had been damaged by the heat of the sun. While one might worry that such dismissing of anomalous evidence was the kind of ad hoc adjustment that Popper warned against, Mayo notes that this is instead a perfectly legitimate case of using evidence to support a hypothesis (that the third result was unreliable) that amounted to that hypothesis having passed a severe test. Mayo concludes that a general prohibition on use-constructed hypothesis “fails to distinguish between problematic and unproblematic use-constructions (or double countings)” (1996: 285). However, Hudson (2003) argues that there is historical evidence that suggests there was legitimate reason to question the hypothesis that the third result was unreliable (he uses this point to support his own contention that the fact that a hypothesis was use-constructed is prima facie evidence that the hypothesis is suspect). Mayo (2003) replies that insofar as the third result was nonetheless suspect the physicists involved were right to discard it.

Mayo (1996: Ch. 9) defends a predictivist-like position attributed to Neyman-Pearson statistical methods—the prohibition on after-trial constructions of hypotheses. To illustrate: Kish (1959) describes a study that investigated the statistical relationship between a large number of infant training experiences (nursing, toilet training, weaning, etc.) and subsequent personality and behavioral traits (e.g., school adjustment, nail biting, etc.) The study found a number of high correlations between certain training experience and later traits. The problem was that the study investigated so many training experiences that it was quite likely that some correlations would appear in the data simply by chance—even if there would ultimately prove to be no such correlation. An investigator who studied many possible correlations thus could survey that data and simply look for statistically significant differences and proclaim evidence for correlations despite such evidence being misleading—thus engaging in the dubious practice of the ‘after-trial construction of hypothesis’. [ 10 ] Mayo notes that such hypotheses should not count as having passed a severe test, thus she endorses the Neyman-Pearson prohibition on such construction. Hitchcock and Sober (2004) note that Mayo’s definition of severity as applied in this case differs from the one she employs in dealing with cases like her SAT example; Mayo (2008) replies at length to their criticism and argues that while she does employ two versions of the severity definition they nonetheless reflect a unified conception of severity.

For critical discussion of Mayo’s account see Iseda 1999 and Worrall 2006: 56–60, 2010: 145–153—see also Mayo’s (1996: 265f, 2010) replies to Worrall.

John Worrall has been an important contributor to the predictivism literature from the 1970s until the present time. He was, along with Elie Zahar, one of the early proponents of the significance of heuristic novelty (e.g., Worrall 1978, 1985). In his more recent work (cf. his 1989, 2002, 2005, 2006, 2010, 2014; also Scerri & Worrall 2001) Worrall has laid out a detailed theory of predictivism that, while sometimes presented in heuristic terms, is “at root a logical theory of confirmation” (2005: 819)—it is thus a weak heuristic account that takes use-novelty of evidence to be symptomatic of underlying logical features that establish strong confirmation of theory.

Worrall’s mature account is based on a view of scientific theories that he credits to Duhem—which claims that a scientific theory is naturally thought of as consisting of a core claim together with some set of more specific auxiliary claims. It is commonly the case that the core theory will leave undetermined certain ‘free parameters’ and the auxiliary claims fix values for such parameters. To cite an example Worrall often uses, the wave theory of light consists of the core theory that light is a periodic disturbance transmitted though some sort of elastic medium. This core claim by itself leaves open various free parameters concerning the wavelengths of particular types of monochromatic light. Worrall proposes to understand the diminished status of evidential support associated with accommodation as follows: when evidence e is ‘used’ in the construction of a theory, it is typically used to establish the value of a free parameter in some core theory T . The fixed version will be a specific version \(T'\) of T . e serves to confirm \(T'\), then, only on the condition that there is independent support for T —thus accommodation provides only ‘conditional confirmation’. Importantly, evidence e that is used in this way will by itself typically provide no evidence for core theory T . Worrall (2002: 201) offers as an illustration the support offered to the wave theory of light ( W ) by the two slit experiment using light from a sodium arc—the data will consist of various alternating light and dark ‘fringes’. The fringe data can be used to compute the wavelength of sodium light—and thus used to generate a more specific version of the wave theory of light \(W'\)—one which conjoins W with a claim about the wavelength of this particular sort of light. But the data offer merely conditional support to \(W'\)—that is the data support \(W'\) only on the condition that there is independent evidence for W .

Predicted evidence for Worrall is thus evidence that is not used to fix free parameters. Worrall cites two forms that predictions can take: one is when a particular evidential consequence falls ‘immediately out of the core’, i.e., is a consequence of the core, together with ‘natural auxiliaries’, and the other is when it is a consequence of a specific version of a theory whose free parameters have been fixed using other data. To illustrate the first: retrograde motion [ 11 ] was a natural consequence of the Copernican core (the claim that the earth and planets orbit the sun) because observation of the planets was carried out on a moving observatory that periodically passed other planets—however it could only be accommodated by Ptolemaic astronomy by proposing and adjusting auxiliary hypotheses that supposed the planet to move on an epicycle (retrograde motion did not follow naturally from the Ptolemaic core idea that the Sun, stars and planets orbit the earth). Thus retrograde motion was predicted by the Copernican theory and thus offered unconditional support to that theory, while it offered only conditional confirmation to the Ptolemaic theory. The second form of prediction is one which follows from a specific version of a theory but was not used to fix a parameter—imagine \(W'\) in the preceding paragraph makes a new prediction p (say for another experiment, such as the one slit experiment)— p offers unconditional confirmation of \(W'\) (and W ; Worrall 2002: 203).

However it is important to understand that Worrall’s repeated expression of his position in terms of the heuristic conception of novelty (particularly after his 1985) does not amount to an endorsement of strong heuristic predictivism. Worrall clarifies this in his 1989 article that focuses on the evidential significance of the ‘white spot’ confirmation of Fresnel’s version of the wave theory of light. The reason the white spot datum carried such important weight is not ultimately that it was not used by Fresnel in the construction of the theory but because this datum followed naturally from the core theory that light is a wave. The reason the fringe data that was used to compute the wavelength of sodium light (cf. above) did not carry such weight is that it is not a consequence of this core idea (nor has the wavelength of sodium light been fixed by some other data). Thus d is novel for T when “there is a heuristic path to [ T ] that does not presuppose [d’s] existence” (Scerri & Worrall 2001: 418). As Worrall sometimes puts it, whether d carries unconditional confirmation for T does not depend on whether d was actually used in constructing T , but whether it was ‘needed’ to construct T (e.g., 1989: 149–151). Thus Worrall is actually a proponent of ‘essential use-novelty’ (Alai 2014: 304). For Worrall, facts about heuristic prediction and accommodation serve to track underlying facts about the logical relationship between theory and evidence. Thus Worrall is ultimately a proponent of weak (not strong) heuristic predictivism. Worrall categorically rejects temporal predictivism, arguing that the fact that the white spot was a temporally novel consequence in itself was of no epistemic importance.

For further discussion of Worrall’s theory of predictivism see Mayo 2010: 155f; Schurz 2014; Votsis 2014; and Douglas & Magnus 2013: 587–8.

Scerri and Worrall 2001 contains a detailed rendering of the historical episode of the scientific community’s assessment of Mendeleev’s theory of the periodic law—it is argued that this story ultimately vindicates Worrall’s theory of predictivism.

For discussion of Scerri and Worrall see Akeroyd 2003; Barnes 2005b (and replies from Worrall 2005 and Scerri 2005); Schindler 2008, 2014; Brush 2007; and Sereno 2020.

A common argument for predictivism is that we should avoid inferring that a theory T is true on the basis of evidence E that it is built to fit because we can explain why T entails E by simply noting how T was built—but if T was not built to fit E then only the truth of T can explain the fact that T fits E . Various philosophers have noted that this reasoning is fallacious. As noted above it makes no sense to offer an explanation (for example, in terms of how the theory was built) for the fact that T entails E —for this latter fact is a logical fact for which no causal explanation can be given. Insofar as there is an explanandum in need of an explanans here it is rather the fact that the theorist managed to construct or ‘choose’ a theory (which turned out to be T ) that correctly entailed E (Collins 1994; Barnes 2002)—that explanandum could be explained by noting that the theorist built a theory (which turned out to be T ) to fit E , or endorsed it because it fit E .

White (2003) offers a theory of predictivism that begins with this same insight—the relevant explanandum is:

• (ES) The theorist selected a datum-entailing theory.

This explanandum could be explained in one of two ways:

• (DS) The theorist designed her theory to entail the datum.
• (RA) The theorist’s selection of her theory was reliably aimed at the truth.

White explains that (RA) means “roughly that the mechanisms which led to her selection of a theory gave her a good chance of arriving at the truth” (2003: 664). (Thus White analogizes the theorist to an ‘archer’ who is more or less reliable in ‘aiming’ at the truth in selecting a theory.) Then White offers a simple argument for predictivism: assuming ~DS, ES provides evidence for RA. But assuming DS, ES provides no evidence for RA. Thus, heuristic predictivism is true.

Interestingly, White bills his account as a strong heuristic account. In making this claim he is claiming that the epistemic advantage of prediction would not be entirely erased for an observer who was completely aware of all relevant evidence and background knowledge possessed by the scientific community at the relevant point in time. This is because the degree to which theorizing is reliable depends upon principles of evidence assessment and causal relations (including the reliability of our perceptual faculties, accuracy of measuring instruments, etc.) that are not entirely “transparent” to us. [ 12 ] Insofar as fully informed scientists may not be fully convinced of just how reliable these principles and relations are, evidence that they lead to the endorsement of theories which are predictively successful continues to redound to their assessed reliability. Thus, White concludes, strong heuristic predictivism is vindicated (2003: 671–4).

Hitchcock and Sober (2004) provide an original theory of weak heuristic predictivism that is based on a particular worry about accommodation. On the assumption that data are noisy (i.e. imbued with observational error), a good theory will almost never fit the data perfectly. To construct a theory that fits the data better than a good theory should, given noisy data, is to be guilty of “overfitting”—if we know a theorist built her theory to accommodate data, we may well worry that she has overfit the data and thus constructed a flawed theory. If we know however that a theorist built her theory without access to such data, or without using it in the process of theory construction, we need not worry that overfitting that data has occurred. When such a theory goes on to make successful predictions, Hitchcock and Sober moreover argue, this provides us with evidence that the data on which the theory was initially based were not overfit in the process of constructing the theory.

Hitchcock and Sober’s approach derives from a particular solution to the curve-fitting problem presented in Forster and Sober 1994. The curve fitting problem is how to select an optimally supported curve on the basis of a given body of data (e.g., a set of \([X,Y]\) points plotted on a coordinate graph). A well-supported curve will feature both ‘goodness of fit’ with the data and simplicity (intuitively, avoiding highly bumpy or irregular patterns). Solving the curve-fitting problem requires some precise way of characterizing a curve’s simplicity, a way of characterizing goodness of fit, and a method of balancing simplicity against goodness of fit to identify an optimal curve.

Forster and Sober cite Akaike’s (1973) result that an unbiased estimate of the predictive accuracy of a model can be computed by assessing both its goodness of fit and its simplicity as measured by the number of adjustable parameters it contains. A model is a statement (a polynomial, in the case of a proposed curve) that contains at least one adjustable parameter. For any particular model M , a given data set, and identifying \(L(M)\) as the likeliest (i.e. best data fitting) curve from M , Akaike showed that the following expression describes an unbiased estimate of the predictive accuracy of model M:

This estimate is deemed a model’s ‘Akaike Information Criterion’ (AIC) score—it measures goodness of fit in terms of the log likelihood of the data on the assumption of \(L(M)\). The simplicity of the model is inversely proportion to k , the number of adjustable parameters in the model. The intuitive idea is that models with a high k value will provide a large variety of curves that will tend to fit data more closely than models with a lower k value—and thus large k values are more prone to overfitting than small k values. So the AIC score assesses a model’s likely predictive accuracy in a way that balances both goodness of fit and simplicity, and the curve-fitting problem is arguably solved.

Hitchcock and Sober (2004) consider a hypothetical example involving two scientists, Penny Predictor and Annie Accommodator. Working independently, they acquire the same set of data D —Penny proposes theory Tp while Annie proposes Ta . The critical difference however was that Penny proposed Tp on the basis of an initial segment of the data D 1—thereafter she predicted the remaining data D 2 to a high degree of accuracy \((D = D1 \cup D2)\). Annie however was in possession of all the data in D prior to proposing Ta and in proposing this theory accommodated D . Hitchcock and Sober ask whether there might be reason to suspect that Penny’s theory will be more predictively accurate in the future, and in this precise sense be better confirmed.

Hitchcock and Sober argue that there is no one answer to this question—and then present a series of several cases. Insofar as predictivism holds in some and not others, their account of predictivism is clearly a local (rather than global) account. In cases in which Penny and Annie propose the same theory, or propose theories whose AIC scores can be computed and directly compared, there is no reason to regard facts about how they built the theory to carry further significance. But if we do not know which theories were proposed, or by what method they were constructed, the fact that Penny predicted data that Annie accommodated can argue for Penny’s theory having a higher AIC score than Annie’s, and thus carry an epistemic advantage.

Insofar as predictivism holds in some cases but not the others, the question whether predictivism holds in actual episodes of science depends on which cases such actual episodes tend to resemble, but Hitchcock and Sober “take no stand on how often the various cases arise” (2004: 21).

Although their account of predictivism is tailored initially to the curve-fitting problem, it is by no means limited to such cases. They note that it is natural to think of a model as analogous to the ontological framework of a scientific theory where the various ontological commitments can function as ‘adjustable parameters’—for example, the Ptolemaic and Copernican world pictures both begin with a claim that a certain entity (the sun or the earth) is at the center, and these models are articulated by producing models with adjustable parameters.

For critical discussion of Sober and Hitchcock’s account, see Lee 2012, 2013 and Douglas & Magnus 2013: 582–584. Peterson (2019) argues that Sober and Hitchcock's approach can be extended to issue methodological recommendations involving methods of cross validation and replication in psychology.

Barnes (2005a, 2008) maintains that predictivism is frequently a manifestation of a phenomenon he calls ‘epistemic pluralism’. A ‘ T -evaluator’ (a scientist who assigns some probability to theory T ) is an epistemic pluralist insofar as she regards one form of evidence to be the probabilities posted (i.e. publicly presented) by other scientists for and against T and other relevant claims (she is an epistemic individualist if she does not do this but considers only the scientific evidence ‘on her own’). One form of pluralistic evidence is the event in which a reputable scientist endorses a theory—this takes place when a scientist posts a probability for T that is (1) no lower than the evaluator’s probability and (2) high enough that subsequent predictive confirmation of T would redound to the scientist’s credibility (2008: 2.2).

Barnes rejects the heuristic conception of novelty on the grounds that it is a mistake to think that what matters epistemically is the process by which the theory was constructed—what matters is on what basis the theory was endorsed (2008: 33f) . In the example above, confirmation of N (a consequence of T ) could carry special weight for an evaluator who learned that the theorist endorsed the theory without appeal to observational evidence for N (irrespective of how the theory was constructed). He proposes to replace the heuristic conception with his endorsement conception of novelty: N (a known consequence of T ) counts as a novel confirmation of T relative to agent X insofar as X posts an endorsement-level probability for T that is based on a body of evidence that does not include observation-based evidence for N .

Barnes claims that the notion of endorsement novelty has several advantages over the heuristic conception—one is that endorsement novelty can account for the fact that prediction is a matter of degree: the more strongly the theorist endorses T , the more strongly its consequence N is predicted (and thus the more evidence for T for pluralist evaluators who trust the endorser). Another is that the orthodox distinction between the context of discovery and the context of justification is preserved. According to the latter distinction, it does not matter for purposes of theory evaluation how a theory was discovered. But this turns out not to be true on the heuristic conception given the central importance it accords to how a theory was built (cf. Leplin 1987). Endorsement novelty respects the irrelevance of the process by which theories are discovered (Barnes 2008: 37–8).

One claim central to this account is that confirmation is a three-way relation between theory, evidence, and background belief (cf. Good 1967). Barnes distinguishes between two types of theory endorser: (1) virtuous endorsers post probabilities for theories that cohere with their evidence and background beliefs and (2) unvirtuous endorsers who post probabilities that do not so cohere. A common way of explaining the predictivist intuition is to note that accommodators tend to be viewed with a certain suspicion—their endorsement of T based on accommodated evidence may reflect a kind of social pressure to endorse T whatever its merits (cf. the ‘fudging explanation’ above). Such an endorser may post a probability for T that is too high given her total evidence and background belief—predictivism thus becomes a strategy by which pluralist endorsers protect themselves from unvirtuous accommodators (Barnes 2008: 61–69).

Barnes then presents a theory of predictivism that is designed to apply to virtuous endorsers. Virtuous predictivism has two roots: (1) the prediction per se, which is constituted by an endorser’s posting an endorsement level probability for T that entails empirical consequence N on a basis that does not include observation-based evidence for T , and (2) predictive success, constituted by the empirical demonstration that N is true. The prediction per se carries epistemic significance for a pluralist endorser because it implies that the predictor possesses reason R (consisting of background beliefs) that supports T . If the endorser views the predictor as credible, this simple act of prediction carries epistemic weight. Predictive success then confirms the truth of R , which thereby counts as evidence for T . Novel confirmation thus has the special virtue of confirming the background beliefs of the predictor—accommodative confirmation lacks this virtue.

Barnes presents two Bayesian thought experiments that purport to establish virtuous predictivism. In each experiment an evaluator Eva faces two scenarios—one in which she confronts Peter who posts an endorsement probability for T without appeal to N -supporting observations (thus Peter predicts N ) and another in which she confronts Alex who posts an endorsement probability for T on a basis that includes observations that establish N (thus Alex accommodates N ). The idea behind both thought experiments is to make the scenarios otherwise as similar as possible—Barnes makes a number of ceteris paribus assumption that render the probability functions of Peter and Alex maximally similar. However it turns out that there is more than one way to keep the scenarios maximally similar: in the first experiment, Peter and Alex have the same likelihood ratio but have different posteriors for T . In the second scenario they have the same posteriors but different likelihood ratios. Barnes demonstrates that Eva’s posterior probability is higher in the predictor scenario in both experiments—thus vindicating virtuous predictivism (2008: 69–80).

Although his defense of virtuous predictivism is the centerpiece of his account, Barnes claims that predictivism can hold true of actual theory evaluation in a variety of ways. He maintains that the position deemed ‘weak predictivism’ is actually ambiguous—it could refer to the claim that scientists actually rely on knowledge that evidence was (or was not) predicted because prediction is symptomatic of a some other feature(s) of theories that is epistemically important (‘tempered predictivism’ [ 13 ] ) or simply to the fact that there is a correlation between prediction and this other feature(s) (‘thin predictivism’). The distinction between tempered and thin predictivism cross classifies with the distinction between virtuous and unvirtuous predictivism to produce four varieties of weak predictivism. Barnes then turns to the case of Mendeleev’s periodic law and argues that all four varieties can be distinguished in the scientific community’s reaction to Mendeleev’s theory of the elements (2008: 82–122). In particular, he argues that it was specifically Mendeleev’s predicted evidence, not his accommodated evidence, that had the power to confirm his scientific and methodological background beliefs from the standpoint of the scientific community.

Critical responses to Barnes’s account are presented in Glymour 2008; Leplin 2009; and Harker 2011. Barnes 2014 responds to these. See also Magnus 2011 and Alai 2016.

It was noted in Section 1 that John Maynard Keynes rejected predictivism—he argued that when a theory T is first constructed it is usually the case that there are reasons R that favor T . If T goes on to generate successful novel predictions E then those reasons combine with R to support T —but if some \(T'\) is constructed ‘merely because it fit E ’ then \(T'\) will be less supported than T . This has been deemed the “Keynesian dissolution of the paradox of predictivism” (Barnes 2008: 15–18)

Colin Howson cites with approval the Keynesian dissolution (1988: 382) and provides the following illustration: consider h and \(h'\) which are rival explanatory frameworks. \(h'\) independently predicts e ; h does not entail e but has a free parameter which is fixed on the basis of e to produce \(h(a_{0})\)—this latter hypothesis thus entails e . So \(h'\) predicts e while \(h(a_{0})\) merely accommodates e . Let us assume that the prior probabilities of h and \(h'\) are equal (i.e., \(p(h) = p(h')\)). Now it stands to reason that \(p(h(a_0)) \lt p(h)\) since \(h(a_{0})\) entails h but not vice versa—thus Howson shows it follows that the effect of e ’s confirmation will be to leave \(h'\) no less probable—and quite possibly more probable—than \(h(a_{0})\) (1990: 236–7). Thus predictivism appears true but the operating factor is the role of unequal prior probabilities. [ 14 ]

The argument from Keynes and Howson against predictivism holds that the evidence which appears to support predictivism is illusory—they are clearly asserting that strong predictivism is false, presumably in its temporal and heuristic forms.

However, it is important to note that the arguments of Keynes and Howson cited above predate the injection of the concept of ‘weak predictivism’ into the literature. [ 15 ] It is thus unclear what stand Keynes or Howson would take on weak predictivism. Likewise, Collins’ 1994 paper “Against the Epistemic Value of Prediction” strongly rejects predictivism, but what he is clearly denying is what has since been deemed strong heuristic predictivism. He might endorse weak heuristic predictivism as he concedes that

all sides to the debate agree that knowing that a theory predicted, instead of accommodated, a set of data can give us an additional reason for believing it is true by telling us something about the structural/relational features of a theory. (1994: 213)

Similarly Harker argues that “it is time to leave predictivism behind” but also concedes that “some weak predictivist theses may be correct” (2008: 451); Harker worries that proclaiming weak predictivism may mislead some into thinking that predictive success is somehow more important than other epistemic indicators (such as endorsement by reliable scientists). White goes so far as to claim that weak predictivism “is not controversial” (2003: 656).

Stephen Brush is the author of a body of historical work much of which purports to show that temporal predictivism does not hold in various episodes of the history of science. [ 16 ] These include the case of starlight bending in the assessment of the General Theory of Relativity (Brush 1989), Alfvén’s theories of space plasma phenomena (Brush 1990), and the revival of big bang cosmology (Brush 1993). However, Brush (1996) argues that temporal novelty did play a role in the acceptance of Mendeleev’s Periodic Table based on Mendeleev’s predictions. Scerri and Worrall (2001) presents considerable historical detail about the assessment of Mendeleev’s theory and dispute Brush’s claim that temporal novelty played an important role in the acceptance of the theory (2001: 428–436). (See also Brush 2007.) Steele and Werndl (2013) argue that predictivism fails to hold in assessing models of climate change, while Frish (2015) affirms that it displays weak predictivism.

Another form of anti-predictivism holds that accommodations are superior to predictions in theory confirmation. “The information that the data was accommodated rather than predicted suggests that the data is less likely to have been manipulated or fabricated, which in turn increases the likelihood that the hypothesis is correct in light of the data” (Dellsen forthcoming).

Scientific realism holds that there is sufficient evidence to believe that the theories of the ‘mature sciences’ are at least approximately true. Appeals to novelty have been important in formulating two arguments for realism—these are the ‘no miracle argument’ and the realist reply to the so-called ‘pessimistic induction’. [ 17 ]

The no-miracle argument for scientific realism holds that realism is the only account that does not make the success of science a miracle (Putnam 1975: 73). ‘The success of science’ here refers to the myriad verified empirical consequences of the theories of the mature sciences—but as we have seen there is a long standing tendency to regard with suspicion those verified empirical consequences the theory was built to fit. Thus the ‘ultimate argument for scientific realism’ refers to a version of the no miracle argument that focuses just on the verified novel consequences of theories—it would be a miracle, this argument proclaims, if a theory managed to have a sustained record of successful novel predictions if the theory were not at least approximately true. Thus, assuming there are no competing theories with comparable records of novel success, we ought to infer that such theories are at least approximately true (Musgrave 1988). [ 18 ]

Insofar as the ultimate argument for realism clearly emphasizes a special role for novel successes, the nature of novelty has been an important focus in the realist account. Leplin 1997 is a book length articulation of the ultimate argument for realism; Leplin proposes a sufficient condition for novelty consisting of two conditions:

An observational result O is novel for T if:

• Independence Condition: There is a minimally adequate reconstruction of the reasoning leading to T that does not cite any qualitative generalization of O .
• Uniqueness Condition: There is some qualitative generalization of O that T explains and predicts, and of which, at the time that T first does so, no alternative theory provides a viable reason to expect instances. (Leplin 1997: 77).

Leplin clarifies that a ‘minimally adequate reconstruction’ of such reasoning will be a valid deduction D of the ‘basic identifying hypotheses’ of T from independently warranted background assumptions—the premises of D cannot be weakened or simplified while preserving D ’s validity. Thus for Leplin what establishes whether O is a novel consequence of T is not whether O was actually used in the construction of T , but rather whether it was ‘needed’ for T ’s construction. As with Worrall’s mature ‘essential use’ conception of novelty, what matters is whether there is a heuristic path to T that does not appeal to O , whether or not O was used in constructing T . The Uniqueness Condition helps bolster the argument for the truth of theories with true novel consequences, for if there were another theory \(T'\) (incompatible with T ) that also provides a viable explanation of O , the imputation of truth could not explain the novel success of both T and \(T'\). The success of at least one would have to be due to chance, but if chance could explain one such success it could explain the other as well.

Both of these conditions for novelty have been questioned. Given the Independence Condition, it is unclear that any observational result O will count as novel for any theory, for it may always be true that the logically weakest set of premises that entail T (which will be cited in a minimally adequate reconstruction of the reasoning that led to T ) will include O as a disjunct of one of the premises (Healey 2001: 779). The Uniqueness Condition insists that there be no available alternative explanation of O at the time T first explains O —but clearly, theories that explain O could be subsequently proposed and would threaten the imputation of truth to T no less. This condition seems arbitrarily to privilege theories depending on when they were proposed (Sarkar 1998: 206–8; Ladyman 1999: 184).

Another conception of novelty whose purpose is to bolster the ultimate argument for realism is ‘functional novelty’ (Alai 2014). A datum d is ‘functionally novel’ for theory T if (1) d was not used essentially in constructing T (viz., there is a heuristic path to T and related auxiliary hypotheses that does not cite d ), (2) d is a priori improbable, and (3) d is heterogeneous with respect to data that is used in constructing T and related auxiliary hypotheses (i.e. d is qualitatively different from such data). Functional novelty is a ‘gradual’ concept insofar as a priori improbability and data heterogeneity come in degrees. If there is more than one theory for which d is functionally novel then the dispute between these theories cannot be settled by the ultimate argument (Alai 2014: 306).

Anti-realists have argued that insofar as we adopt a naturalistic philosophy of science, the same standards should be used for assessing philosophical theories as scientific theories. Consequently, if novel confirmations are necessary for inferring a theory’s truth then scientific realism should not be accepted as true, as the latter thesis has no novel confirmations to its credit (Frost-Arnold 2010, Mizrahi 2012).

Another component of the realist/anti-realist debate in which appeals to novel success figure importantly is the debate over the ‘pessimistic induction’ (or ‘pessimistic meta-induction’). According to this argument, the history of science is almost entirely a history of theories that were judged empirically successful in their day only to be shown subsequently to be entirely false. There is no reason to think that currently accepted theories are any different in this regard (Laudan 1981b).

In response some realists have defended ‘selective realism’ which concedes that while the majority of theories from the history of science have proven false, some of them have components that were retained in subsequent theories—these tend to be the components that were responsible for novel successes. Putative examples of this phenomenon are the caloric theory of heat and nineteenth century optical theories (Psillos 1999: Ch. 6), both of which were ultimately rejected as false but which had components that were retained in subsequent theories; these were the portions that were responsible for their novel confirmations. [ 19 ] So in line with the ultimate argument the claim is made that novel successes constitute a serious argument for the truth of the theory component which generates them. However, antirealists have responded by citing cases of theoretical claims that were subsequently determined to be entirely false but which managed nonetheless to generate impressive records of novel predictions. These include certain key claims made by Johannes Kepler in his Mysterium Cosmographicum (1596), assumptions used by Adams and Leverrier in the prediction of the planet Neptune’s existence and location (Lyons 2006), and Ptolemaic astronomy (Carman & Díez 2015). Leconte (2017) maintains that predictive success legitimates only sceptical realism – the claim that some part of a theory is true, but it is not known which part.

• Achinstein, Peter, 1994, “Explanation vs. Prediction: Which Carries More Weight”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , 1994(2): 156–164. doi:10.1086/psaprocbienmeetp.1994.2.192926
• –––, 2001, The Book of Evidence , Oxford: Oxford University Press. doi:10.1093/0195143892.001.0001
• Akaike, Hirotugu, 1973, “Information Theory as an Extension of the Maximum Likelihood Principle”, in B.N. Petrov and F. Csaki, (eds.) Second International Symposium on Information Theory , Budapest, Akademiai Kiado, pp. 267–281.
• Akeroyd, F. Michael, 2003, “Prediction and the Periodic Table: A Response to Scerri and Worrall”, Journal for General Philosophy of Science , 34(2): 337–355. doi:10.1023/B:JGPS.0000005277.60641.ca
• Alai, Mario, 2014, “Novel Predictions and the No Miracle Argument”, Erkenntnis , 79(2): 297–326. doi:10.1007/s10670-013-9495-7
• –––, 2016, “The No Miracle Argument and Strong Predictivism vs. Barnes”, in Lorenzo Magnini and Claudia Casadio (eds.), Model Based Reasoning in Science and Technology , (Studies in Applied Philosophy, Epistemology and Rational Ethics, 27), Switzerland: Springer International Publishing, pp.541–556. doi:10.1007/978-3-319-38983-7_30
• Bamford, Greg, 1993, “Popper’s Explication of Ad Hoc ness: Circularity, Empirical Content, and Scientific Practice”, British Journal for the Philosophy of Science , 44(2): 335–355. doi:10.1093/bjps/44.2.335
• Barnes, Eric Christian, 1996a, “Discussion: Thoughts on Maher’s Predictivism”, Philosophy of Science , 63: 401–10. doi:10.1086/289918
• –––, 1996b, “Social Predictivism”, Erkenntnis , 45(1): 69–89. doi:10.1007/BF00226371
• –––, 1999, “The Quantitative Problem of Old Evidence”, British Journal for the Philosophy of Science , 50(2): 249–264. doi:10.1093/bjps/50.2.249
• –––, 2002, “Neither Truth Nor Empirical Adequacy Explain Novel Success”, Australasian Journal of Philosophy , 80(4): 418–431. doi:10.1080/713659528
• –––, 2005a, “Predictivism for Pluralists”, British Journal for the Philosophy of Science , 56(3): 421–450. doi:10.1093/bjps/axi131
• –––, 2005b, “On Mendeleev’s Predictions: Comment on Scerri and Worrall”, Studies in the History and Philosophy of Science , 36(4): 801–812. doi:10.1016/j.shpsa.2005.08.005
• –––, 2008, The Paradox of Predictivism , Cambridge: Cambridge University Press. doi:10.1017/CBO9780511487330
• –––, 2014, “The Roots of Predictivism”, Studies in the History and Philosophy of Science , 45: 46–53. doi:10.1016/j.shpsa.2013.10.002
• Brush, Stephen G., 1989, “Prediction and Theory Evaluation: The Case of Light Bending”, Science , 246(4934): 1124–1129. doi:10.1126/science.246.4934.1124
• –––, 1990, “Prediction and Theory Evaluation: Alfvén on Space Plasma Phenomena”, Eos , 71(2): 19–33. doi:10.1029/EO071i002p00019
• –––, 1993, “Prediction and Theory Evaluation: Cosmic Microwaves and the Revival of the Big Bang”, Perspectives on Science , 1(4):: 565–601.
• –––, 1994, “Dynamics of Theory Change: The Role of Predictions”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , 1994(2): 133–145. doi:10.1086/psaprocbienmeetp.1994.2.192924
• –––, 1996, “The Reception of Mendeleev’s Periodic Law in America and Britain”, Isis , 87(4): 595–628. doi:10.1086/357649
• –––, 2007, “Predictivism and the Periodic Table”, Studies in the History and Philosophy of Science Part A , 38(1): 256–259. doi:10.1016/j.shpsa.2006.12.007
• Campbell, Richmond and Thomas Vinci, 1983, “Novel Confirmation”, British Journal for the Philosophy of Science , 34(4): 315–341. doi:10.1093/bjps/34.4.315
• Carman, Christián and José Díez, 2015, “Did Ptolemy Make Novel Predictions? Launching Ptolemaic Astronomy into the Scientific Realism Debate”, Studies in the History and Philosophy of Science , 52: 20–34. doi:10.1016/j.shpsa.2015.04.002
• Carrier, Martin, 2014, “Prediction in context: On the comparative epistemic merit of predictive success”, Studies in the History and Philosophy of Science , 45: 97–102. doi:10.1016/j.shpsa.2013.10.003
• Chang, Hasok, 2003, “Preservative Realism and Its Discontents: Revisiting Caloric”, Philosophy of Science , 70(5): 902–912. doi:10.1086/377376
• Christiansen, David, 1999, “Measuring Confirmation”, Journal of Philosophy , 96(9): 437–461. doi:10.2307/2564707
• Collins, Robin, 1994, “Against the Epistemic Value of Prediction over Accommodation”, Noûs , 28(2): 210–224. doi:10.2307/2216049
• Dawid, R. and Stephan Hartmann, 2017, “The No Miracles Argument without the Base-Rate Fallacy”, Synthese . doi:10.1007/s11229-017-1408-x
• Dellsen, Finnur, (forthcoming), “An Epistemic Advantage of Accommodation Over Prediction”, Philosophers' Imprint
• Dicken, P., 2013, “Normativity, the Base-Rate Fallacy, and Some Problems for Retail Realism”, Studies in the History and Philosophy of Science Part A, 44 (4): 563–570.
• Douglas, Heather and P.D. Magnus, 2013, “State of the Field: Why Novel Prediction Matters”, Studies in the History and Philosophy of Science , 44(4): 580–589. doi:10.1016/j.shpsa.2013.04.001
• Eells, Ellery and Branden Fitelson, 2000, “Measuring Confirmation and Evidence”, Journal of Philosophy , 97(12): 663–672. doi:10.2307/2678462
• Forster, Malcolm R., 2002, “Predictive Accuracy as an Achievable Goal of Science”, Philosophy of Science , 69(S3): S124–S134. doi:10.1086/341840
• Forster, Malcolm and Elliott Sober, 1994, “How to Tell when Simpler, More Unified, or Less Ad Hoc Theories Will Provide More Accurate Predictions”, British Journal for the Philosophy of Science , 45(1): 1–35. doi:10.1093/bjps/45.1.1
• Frankel, Henry, 1979, “The Career of Continental Drift Theory: An application of Imre Lakatos’ analysis of scientific growth to the rise of drift theory”, Studies in the History and Philosophy of Science , 10(1): 21–66. doi:10.1016/0039-3681(79)90003-7
• Frisch, Mathias, 2015, “Predictivism and Old Evidence: A Critical Look at Climate Model Tuning”, European Journal for the Philosophy of Science , 5(2): 171–190. doi:10.1007/s13194-015-0110-4
• Frost-Arnold, Greg, 2010, “The No-Miracles Argument for Scientific Realism: Inference to an Unacceptable Explanation”, Philosophy of Science , 77(1): 35–58. doi:10.1086/650207
• Gardner, Michael R., 1982, “Predicting Novel Facts”, British Journal for the Philosophy of Science , 33(1): 1–15. doi:10.1093/bjps/33.1.1
• Giere, Ronald N., 1984, Understanding Scientific Reasoning , second edition, New York: Holt, Rinehart, and Winston. First edition 1979.
• Glymour, Clark N., 1980, Theory and Evidence , Princeton, NJ: Princeton University Press.
• –––, 2008, “Review: The Paradox of Predictivism by Eric Christian Barnes”, Notre Dame Philosophical Reviews , 2008.06.13. [ Glymour 2008 available online ]
• Good, I.J. 1967, “The White Shoe is a Red Herring”, British Journal for the Philosophy of Science , 17(4): 322. doi:10.1093/bjps/17.4.322
• Goodman, Nelson, 1983, Fact, Fiction and Forecast , fourth edition, Cambridge, MA: Harvard University Press. First edition 1950.
• Grünbaum, Adolf, 1976, “ Ad Hoc Auxiliary Hypotheses and Falsificationism”, British Journal for the Philosophy of Science , 27(4): 329–362. doi:10.1093/bjps/27.4.329
• Hacking, Ian, 1979, “Imre Lakatos’s Philosophy of Science”, British Journal for the Philosophy of Science , 30(4): 381–410. doi:10.1093/bjps/30.4.381
• Harker, David, 2006, “Accommodation and Prediction: The Case of the Persistent Head”, British Journal for the Philosophy of Science , 57(2): 309–321. doi:10.1093/bjps/axl004
• –––, 2008, “The Predilections for Predictions”, British Journal for the Philosophy of Science , 59(3): 429–453. doi:10.1093/bjps/axn017
• –––, 2010, “Two Arguments for Scientific Realism Unified”, Studies in the History and Philosophy of Science , 41(2): 192–202. doi:10.1016/j.shpsa.2010.03.006
• –––, 2011, “ Review: The Paradox of Predictivism by Eric Christian Barnes”, British Journal for the Philosophy of Science , 62(1): 219–223. doi:10.1093/bjps/axq027
• Hartman, Stephan and Branden Fitelson, 2015, “A New Garber-Style Solution to the Problem of Old Evidence”, Philosophy of Science , 82(4): 712–717. doi:10.1086/682916
• Healey, Richard, 2001, “Review: A Novel Defense of Scientific Realism by Jarrett Leplin”, Mind , 110(439): 777–780. doi:10.1093/mind/110.439.777
• Henderson, Leah, 2017, “The No Miracles Argument and the Base-Rate Fallacy”, Synthese (4): 1295–1302.
• Hitchcock, Christopher and Elliott Sober, 2004, “Prediction versus Accommodation and the Risk of Overfitting”, British Journal for the Philosophy of Science , 55(1): 1–34. doi:10.1093/bjps/55.1.1
• Holton, Gerald, 1988, Thematic Origins of Scientific Thought: Kepler to Einstein , revised edition, Cambridge, MA and London, England: Harvard University Press. First edition 1973.
• Howson, Colin, 1984, “Bayesianism and Support by Novel Facts”, British Journal for the Philosophy of Science , 35(3): 245–251. doi:10.1093/bjps/35.3.245
• –––, 1988, “Accommodation, Prediction and Bayesian Confirmation Theory”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1988 , 2: 381–392. doi:10.1086/psaprocbienmeetp.1988.2.192899
• –––, 1990, “Fitting Your Theory to the Facts: Probably Not Such a Bad Thing After All”, in Scientific Theories , ( Minnesota Studies in the Philosophy of Science , Vol. XIV), C. Wade Savage (ed.), Minneapolis: University of Minnesota Press, pp. 224–244. [ Howson 1990 available online ]
• Howson, Colin and Allan Franklin, 1991, “Maher, Mendeleev and Bayesianism”, Philosophy of Science , 58(4): 574–585. doi:10.1086/289641
• Hudson, Robert G., 2003, “Novelty and the 1919 Eclipse Experiments”, Studies in the History and Philosophy of Modern Physics , 34(1): 107–129. doi:10.1016/S1355-2198(02)00082-5
• –––, 2007, “What’s Really at Issue with Novel Predictions?” Synthese , 155(1): 1–20. doi:10.1007/s11229-005-6267-1
• Hunt, J. Christopher, 2012, “On Ad Hoc Hypotheses”, Philosophy of Science , 79(1): 1–14. doi:10.1086/663238
• Iseda, Tetsuji, 1999, “Use-Novelty, Severity, and a Systematic Neglect of Relevant Alternatives”, Philosophy of Science , 66: S403–S413. doi:10.1086/392741
• Kahn, J.A., S.E. Landsberg, and A.C. Stockman, 1990, “On Novel Confirmation”, British Journal for the Philosophy of Science , 43, 503–516.
• Keynes, John Maynard, 1921, A Treatise on Probability , London: Macmillan.
• Kish, Leslie, 1959, “Some Statistical Problems in Research Design”, American Sociological Review , 24(3): 328–338; reprinted in Denton E. Morrison and Ramon E. Henkel (eds.), The Significance Test Controversy: A Reader , Chicago: Aldine, pp. 127–141. doi:10.2307/2089381
• Kitcher, Philip, 1993, The Advancement of Science: Science without Legend, Objectivity without Illusions , Oxford: Oxford University Press.
• Ladyman, James, 1999, “Review: Jarrett Leplin, A Novel Defense of Scientific Realism ”, British Journal for the Philosophy of Science , 50(1): 181–188. doi:10.1093/bjps/50.1.181
• Lakatos, Imre, 1970, “Falsification and the Methodology of Scientific Research Programmes”, in Imre Lakatos and Alan Musgrave (eds.), Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London, 1965 , Cambridge: Cambridge University Press, pp. 91–196. doi:10.1017/CBO9781139171434.009
• –––, 1971, “History of Science and its Rational Reconstructions”, in Roger C. Buck and Robert S. Cohen (eds.), PSA 1970 , ( Boston Studies in the Philosophy of Science , 8), Dordrecht: Springer Netherlands, pp. 91–135. doi:10.1007/978-94-010-3142-4_7
• Lange, Marc, 2001, “The Apparent Superiority of Prediction to Accommodation: a Reply to Maher”, British Journal for the Philosophy of Science , 52(3): 575–588. doi:10.1093/bjps/52.3.575
• Laudan, Larry, 1981a, “The Epistemology of Light: Some Methodological Issues in the Subtle Fluids Debate”, in Science and Hypothesis: Historical Essays on Scientific Methodology (University of Western Ontario Series in Philosophy of Science, 19), Dordrecht: D. Reidel, pp. 111–140.
• –––, 1981b, “A Confutation of Convergent Realism”, Philosophy of Science , 48(1): 19–49. doi:10.1086/288975
• Leconte, Gauvain, 2017, “Predictive Success, Partial Truth, and Duhemian Realism”, Synthese , 194(9): 3245–3265. doi:10.1007/s11229-016-1305-8
• Lee, Wang-Yen, 2012, “Hitchcock and Sober on Weak Predictivism”, Philosophia , 40(3): 553–562. doi:10.1007/s11406-011-9331-8
• –––, 2013, “Akaike’s Theorem and Weak Predictivism in Science” Studies in the History and Philosophy of Science Part A , 44(4): 594–599. doi:10.1016/j.shpsa.2013.06.001
• Leplin, Jarrett, 1975, “The Concept of an Ad Hoc Hypothesis”, Studies in History and Philosophy of Science , 5 No. 3: 309–345. doi:10.1016/0039-3681(75)90006-0
• –––, 1982, “The Assessment of Auxiliary Hypotheses”, British Journal for the Philosophy of Science , 33(3): 235–249. doi:10.1093/bjps/33.3.235
• –––, 1987, “The Bearing of Discovery on Justification”, Canadian Journal of Philosophy , 17: 805–814. doi:10.1080/00455091.1987.10715919
• –––, 1997, A Novel Defense of Scientific Realism , New York, Oxford: Oxford University Press.
• –––, 2009, “Review: The Paradox of Predictivism by Eric Christian Barnes”, The Review of Metaphysics , 63(2): 455–457.
• Lipton, Peter 1990, “Prediction and Prejudice”, International Studies in the Philosophy of Science , 4(1): 51–65. doi:10.1080/02698599008573345
• –––, 1991, Inference to the Best Explanation , London/New York: Routledge.
• Lyons, Timothy D., 2006, “Scientific Realism and the Strategema de Divide et Impera”, British Journal for the Philosophy of Science , 57(3): 537–560. doi:10.1093/bjps/axl021
• Magnus, P.D., 2011, “Miracles, trust, and ennui in Barnes’ Predictivism”, Logos & Episteme , 2(1): 103–115. doi:10.5840/logos-episteme20112152
• Magnus, P.D. and Craig Callender, 2004, “Realist Ennui and the Base Rate Fallacy”, Philosophy of Science , 71(3): 320–338. doi:10.1086/421536
• Maher, Patrick, 1988, “Prediction, Accommodation, and the Logic of Discovery”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988 , 1: 273–285. doi:10.1086/psaprocbienmeetp.1988.1.192994
• –––, 1990, “How Prediction Enhances Confirmation”, in J. Michael Dunn and Anil Gupta (eds.), Truth or Consequences: Essays in Honor of Nuel Belnap , Dordrecht: Kluwer, pp. 327–343.
• –––, 1993, “Howson and Franklin on Prediction”, Philosophy of Science , 60(2): 329–340. doi:10.1086/289736
• Martin, Ben and Ole Hjortland, 2021, “Logical Predictivism”, Journal of Philosophical Logic , 50: 285–318.
• Mayo, Deborah G., 1991, “Novel Evidence and Severe Tests”, Philosophy of Science , 58(4): 523–552. doi:10.1086/289639
• –––, 1996, Error and the Growth of Experimental Knowledge , Chicago and London: University of Chicago Press.
• –––, 2003, “Novel Work on the Problem of Novelty? Comments on Hudson”, Studies in the History and Philosophy of Modern Physics , 34: 131–134. doi:10.1016/S1355-2198(02)00083-7
• –––, 2008, “How to Discount Double-Counting When It Counts: Some Clarifications”, British Journal for the Philosophy of Science , 59(4): 857–879. doi:10.1093/bjps/axn034
• –––, 2010, “An Ad Hoc Save of a Theory of Adhocness? Exchanges with John Worrall” in Mayo and Spanos 2010: 155–169.
• –––, 2014, “Some surprising facts about (the problem of) surprising facts (from the Dusseldorf Conference, February 2011)”, Studies in the History and Philosophy of Science , 45: 79–86. doi:10.1016/j.shpsa.2013.10.005
• Mayo, Deborah G. and Aris Spanos (eds.), Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science , Cambridge: Cambridge University Press. doi:10.1017/CBO9780511657528
• McCain, Kevin, 2012, “A Predictivist Argument Against Skepticism” Analysis , 72(4): 660–665. doi:10.1093/analys/ans109
• McIntyre, Lee, 2001, “Accommodation, Prediction, and Confirmation”, Perspectives on Science , 9(3): 308–328. doi:10.1162/10636140160176161
• Menke, C., 2014, “Does the Miracle Argument Embody a Base-Rate Fallacy?”, Studies in the History and Philosophy of Science Part A, 45: 103–108.
• Mill, John Stuart, 1843, A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation , Vol. 2, London: John W. Parker.
• Mizrahi, Moti, 2012, “Why the Ultimate Argument for Scientific Realism Fails”, Studies in the History and Philosophy of Science , 43(1): 132–138. doi:10.1016/j.shpsa.2011.11.001
• Murphy, Nancey, 1989, “Another Look at Novel Facts”, Studies in the History and Philosophy of Science , 20(3): 385–388. doi:10.1016/0039-3681(89)90014-9
• Musgrave, Alan, 1974, “Logical versus Historical Theories of Confirmation”, British Journal for the Philosophy of Science , 25(1): 1–23. doi:10.1093/bjps/25.1.1
• –––, 1988, “The Ultimate Argument for Scientific Realism”, in Robert Nola (ed.), Relativism and Realism in Science , Dordrecht: Kluwer Academic Publishers, pp. 229–252. doi:10.1007/978-94-009-2877-0_10
• Nunan, Richard, 1984, “Novel Facts, Bayesian Rationality, and the History of Continental Drift”, Studies in the History and Philosophy of Science , 15(4): 267–307. doi:10.1016/0039-3681(84)90013-X
• 1937, “I. The Levity of Phlogiston”, 2(4): 361–404, doi:10.1080/00033793700200691
• 1938a, “II. The Negative Weight of Phlogiston”, 3(1): 1–58, doi:10.1080/00033793800200781
• 1938b, “III. Light and Heat in Combustion”, 3(4): 337–371, doi:10.1080/00033793800200951
• Peterson, Clayton, 2019, “Accommodation, Prediction, and Replication: Model Selection in Scale Construction”, Synthese , 196: 4329–4350.
• Popper, Karl, 1963, Conjectures and Refutations: The Growth of Scientific Knowledge , New York and Evanston: Harper and Row.
• –––, 1972, Objective Knowledge , Oxford: Clarendon Press.
• –––, 1974, “Replies to my critics”, in Paul Arthur Schilpp (ed.), The Philosophy of Karl Popper , Book II, 961–1197, La Salle, Illinois: Open Court.
• Psillos, Stathis, 1999, Scientific Realism: How Science Tracks the Truth , London and New York: Routledge.
• Putnam, Hilary, 1975, Philosophical Papers,Vol. 1, Mathematics, Matter, and Method , Cambridge: Cambridge University Press.
• Redhead, Michael, 1978, “Adhocness and the Appraisal of Theories”, British Journal for the Philosophy of Science , 29: 355–361.
• Salmon, Wesley C., 1981, “Rational Prediction”, British Journal for the Philosophy of Science , 32(2): 115–125. doi:10.1093/bjps/32.2.115
• Sarkar, Husain, 1998, “Review of A Novel Defense of Scientific Realism by Jarrett Leplin”, Journal of Philosophy , 95(4): 204–209. doi:10.2307/2564685
• Scerri, Eric R., 2005, “Response to Barnes’s critique of Scerri and Worrall”, Studies in the History and Philosophy of Science , 36(4): 813–816. doi:10.1016/j.shpsa.2005.08.006
• Scerri, Eric R. and John Worrall, 2001, “Prediction and the Periodic Table”, Studies in the History and Philosophy of Science , 32(3): 407–452. doi:10.1016/S0039-3681(01)00023-1
• Schindler, Samuel, 2008, “Use Novel Predictions and Mendeleev’s Periodic Table: Response to Scerri and Worrall (2001)”, Studies in the History and Philosophy of Science Part A , 39(2): 265–269. doi:10.1016/j.shpsa.2008.03.008
• –––, 2014, “Novelty, coherence, and Mendeleev’s periodic table”, Studies in the History and Philosophy of Science Part A , 45: 62–69. doi:10.1016/j.shpsa.2013.10.007
• Schlesinger, George N., 1987, “Accommodation and Prediction”, Australasian Journal of Philosophy , 65(1): 1 33–42. doi:10.1080/00048408712342751
• Schurz, Gerhard, 2014, “Bayesian Pseudo-Confirmation, Use-Novelty, and Genuine Confirmation”, Studies in History and Philosophy of Science Part A , 45: 87–96. doi:10.1016/j.shpsa.2013.10.008
• Sereno, Sergio Gabriele Maria, 2020, “Prediction, Accommodation, and the Periodic Table: A Reappraisal”, Foundations of Chemistry , 22: 477–488.
• Stanford, P. Kyle, 2006, Exceeding Our Grasp: Science, History, and the Problem of Unconceived Altenatives , Oxford: Oxford University Press. doi:10.1093/0195174089.001.0001
• Steele, Katie and Charlotte Werndl, 2013, “Climate Models, Calibration, and Confirmation”, The British Journal for the Philosophy of Science , 64 (30): 609–635.
• Swinburne, Richard, 2001, Epistemic Justification , Oxford: Oxford University Press. doi:10.1093/0199243794.001.0001
• Thomason, Neil, 1992, “Could Lakatos, Even with Zahar’s Criterion of Novel Fact, Evaluate the Copernican Research Programme?”, British Journal for the Philosophy of Science , 43(2): 161–200. doi:10.1093/bjps/43.2.161
• Votsis, Ioannis, 2014, “Objectivity in Confirmation: Post Hoc Monsters and Novel Predictions”, Studies in the History and Philosophy of Science Part A , 45: 70–78. doi:10.1016/j.shpsa.2013.10.009
• Whewell, William, 1849 [1968], “Mr. Mill’s Logic”, originally published 1849, reprinted in Robert E. Butts (ed.), William Whewell’s Theory of Scientific Method , Pittsburgh, PA: University of Pittsburgh Press, pp. 265–308.
• White, Roger, 2003, “The Epistemic Advantage of Prediction over Accommodation”, Mind , 112(448): 653–683. doi:10.1093/mind/112.448.653
• Worrall, John, 1978, “The Ways in Which the Methodology of Scientific Research Programmes Improves Upon Popper’s Methodology”, in Gerard Radnitzky and Gunnar Andersson (eds.) Progress and Rationality in Science , (Boston studies in the philosophy of science, 58), Dordrecht: D. Reidel, pp. 45–70. doi:10.1007/978-94-009-9866-7_3
• –––, 1985, “Scientific Discovery and Theory-Confirmation”, in Joseph C. Pitt (ed.), Change and Progress in Modern Science: Papers Related to and Arising from the Fourth International Conference on History and Philosophy of Science, Blacksburg, Virginia, November 1982 , Dordrecht: D. Reidel, pp. 301–331. doi:10.1007/978-94-009-6525-6_11
• –––, 1989, “Fresnel, Poisson and the White Spot: The Role of Successful Predictions in the Acceptance of Scientific Theories”, in David Gooding, Trevor Pinch, and Simon Schaffer (eds.), The Uses of Experiment: Studies in the Natural Sciences , Cambridge: Cambridge University Press, pp. 135–157.
• –––, 2002, “New Evidence for Old”, in Peter Gärdenfors, Jan Wolenski, and K. Kijania-Placek (eds.), In the Scope of Logic, Methodology and Philosophy of Science: Volume One of the 11th International Congress of Logic, Methodology and Philosophy of Science, Cracow, August 1999 , Dordrecht: Kluwer Academic Publishers, pp. 191–209.
• –––, 2005, “Prediction and the ‘Periodic Law’: A Rejoinder to Barnes”, Studies in the History and Philosophy of Science , 36(4): 817–826. doi:10.1016/j.shpsa.2005.08.007
• –––, 2006, “Theory-Confirmation and History”, in Colin Cheyne and John Worrall. (eds.), Rationality and Reality: Conversations with Alan Musgrave , Dordrecht: Springer, pp. 31–61. doi:10.1007/1-4020-4207-8_4
• –––, 2010, “Errors, Tests, and Theory Confirmation”, in Mayo. and Spanos 2010: 125–154.
• –––, 2014, “Prediction and Accommodation Revisited”, Studies in History and Philosophy of Science Part A , 45: 54–61. doi:10.1016/j.shpsa.2013.10.001
• Wright, John, 2012, Explaining Science’s Success: Understanding How Scientific Knowledge Works , Durham, England: Acumen.
• Zahar, Elie, 1973, “Why did Einstein’s Programme supersede Lorentz’s? (I)”, British Journal for the Philosophy of Science , 24(2): 95–123. doi:10.1093/bjps/24.2.95
• –––, 1983, Einstein’s Revolution: A Study In Heuristic , La Salle, IL: Open Court.

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confirmation | epistemology: Bayesian | Lakatos, Imre | Mill, John Stuart | Popper, Karl | realism: and theory change in science | scientific discovery | scientific explanation | scientific method | scientific realism | Whewell, William

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Ad-hoc hypothesis

A hypothesis added to avoid falsification; more specifically, a hypothesis that does not increase the overall content, hence falsifiability, of the theory. An example is the hypothesis of the cosmological constant, which Albert Einstein added to his theory of general relativity to allow a static universe.

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• > Journals
• > Journal of the American Philosophical Association
• > Volume 9 Issue 4
• > The Magic of Ad Hoc Solutions

Article contents

Introduction.

• Some Stubborn Associations
• Ad Hoc Solutions
• (Ad Hoc) Applications
• Concluding Remarks

The Magic of Ad Hoc Solutions

Published online by Cambridge University Press:  18 August 2022

When a theory is confronted with a problem such as a paradox, an empirical anomaly, or a vicious regress, one may change part of the theory to solve that problem. Sometimes the proposed solution is considered ad hoc. This paper gives a new definition of ‘ad hoc solution’ as used in both philosophy and science. I argue that a solution is ad hoc if it fails to live up to the explanatory requirements of a theory because the solution is not backed by an explanation or because it does not diagnose the problem. Ad hoc solutions are thus magical: they solve a problem without providing insight. This definition helps to explain both why ad hoc solutions are bad and why there may be disagreement about cases.

From the late 1950s until the 1980s ad hoc hypotheses were all the rage. Not that science was in a particularly bad state at that time; but due to Popper, philosophers of science were obsessed with ad hoccery. If science progresses via falsification, as Popper thought, we should ensure that theorists do not immunize their pet theories by devising additional hypotheses whenever experimental data contradicts their theory. But the history of science shows that additional hypotheses do sometimes constitute fruitful developments of a theory. For Popper and his school, the problem of determining which hypotheses are degenerative rather than progressive is the problem of determining which hypotheses are ad hoc. (The term ‘ad hoc’ has a pejorative and nonpejorative meaning. Here I am only interested in its pejorative sense.)

Despite the benefit of hindsight, the falsificationists were unable to give a definition of ‘ad hoc hypothesis’ that conformed to the usage of scientists in the examples they discussed. The main problem was that they considered empirical testability a cornerstone of science, and (thence?) ad hoccery should be some lack of testability. But nothing in the scientific literature suggests that scientists consider a hypothesis ad hoc if it lacks testable consequences. Worse, some hypotheses were considered ad hoc even though they did have independently testable consequences. Jarrett Leplin mockingly observes that what followed were ‘distinctions and refinements [that] constitute something like a degenerating research program, many of whose entries are patently ad hoc ’ ( Reference Leplin 1975 : 314 fn.16).

Leplin's comment illustrates that philosophers are not immune to giving ad hoc solutions. But although there is a large body of philosophical literature about ad hoc hypotheses in science, there is little work on ad hoccery more generally. Worse, many definitions of ad hoccery only apply to solutions suggested when faced with an empirical anomaly, thus excluding most parts of philosophy. But there is nothing to suggest that when a physicist claims some solution is ‘ad hoc’, they mean something quite different from when a philosopher makes a similar claim. On the contrary, it is likely that ‘ad hoc solution’ means roughly the same thing in different fields. There are differences between specific fields: physics uses different methods than (say) history. But at a very general level, in all fields of rational inquiry one develops theories based on evidence with the aim of explaining certain aspects of the world. Such theories may run into problems for which solutions are then proposed. Some of these solutions are called ‘ad hoc’. Other semitechnical terms in the vicinity of ‘ad hoc solution’—‘begging the question’, ‘special pleading’, and ‘moving the goalposts’—mean the same thing whether used by physicists, historians, or philosophers. This is one reason to think ‘ad hoc solution’ is not polysemous.

A second reason is that ‘ad hoc solution’ fails three standard tests for polysemy. The first is conjunction reduction. For example, ‘credit’ can mean praise as well as a type of loan from a bank. Conjoining sentences that use these different senses results in ambiguity. For example, ‘Jane and Anna got credit from the bank for their work’ is ambiguous, while ‘Jane got credit from the bank’ and ‘Anna got credit for her work’ are unambiguous. However, ‘Jane gave an ad hoc solution to a paradox’ and ‘Anna gave an ad hoc solution to an experimental anomaly’ can be conjoined unambiguously into ‘Jane and Anne gave ad hoc solutions to a paradox and an experimental anomaly’.

Another test is ellipsis: unless a polysemous term is used univocally, it is inappropriate to ellipse it. Thus, if Jane wants to participate as a runner in a marathon, while Anna wants to organize that marathon, one cannot express this as ‘Jane tried to run the marathon and Anna did too’. However, ‘Lorentz once proposed an ad hoc solution and so did Tarski’ is perfectly all right. Finally, polysemous terms can avoid contradictory readings. Since Jane wants to participate in, but not organize, the marathon, one can say without contradiction that Jane wanted to run the marathon, but she did not want to run the marathon. It is an awkward formulation, but contradiction is avoided because of polysemy. No such noncontradictory reading seems available for ‘Lorentz's contraction hypothesis was an ad hoc solution, but it was not an ad hoc solution’.

Thus, pace Lakatos ( Reference Lakatos, Lakatos and Musgrave 1970 ), ‘ad hoc’ does not have multiple senses and unless we find good evidence that ‘ad hoc solution’ means something different in the context of one field than it does in another, we better have a definition of ‘ad hoc solution’ that applies across the board. But currently there is not even any attempt made at such a definition.

This paper aims to fill that lacuna by giving a definition of ‘ad hoc solution’ that applies to science and also to philosophy. I argue in particular that once we add the concept of explanation, we gain an adequate understanding of ad hoccery. This more general definition also gives insight into why ad hoc solutions are bad, and it helps explain why some may disagree whether a solution is indeed ad hoc.

Before giving my definition, I discuss the most common associations people have with ad hoccery in section 1 and show how those fail to provide necessary or sufficient conditions for ad hoccery. In section 2 I define ‘ad hoc solution’ in terms of explanatory failure, and in section 3 I apply this definition to the discussion about the Church-Fitch paradox of knowability, the discussion about the axioms of Zermelo-Fraenkel (ZF) set theory, and the Lorentz-FitzGerald contraction hypothesis. I conclude with some remarks about the relation between ad hoccery and our theories of explanation.

1. Some Stubborn Associations

The Latin phrase ‘ad hoc’ translates ‘to this’, and the adjective ‘ad hoc’ is commonly defined as ‘created for a specific purpose’. The many definitions given in the philosophy of science literature may suggest that ‘ad hoc’ is not used for a specific purpose but is rather a highly polysemous term. To restore order, we should rid ourselves of some stubborn associations by showing that none of these are necessary or sufficient for something to count as ad hoc.

The first of these associations is that ad hoc hypotheses lack testability or empirical content. Popper made this the cornerstone of his notion of ad hoccery ( Reference Popper 1959 : 83; Reference Popper 1965 : 241). But scientists do consider some testable hypotheses ad hoc—even when the hypothesis makes predictions beyond the specific experiment that brought about the problem for the original theory. The endlessly discussed Lorentz-FitzGerald contraction hypothesis (LFC), which Popper ( Reference Popper 1959 : 83) considered a paradigmatic example of an ad hoc hypothesis, did have (novel) testable consequences: the result of the Kennedy-Thorndike experiment in 1931 constituted an empirical refutation of it (Grünbaum Reference Grünbaum 1959 : 49ff.).

Neither is lack of testability sufficient for ad hoccery unless virtually all hypotheses in fields such as philosophy, mathematics, or history count as ad hoc. Hypotheses in these fields are commonly not experimentally testable. Popper and others in this tradition usually limit their definition to the use of ‘ad hoc’ in the sciences and in particular physics, thus implicitly holding that ‘ad hoc’ is polysemous. Worse, it is not obvious that hypotheses in physics that lack testable consequences are ad hoc. String theory is currently untestable, and the multiverse hypothesis seems untestable in principle. But to the best of my knowledge, no one currently complains that they therefore are ad hoc: testability thus does not seem sufficient for ad hoccery. Better to abandon this ‘strange fixation on testability’ (Leplin Reference Leplin 1975 : 345). (For more arguments against lack of testability as a cornerstone for ad hoccery, see inter alia : Bamford Reference Bamford 1993 , Grünbaum Reference Grünbaum 1976 : 342ff., and Hunt Reference Hunt 2012 : 3ff.)

A second association is with circular explanations. Popper takes ad hoc explanations to be ‘almost circular’ ( Reference Popper 1972 : 192), and David Miller gives ‘it is the dormitive virtue of opium that induces sleep’ as an example of an ad hoc hypothesis that is ‘supposedly explanatory’ ( Reference Miller, Bynum, Browne and Porter 1981 : 6–7). Since ‘dormitive virtue’ just means ‘the ability to induce sleep’, this is a circular explanation. But it is unclear what is ad hoc about it—unless, of course, all explanatory failures are ad hoc. Conversely, there are paradigmatic cases of ad hoccery, such as the LFC, that are clearly not circular explanations. If the LFC were a circular explanation, then the phenomena it explained should provide (part of) its explanation. The phenomena it explained did not provide the explanation for the LFC but were (part of) the justification for the LFC. But justification and explanation are distinct notions. My justification for believing that it is raining is that I see the rain, but (me seeing) the rain does not explain why it is raining. (Although it does help explain why I believe it is raining. But the target of explanation is the fact that it rains, not the fact that I believe that it is raining.) It thus seems that two fallacies are here combined by a fallacy of association. (For more on why circular explanations are different from ad hoc explanations, see Bamford Reference Bamford 1993 : 336ff.)

A third, related association is that ad hoc solutions lack independent evidence or independent reasons (Schaffner Reference Schaffner 1974 : 68; Zahar Reference Zahar 1973 : 101ff.). Roughly, the idea is that a solution is ad hoc if the problem it solves is the only evidence or reason that can be given for it. Of course, it is a good thing when your hypothesis is corroborated by various pieces of independent evidence. But the history of science suggests that a lack of independent evidence is not sufficient to consider a hypothesis ad hoc. The only empirical evidence for the postulation of Neptune was an anomaly in the expected movement of Uranus; yet, there is no evidence that scientists considered it ad hoc (Leplin Reference Leplin 1982 : 237). Similarly, the redshift of a galaxy's characteristic spectrum is explained by the velocity of the galaxy although there is little evidence for the velocity of a galaxy beyond its redshift (Lipton Reference Lipton, Hon and Rakover 2001 : 45).

Conversely, no scientist at the time seemed to think that additional (experimental) evidence for the LFC would make it less ad hoc (Holton Reference Holton 1969 : 177). And, as a more extreme example, a parapsychologist who holds that psychic phenomena are disturbed by the presence of inquisitive or skeptical observers can point to a wide range of corroborating cases where psychic phenomena were different from their expectations (Boudry Reference Boudry 2013 : 249). Still, the parapsychologist's hypothesis is ad hoc. In sum, there is little evidence for the idea that a hypothesis is ad hoc if and only if it lacks independent evidence.

A lack of generality or a failure to unify is a fourth association (Lange Reference Lange 2001 ; Leplin Reference Leplin 1975 : 336ff.). The idea is that non-ad hoc solutions solve similar problems and therefore unify these problems. Unfortunately, some solutions are ad hoc even if they take care of various related problems. I solve Russell's paradox by holding that every predicate specifies a set except in those cases where this would result in paradox. Moreover, my solution is general and unified: all these paradoxes have in common that supposing the existence of some set leads to a paradox. Still, the solution is blatantly ad hoc (Hand and Kvanvig Reference Hand and Kvanvig 1999 : 426). (Another example would be the parapsychologist's hypothesis mentioned in the previous paragraph.)

Conversely, not every exception to a general rule is ad hoc. Many sweeping scientific generalizations are, in the face of new data, restricted, and this is often considered progress. Bamford ( Reference Bamford 1993 ) illustrates this by Hooke's law, which states that the extension of a spring is proportional to the force exerted on the spring. Springs do not always behave in accordance with Hooke's law; the point at which they stop behaving in that way is their elastic limit. Knowledge of the elastic limit of a material and how this limit changes due to fatigue is indeed crucial for designing bridges (Bamford Reference Bamford 1993 : 305ff.). But all these exceptions to Hooke's law do not make the theory of springs ad hoc. (At least to my knowledge no one ever made that complaint.)

Some accounts of ad hoccery combine some of these associations. For example, Leplin's ( Reference Leplin 1975 : 337) detailed analysis of ad hoccery states, among other things, that if a hypothesis is ad hoc, then (i) there is no other evidence for it other than the experiment for which the hypothesis was formulated, (ii) the hypothesis has no applications outside of that experiment, and (iii) it has no independent theoretical support. But as we just saw, neither lack of independent evidence nor lack of generalizability is necessary for ad hoccery. Moreover, Leplin thinks ad hoccery is a global affair. He states that if a hypothesis is ad hoc, there are problems other than the specific experimental anomaly that triggered the hypothesis. These other problems indicate that the theory is ‘non-fundamental’: that the problems cannot be solved unless the non-fundamentality is removed, and that ‘a satisfactory solution to any of these problems . . . must contribute to the solution of the others’ ( Reference Leplin 1975 : 337). I do not see why ad hoccery cannot be local. Below I discuss two examples (a theory of bread and the Church-Fitch paradox) that are local: there are no obvious other problems that need to be dealt with too.

This ends our association game. Time to look at the problem of ad hoccery with fresh eyes.

2. Ad Hoc Solutions

Let us start with the classic toy example of the nourishment of bread. Suppose our basic bread theory states that all bread nourishes. This helps explain various bread-related facts, but it also faces a challenge. In August 1951 at least five people from the French village Pont Saint-Esprit died after eating bread. Not all bread nourishes, it seems, and our basic bread theory needs changing. A straightforward solution is to restrict the general statement of our theory: all bread nourishes, except the bread in Pont Saint-Esprit in August 1951. Now the tragedy of Pont Saint-Esprit no longer contradicts our theory. This is a good thing. At the same time, the solution is fishy and a paradigm of ad hoccery. Why?

It is important to note that the exception is true. The bread in Pont Saint-Esprit did not nourish while bread normally does. Every solution should thus state that the bread in Pont Saint-Esprit was not nourishing or at least be compatible with this claim; otherwise the resulting theory is simply false. The restriction itself can thus not be what is ad hoc: all solutions should exclude the bread from Pont Saint-Esprit from the nourishing bread. But not all solutions are considered ad hoc. We can understand why some are ad hoc if we focus on explanation. The simple exclusion solution gives no clue as to why the bread from Pont Saint-Esprit did not nourish while any satisfactory solution should explain this fact. Its explanatory failure, I submit, is what makes the simple exclusion solution ad hoc.

Contrast the simple exclusion with the ergot solution that states that all bread nourishes except bread that contains ergot and that the bread from Pont Saint-Esprit contained ergot. Neither solution is contradicted by the tragedy of Pont Saint-Esprit so they are equal in that respect. But the ergot solution has more explanatory depth: it can answer the question why the bread of Pont Saint-Esprit did not nourish. While the simple exclusion solution takes this as an unexplained fact, the ergot solution explains it: the bread contained ergot, and bread containing ergot does not nourish. The ergot solution thus explains or, as I prefer to put it, diagnoses the problem by pointing to a feature of the bread in Pont Saint-Esprit that is responsible for its failure to nourish. By ‘diagnosing a problem’ I thus mean an explanation for why the problem arose. (Note that this need not be an explanation for why the problem is indeed a problem. In our example we want an explanation for why the bread in Pont Saint-Esprit did not nourish. We are not interested in explaining why it is a problem for the original theory that the bread in Pont Saint-Esprit did not nourish. One should explain why theories should be empirically adequate to meet this latter explanatory demand. A diagnosis merely explains how the problem arose and takes it for granted that the problem is indeed a problem.)

The ergot solution as it stands may still be somewhat wanting. It solves the problem of the bread in Pont Saint-Esprit using an entity that (apparently) counters bread's capacity to nourish. But why does bread containing ergot fail to nourish? And what exactly is ergot? Some might say this solution is still not free of ad hoccery. Compare it with the poison solution, which holds that the bread in Pont Saint-Esprit contained a poison and that all bread nourishes except when it contains a poison. While the ergot solution triggers the question ‘why does bread containing ergot fail to nourish?’, the poison solution triggers no analogous question. In many contexts it is considered obvious that bread containing a poison fails to nourish. Poisons are bad for human beings, and therefore bread containing them will have a bad effect on human beings eating that bread. The poison solution is thus backed by a sufficient explanation.

Despite this, the poison solution may not be overall better than the ergot solution, because the first provides a less specific diagnosis than the latter. The diagnosis of the poison solution is that the bread in Pont Saint-Esprit contained a poison. But this is arguably too general. There are many poisons, and the poison solution does not single out a particular one that the bread in Pont Saint-Esprit was supposed to contain. It raises the question which poison was in the bread exactly? Ideally, we would thus want a theory that provides both a specific diagnosis and is backed by an explanation. Of course, in our example this is achieved by combining the last two solutions, that is, the ergot-poisoning solution, which states that (a) all bread nourishes except when it contains a poison; (b) ergot is a poison; and (c) the bread in Pont Saint-Esprit contained ergot. In many contexts claim (a) is not in need of any further explanation. The diagnosis (c) is now backed by (a) and (b) because these latter two answer the question why bread containing ergot fails to nourish. The resulting theory thus provides a non-ad hoc solution to the problem of the bread of Pont Saint-Esprit because it diagnoses the problem, and the diagnosis is backed by an explanation. The simple exclusion solution, on the other hand, provides an ad hoc solution because it fails to diagnose the problem, and, trivially, its diagnosis is not backed by an explanation.

More generally, I claim that ‘ad hoc’ is used in philosophy and science for solutions that are non-explanatory, thus:

(Ad Hoc) A solution to a problem is ad hoc if and only if

(a) the solution does not diagnose the problem, or [Diagnosis]

(b) the solution is not backed by a good explanation; and [Explanation]

(ii) it is reasonable to demand a solution that diagnoses the problem and is backed by a good explanation. [Reasonable]

An ad hoc solution is thus mysterious either because it does not diagnose the problem or because it is not backed by a good explanation. And this mystery is problematic because a non-mysterious solution is reasonably demanded. I have defined ad hoccery for solutions rather than for hypotheses because ad hoccery mostly comes up in the context of problems: empirical anomalies, paradoxes, vicious regresses, and so on. (Many definitions of ‘ad hoc hypothesis’ therefore state that the hypothesis is proposed as a solution to some empirical anomaly.) It may help to go over the conditions in (Ad Hoc) in some more detail.

The first condition states that the solution is not explanatory because (a) it fails to diagnose the problem or (b) it is not backed by an explanation. To diagnose a problem is to explain how it arose in the first place. In the above example both the ergot solution and the ergot-poison solution diagnosed the problem as arising from ergot in the bread. The diagnosis in this case thus introduces an object that is held responsible, but a diagnosis may instead delete rather than introduce an object. The problems of phlogiston theory may, for example, be diagnosed as arising from the mistaken assumption that phlogiston exists. (Diagnosing is easier with the benefit of hindsight.) And some diagnoses are orthogonal to matters of existence: a diagnosis of the Grelling-Nelson paradox (‘Is “heterological” a heterological word?’) would not point to an object that is responsible for the paradox but may point out a property of natural languages (that they are semantically closed, for example).

A solution is backed by an explanation when it is explained how the solution solves the problem. In the bread example, the simple exclusion solution was not backed by an explanation because there was no answer to the question why the bread in Pont Saint-Esprit did not nourish. But neither was the ergot solution backed by an explanation because (to most people) it would be unclear why the presence of ergot in the bread ensures that it no longer nourishes. The poison solution was backed by an explanation: something that is nutritious in normal circumstances is no longer nutritious when it contains a poison. And the final solution we discussed partly used this same explanatory backing: ergot is a poison, and something that is nutritious in normal circumstances is no longer nutritious when it contains a poison; therefore, bread containing ergot fails to nourish.

In the bread example we saw also that more general diagnoses, which may apply to more cases than the case at hand, are not necessarily better. Blaming poison whenever a nourishing substance fails to nourish is a general solution, but we often want to know specifics. On the other hand, a good diagnosis can often be generalized—other products made from grain and containing ergot will also fail to nourish. Generality is thus a bad predictor for the quality of a diagnosis: good diagnoses can often be generalized, but a general diagnosis may be too general to be informative. Clearly, it may be debatable whether a diagnosis is good, which explains why we may disagree about ad hoccery.

I should stress that the distinction between diagnoses and explanations is artificial: a diagnosis is a kind of explanation. But the bread example shows that not every diagnosis is backed by an explanation, and therefore I have chosen the term ‘diagnosis’ for that which explains how the problem arose so that ‘explanation’ can be unambiguously used for that which backs the solution. I take the term ‘diagnosis’ from Stephen Read who argues that Buridan's solution to the liar and revenge paradoxes is ‘an ad hoc device designed solely, and without any real diagnosis, to block the paradoxes’ ( Reference Read 2002 : 202). (Indeed, not everyone agrees with Read's claim, see Benétreau-Dupin Reference Benétreau-Dupin 2015 ; Hughes Reference Hughes 1984 : 20; and Klima Reference Klima, Rahman, Tulenheimo and Genot 2008 .)

In the context of theories of truth, there is another good example of a solution that does not diagnose a problem. Deflationists hold that there is not much to truth; it is completely characterized by ( T ): ‘ p ’ is true if and only if p . Like many other theories of truth, deflationism faces a problem with the liar sentence: ‘this sentence is not true’. By applying ( T ) to the liar and using some basic logic, we get a contradiction. One way out for deflationists is to restrict ( T ) so it does not apply to those propositions that lead to a paradox. This solves the problem but without diagnosing it because it does not tell us why applying ( T ) to some sentences leads to a contradiction.

Contrast this with a solution that bans all self-referential sentences from ( T ). This solution diagnoses the problem as due to self-referentiality; the liar results in paradox because it is self-referential. This response might still be ad hoc, though, for it seems to meet condition (i) (b): the solution is not backed by an explanation. The claim that self-referentiality is problematic needs to be backed by an explanation if only because not all self-referential sentences seem problematic. ‘This sentence contains five words’ is a perfectly consistent self-referential sentence. Hence, unless backed by an explanation, the self-referentiality response may be ad hoc although for a slightly different reason than the previous solution. (Of course, the self-referentiality response might just be bad because it is false. Or maybe it is both false and ad hoc: ad hoccery offers no protection against other vices.)

To avoid satisfying condition (i) of (Ad Hoc) a solution should both diagnose the problem and, unless the solution is not in need of an explanation, be backed by an explanation. This link between ad hoccery and explanatory failure can also be found in Read's assessment of Paul Horwich's deflationist solution to the liar:

The fact that he [Horwich] excludes the paradoxical cases of ( T ) from the account of truth shows, first, the ad hoc and unsatisfactory nature of his account of the paradoxes—after all, he has no further account of truth to which he can appeal to explain the exclusion. (Read Reference Read 2002 : 214)

A similar sentiment is expressed by J.C. Beall and Bradley Armour-Garb:

Nothing in deflationism itself yields a principled explanation of why such sentences should not be within the range of (T)'s variables (as it were). This leaves open the possibility that deflationists may none the less resort to ad hoc restrictions. (Beall and Armour-Garb Reference Beall and Armour-Garb 2003 : 313)

It may of course happen that a solution lacks both a diagnosis and an explanatory backing. For example, Read seems to think that ‘to explain the exclusion’ Horwich should provide both a diagnosis of the paradox and an explanatory backing for the exclusion of the problematic sentences.

I will add one small aside about Samuel Schindler's ( Reference Schindler 2018 : 59) analysis of ad hoccery because it resembles (Ad Hoc) in some sense. Schindler holds that a hypothesis is non-ad hoc if it coheres with the theory at hand or the relevant background theories, and a hypothesis coheres with the (background) theory just in case the theory provides theoretical reasons for believing the hypothesis. If the hypothesis can be deduced from the (background) theory, then, for Schindler, this constitutes a theoretical reason to believe the hypothesis. Another theoretical reason for believing a hypothesis is if the (background) theory explains why the hypothesis is true. This latter idea is somewhat similar to condition (i) (b) of (Ad Hoc). But note that coherence plays no role in (Ad Hoc) and that mere deduction of a solution is, under (Ad Hoc), insufficient to save it from ad hoccery. Moreover, Schindler's definition of ‘ad hoc hypothesis’ only covers hypotheses that are ‘are introduced to save a theory . . . from empirical refutation’ ( Reference Schindler 2018 : 59) and is thus inapplicable in most philosophical contexts.

Just as there may be disagreement about the quality of a diagnosis or about the quality of the explanation backing the diagnosis, there may be disagreement about whether the diagnosis needs an explanation. In the bread example, someone might demand a further explanation for why ergot is poisonous. This demand is reasonable in the context of chemistry and biology where we seek to explain why some substances are poisonous. But the demand may be unreasonable in the context of history.

Which brings us to the second condition: just because you can cook up a why-question that the solution does not answer, does not mean that the solution is ad hoc. Some demands for explanation are unreasonable, and condition (ii) ensures that failing to live up to an unreasonable demand does not make a solution ad hoc. Again, there may be disagreement about whether demanding an explanation is reasonable and thus disagreement about whether a solution is ad hoc. I have no theory to offer on when an explanation is reasonably demanded, and it is beyond of the scope of this paper to construct one. (But see Bromberger Reference Bromberger 1992 for an illuminating discussion.)

Conditions (i) and (ii) show that a solution may become non-ad hoc if it becomes possible to diagnose the problem, if a reasonably demanded explanation starts backing it, or if it becomes unreasonable to demand an explanation for it. In the next section I show that philosophers and scientists use ‘ad hoc’ in accordance with (Ad Hoc).

3. (Ad Hoc) Applications

Philosophers often complain that something is ad hoc. Within the philosophy of language, ‘many philosophers regard [Tarski's solution to the liar] as ad hoc’ (Sher and Bo Reference Sher and Bo 2019 : 38). (For example, Fox Reference Fox 1989 : 177 and Priest Reference Priest 2000 : 309.) In the philosophy of mathematics, the axioms of ZF set theory are often considered to provide an ad hoc solution to the set-theoretical paradoxes (Cook and Hellman Reference Cook, Hellman, Cook and Hellman 2018 : 53; Menzel Reference Menzel 1986 : 37–39; Putnam Reference Putnam, Sher and Tieszen 2000 : 24). And in metaphysics it has been argued that universals and tropes are pieces of ad hoc ontology (Rodriguez-Pereyra Reference Rodriguez-Pereyra 2002 : 210ff.) and that postulating a primitive non-mereological form of composition for facts is an ad hoc solution to the unity problem (Betti Reference Betti 2015 : ch. 2).

In science the complaint of ad hoccery seems to be less often made than in philosophy. Examples of alleged ad hoc hypotheses that are often discussed by philosophers of science are Ptolemy's epicycles, the LFC, and the neutrino hypothesis. Of these three, the LFC is arguably the strongest example because even Lorentz himself thought it was ad hoc.

Since I lack the space to discuss all cases where the complaint of ad hoccery is made, I will only discuss the use of ‘ad hoc’ in the debate about the Church-Fitch paradox of knowability, in the discussion about the axioms of ZF set theory, and in the evaluation of the LFC. In each case I show that the use of ‘ad hoc’ corresponds to (Ad Hoc).

3.1 An Unknown Truth

The Church-Fitch paradox shows that all truths are known if all truths can be known. (For a general introduction to this paradox, see Brogaard and Salerno Reference Brogaard, Salerno and Zalta 2019 .) Some antirealists are committed to the claim that all truths can be known, and the paradox threatens their position because it seems absurd to hold that all truths are known. Besides the rules of elementary logic, the paradox assumes that knowledge is factive and distributes over conjunctions and that absurd propositions are impossible. Here is a sketch of the problem. Suppose that all truths can be known (TCK), that is,

(TCK) For all propositions p , if p is true then it is possible to know p .

Suppose, for contradiction, that there is a truth, q , that is not known. By (TCK) it is possible to know the following conjunction: q is true and q is not known. Suppose this conjunction is known. Then it follows from knowledge's distribution over conjunctions that q is known and that it is known that q is not known; from this, by the factivity of knowledge, it follows that it is known and not known that q— contradiction. Hence, if all truths are knowable, all truths are known.

Neil Tennant ( Reference Tennant 1997 ) offers a solution to the paradox based on distinguishing Cartesian from anti-Cartesian propositions and restricting (TCK) to Cartesian propositions. A proposition p is anti-Cartesian if and only if we can derive a contradiction from the assumption that p is known. Tennant distinguishes three ways in which a proposition might be anti-Cartesian. First, the proposition itself may be inconsistent, in which case a contradiction can be derived from the assumption that we know it. Second, a proposition such as ‘No thinking thing exists’ may be consistent but false whenever it is the object of a propositional attitude. Finally, there are claims of the forms ‘ p and it is not known that p ’ from which we can derive a contradiction if we assume that knowledge distributes over conjunctions. By restricting (TCK) to Cartesian propositions, paradox is avoided because ‘ q and it is not known that q’ is an anti-Cartesian proposition. Tennant's diagnosis of the Church-Fitch paradox is thus that anti-Cartesian propositions are wrongly taken to be within the scope of (TCK).

Not everyone likes Tennant's solution. Michael Hand and Jonathan Kvanvig ( Reference Hand and Kvanvig 1999 ) argue that it is ad hoc. A non-ad hoc solution to the paradox must not merely exclude those propositions that lead to a problem, but

one must go beyond such arbitrary approaches. Realists do this by observing that truth is ‘radically nonepistemic’, thereby giving themselves a reason based on their conception of truth for denying [(TCK)]. Tennant must do something comparable. We should expect him to find some feature of truth, antirealistically conceived, that disarms the paradox by allowing some truths to be unknowable. (Hand and Kvanvig Reference Hand and Kvanvig 1999 : 423, my italics)

Hand and Kvanvig demand some theory of truth that provides a reason or explanation for restricting (TCK). Note that Hand and Kvanvig do not deny that Tennant's solution is general. They simply think that generality is no defeater for ad hoccery. As a toy example they mention the claim that any grammatically predicative expression defines a set, except when this assumption leads to a contradiction. This solution to Russell's paradox is quite general but ‘clearly ad hoc’ (Hand and Kvanvig Reference Hand and Kvanvig 1999 : 426).

Hand and Kvanvig grant that Tennant has given a diagnosis of the problem: the problem arises for (TCK) because it uses an anti-Cartesian proposition. But they seem to think that the diagnosis is wrong or lacks an explanatory backing. For example, they argue that Tennant's solution works for (TCK) but not for its necessitation; it should also work for this modalized cousin because the antirealist holds that it is essential to truth that it is knowable. This suggests that Tennant's diagnosis is incorrect by not going to the heart of the matter. After considering some ways to deal with the stronger version, Hand and Kvanvig claim these are all ad hoc because they do ‘do not cite some feature of truth that calls for the restriction in question’ ( Reference Hand and Kvanvig 1999 : 425). They thus want the diagnosis to be backed by an explanation: some feature of truth should explain the restriction.

In his response to Hand and Kvanvig, Tennant operates with a different conception of ad hoc, for he stresses the generality of his approach and compares it favorably to other general solutions to various problems. For example, he considers the following restriction to ( T ) to avoid the liar paradox: For all propositions p , ‘ p ’ is true if and only if p , except for those propositions from which we can derive a contradiction. This restricted schema ‘is substantive, informative and important. The objection that the restriction invoked is ad hoc is groundless’ (Tennant Reference Tennant 2001 : 110).

I beg to differ. This recipe for restricting general principles is a get-out-of-jail-free card that immunizes principles like (T) and (TCK) against defeat. It also leaves it completely mysterious why some propositions are excluded. This is as (Ad Hoc) prescribes: restricting a general principle by simply excluding the instances that lead to problems fails to diagnose the problem because it does not even try to explain how the problem came about. This makes such solutions unsatisfactory and triggers the reproach of ad hoccery. I am not alone in thinking this: Igor Douven ( Reference Douven 2005 : 50–51) makes the same point before offering a more principled case for Tennant's solution.

Douven's account of what it takes to be non-ad hoc is quite similar to that of Hand and Kvanvig although Douven rightly objects to the idea that one's solution to the Church-Fitch paradox should be based on one's theory of truth. Why, Douven asks, ‘could it not be something about one's conception of, for instance, knowledge that explains what is wrong with [(TCK)]?’ ( Reference Douven 2005 : 49). Douven provides the following criterion:

In order to qualify as principled or non- ad hoc , it is necessary and sufficient that a proposal for restricting [(TCK)] in a particular way be accompanied by a reason for adopting it other than its capability to solve the paradox, and that reason must be related, in an informative or explanatory way, to one or more of the concepts that are either implicitly or explicitly involved in [(TCK)]. ( Reference Douven 2005 : 50)

Douven thus thinks that the restriction imposed on (TCK) is not ad hoc only if it is backed up by some explanatory or informative reason. Douven is thus appealing to (i) (b) of (Ad Hoc). He then provides such a reason for Tennant's (anti-)Cartesian solution based on the idea that anti-Cartesian propositions cannot be consistently believed. He takes this to be both independently motivated (because it also helps to solve a version of Moore's paradox) and an explanation for why there are unknowable truths (there are unknowable truths because there are propositions that cannot be consistently believed; Douven Reference Douven 2005 : 57–58). This last point illustrates that although Douven does not explicitly mention the need for a diagnosis in his conditions for non-ad hoccery, he does provide such a diagnosis.

I do not wish to pass judgement on Douven's solution but only want to note the strategy. Although he ends up with a more general restriction of (TCK) than Tennant, Douven nowhere suggests that this is part of the reason his solution is not ad hoc. Instead Douven attempts to explain the restriction, and this explanation also diagnoses the paradox: exactly as (Ad Hoc) prescribes.

3.2 An Iteration

To illustrate the adequacy of (Ad Hoc) further I apply it to the philosophical debate about the axioms of ZF set theory. Any student of set theory knows that naive set theory leads to problems such as Russell's paradox and the Burali-Forti paradox. The main suspect is the axiom schema of (naive) comprehension whose instances ensure that any grammatically predicative expression defines a set. In ZF set theory one replaces this schema either with the axiom schema of replacement (together with an axiom stating the existence of the empty set) or with the axiom schema of separation. This avoids the known set theoretic paradoxes—but not to everyone's satisfaction.

Zermelo's approach, however, offers no justification of the restrictions imposed upon P [i.e., the naive comprehension principle] other than the fact that the paradoxes are avoided. But that is ad hoc. What we would like is some sort of explanation of why there is no Russell set or no set of all ordinals, or why, at least, we shouldn't be able to prove there are such sets from our axioms. (Menzel Reference Menzel 1986 : 39, italics in the original)

In line with (Ad Hoc) Menzel wants a solution that offers a diagnosis: why do the paradoxical sets not exist? Menzel is not alone in finding the solution ad hoc: ‘the “resolution” offered by first-order ZFC is a paradigm of the ad hoc’ (Cook and Hellman Reference Cook, Hellman, Cook and Hellman 2018 : 53). (And although Putnam [ Reference Putnam, Sher and Tieszen 2000 : 24] does not use the term ‘ad hoc’, I agree with Douven [ Reference Douven 2005 : 51] that Putnam is best understood as saying that ZF is ad hoc.)

These critics of ZF demand an explanation for the selection of axioms as well as a diagnosis of the paradoxes of naive set theory, preferably in one sweep. This may be provided by the iterative conception of sets: the idea that sets are ‘constructed’ in stages and that each stage contains all previously constructed sets plus all subsets that can be constructed out of them. Boolos ( Reference Boolos 1971 ) popularized this conception among philosophers, and it diagnoses Russell's paradox as a problem of trying to construct a set consisting both of elements one previously constructed and of an element one has not yet constructed. But at each stage one can only use previously constructed sets. (Of course, all this talk of ‘constructing’ should not be taken literally.) Moreover, Boolos takes the iterative conception of a set to explain the axioms of ZF such that they are ‘not at all ad hoc’ ( Reference Boolos 1971 : 218).

Interestingly, Boolos notes that the axiom schema of replacement does not ‘follow from the iterative conception’ ( Reference Boolos 1971 : 228) but has ‘many desirable consequences and (apparently) no undesirable ones’ (229). This provides at best an abductive argument for replacement but may fall short of the kind of explanation that someone like Putnam demands. This illustrates that disagreement about ad hoccery can be due to disagreement about whether a solution is (sufficiently) backed by an explanation.

Instead of trying to meet the demand for a satisfactory explanation, Penelope Maddy ( Reference Maddy 2011 ) defends contemporary set theory against the charge of ad hoccery by holding that such an explanation is unreasonable, effectively saying that condition (ii) of (Ad Hoc) is not met. (To be sure, Maddy does not frame her argument in terms of ad hoccery.) Maddy argues that the axioms of a mathematical theory need no explanation or ‘intrinsic justification’, that is, justification coming from some pretheoretic notion of a set. Rather, the axioms are extrinsically justified: they are as simple and powerful as possible while (for all we know) avoiding contradiction. According to Maddy, it thus is unreasonable to demand an explanation; hence none of the axioms of set theory are ad hoc because condition (ii) of (Ad Hoc) is not satisfied.

3.3 LFC Revisited

The LFC hypothesis was one of Popper's main examples of an ad hoc hypothesis ( Reference Popper 1959 : 83), and it is now a litmus test for any definition of ‘ad hoc solution’. The LFC states that an object contracts in its direction of travel. It was proposed by FitzGerald and, independently, by Lorentz after the famous null results of the Michelson-Morley experiments. These experiments used an interferometer designed to detect the ether on the basis of its effect on the speed of light. A light beam was first split into two beams traveling in perpendicular directions, and both beams were then sent back to a single screen. The light beam that would travel parallel to the direction of the earth relative to the ether should take longer than the light beam that travelled perpendicular to the earth's direction of travel. However, the two light beams always arrived at (virtually) the same time, no matter when the experiment was conducted or which direction the interferometer was facing. Thus, either the speed of light was constant, which was hard to square with the idea that light travelled through the ether, or—as the LFC states—objects contract in their direction of travel, which explains why the ‘slower’ light beam arrives at the same time as the ‘faster’ one. Current physics holds that, in a sense, both are true. The speed of light is constant and, stated in relativistic terms, the length of a moving object is shorter than its proper length, which is its length as measured in its own rest frame. Note that this does not mean a moving object is physically deformed—its proper length does not change—but ‘merely’ that the measured length of an object depends on whether the object is in motion relative to the observer. Crucially, the LFC was not originally stated in relativistic terms, and it was clear to everyone that the hypothesis was fishy.

The LFC is a rather good litmus test for any theory of ad hoccery because physicists at the time, including Lorentz, were dissatisfied with it (Holton Reference Holton 1969 : 139). But it should be noted that because this is a much-discussed case study, there are a few myths surrounding the Michelson-Morley experiments and the LFC. One is that the experiments played a key role in Einstein's formulation of special relativity. Instead, it is unclear whether Einstein was even aware of these experiments when writing his 1905 paper. Einstein ( Reference Einstein 1905 ) suggests he arrived at his theory mainly via his dissatisfaction with the asymmetries in Maxwell's theory of electrodynamics. Another myth is that the LFC had no new testable consequences. It did, and these consequences were refuted by the Kennedy-Thorndike experiments. (For detailed myth busting, see Grünbaum Reference Grünbaum 1959 and Holton Reference Holton 1960 , Reference Holton 1969 .)

In this subsection I show that Lorentz considered the LFC an ad hoc solution in the sense of (Ad Hoc). I argue that Lorentz thought the LFC provided a diagnosis but was not backed by a good explanation. Thus, the problem with the LFC was that no reasonable explanation could be given for why objects contracted in their direction of travel. The explanatory backing Lorentz ended up giving was not fully satisfactory—not even to himself—because it depended on assumptions for which he could at most give analogical arguments. Accordingly, the LFC was ad hoc because it satisfied conditions (i) (b) and (ii) of (Ad Hoc).

In a letter to Einstein dated 23 January 1915, Lorentz writes that, like Einstein, he also thought that the LFC was ad hoc and that he had said so in print (Kox Reference Kox 2008 : 410; Lorentz seems to refer to his Reference Lorentz and Sommerfeld 1904a .) Lorentz also states that in the absence of a general theory one should be content with explaining a single fact, ‘as long as the explanation is not artificial’ (‘ wenn diese Erklärung nur nicht erkünstelt ist ’, Kox Reference Kox 2008 : 410). He thought that the LFC was not artificial, but rather the only possible explanation (‘ die einzig mögliche’ ) and one that would have seemed less ad hoc and even quite natural when one assumes that the transformation properties of electromagnetic forces also hold for other forces, in particular molecular forces (Kox Reference Kox 2008 : 411). Lorentz thus assumed an analogy: molecular forces are affected in a moving body similar to the way electromagnetic forces change around a moving body. (Note, incidentally, that this assumption is both unifying and, in principle, testable.)

This assumption provides a crucial part of Lorentz's attempt to give a satisfactory explanatory backing of the LFC. Because this, together with other assumptions, allowed him to derive the LFC from the Maxwell equations. But as Lorentz admitted elsewhere, the assumption that molecular forces are affected in a moving body in a way similar to the way electromagnetic forces change around a moving body was by no means unquestionable. He called it ‘bold’ (Dutch: ‘ gewaagd ’, Reference Lorentz 1892 : 78), admitted that ‘we really have no reason’ to suppose it (‘ wozu freilich kein Grund vorliegt’ , Reference Lorentz 1895 : §92), and thought it ‘cannot in itself be pronounced to be either plausible or inadmissible’, Reference Lorentz 1904b : 825).

In The Theory of Electrons ( Reference Lorentz 1915 ) Lorentz seems very much aware that this assumption is on shaky grounds:

We can understand the possibility of the assumed change of dimensions, if we keep in mind that the form of a solid body depends on the forces between its molecules, and that, in all probability, these forces are propagated by the intervening ether in a way more or less resembling that in which electromagnetic actions are transmitted through this medium. From this point of view, it is natural to suppose that, just like the electromagnetic forces the molecular attractions and repulsions are somewhat modified by a translation imparted to the body, and this may very well result in a change of its dimensions. ( Reference Lorentz 1915 : 201–2)

Notice how cautious Lorentz expresses himself: ‘in all probability’, ‘more or less resembling’, ‘it is natural to suppose’, and ‘may very well’. Moreover, the assumption that molecular forces behave similarly to electromagnetic forces is not the only assumption Lorentz makes to derive the LFC. According to one count, Lorentz's explanatory backing of the LFC contains at least eleven additional hypotheses. For a paper dealing with fundamental physics ‘it is veritably obsessed with making hypotheses’ (Holton Reference Holton 1960 : 630).

It is fair to say that Lorentz was not completely convinced by his own solution. In the concluding remarks of The Theory of Electrons ( Reference Lorentz 1915 ) he contrasts his overall solution with Einstein's theory of relativity: ‘Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily , from the fundamental equations of the electromagnetic field’ ( Reference Lorentz 1915 : 230, my italics).

The LFC provided a diagnosis of the null result of Michelson and Morley, but it lacked a satisfactory explanatory backing. Lorentz tried to provide such a backing by deriving the LFC from the Maxwell equations using certain assumptions about the electron. But the backing that Lorentz gave depended on at least one assumption for which there was at best an analogical argument: the idea that molecular forces are affected in a moving body similar to the way electromagnetic forces change around a moving body. Moreover, everyone in the scientific community, including Lorentz, demanded a solution that diagnosed the problem and was backed by a satisfactory explanation. The best explanation that Lorentz was able to give was, however, not fully satisfactory. Hence, the LFC was an ad hoc solution in the sense defined by (Ad Hoc).

4. Concluding Remarks

When an otherwise successful theory is confronted with an empirical anomaly, a paradox, a vicious infinite regress, or some other defect, one may always change the theory to solve the problem. But not every solution is an improvement, and degenerative solutions are often called ‘ad hoc’. A good definition of ‘ad hoc solution’ should help explain why, despite solving more problems than the original theory, the new theory is no improvement. I have argued that the answer lies in its explanatory failure: ad hoc solutions do not diagnose the problem or are not backed up by an explanation. Since a theory should not merely list facts or solve problems but also provide explanations, ad hoc solutions go against the raison d’être of a theory. We thus eschew ad hoc solutions for more than merely aesthetic reasons ( pace Hunt Reference Hunt 2012 ).

My analysis of ad hoc solution applies to all fields of rational inquiry insofar as these fields aim to provide explanations. This is an advantage over other accounts of ad hoccery, which all focus on ad hoc hypotheses that answer to empirical anomalies. Still, other definitions of ad hoccery can supplement (Ad Hoc). (Thanks to a reviewer for this journal for suggesting this to me.) (Ad Hoc) does not detail when a diagnosis or explanation is not good enough. Here Leplin's ( Reference Leplin 1975 ) discussion about ad hoccery might be useful: it may be that the explanation is no good because it fails to be fundamental or because it cannot be generalized. Or one might agree with Schindler ( Reference Schindler 2018 ) that a good explanation must cohere with relevant background theories to be satisfactory.

This also shows that (Ad Hoc) can explain why there are so many different definitions of ‘ad hoc hypothesis’ in the philosophy of science: because there are competing notions of what a good scientific explanation looks like. For example, Popper famously held that a good scientific explanation is falsifiable. It is no wonder, then, that he considered lack of testability—that is, nonfalsifiability—a cornerstone of ad hoccery. Similarly, those who think good explanations are generalizable will likely consider ungeneralizable solutions ad hoc.

Because explanation is what distinguishes ad hoc solutions from genuine solutions, we should thus investigate explanations to gain a better understanding of ad hoccery. Given the current interest in explanation—both in the philosophy of science (Lange Reference Lange 2016 ; Lipton Reference Lipton 2004 ; Reutlinger and Saatsi Reference Reutlinger and Saatsi 2018 ; Woodward Reference Woodward 2003 ) and in metaphysics (Correia and Schnieder Reference Correia and Schnieder 2012 ; Kment Reference Kment 2014 ; Ruben Reference Ruben 2012 )—our understanding of ad hoccery is bound to grow in the foreseeable future.

I am grateful to the Swedish Research Council (Vetenskapsrådet International Postdoc Grant 2017-06160_3) and the Dutch Research Council (NWO grant VI.Veni.201F.006 ‘The Whole Explanation, Part by Part’) for funding my research. This paper was presented at the Higher Seminar in Lund in 2021: thanks to the audience for their constructive feedback. Thanks also to Chris Daly, Hein van den Berg, Ylwa Sjölin Wirling, and three anonymous reviewers for this journal for comments on a previous draft of this paper. Finally, I am especially grateful to David Liggins for the many entertaining and enlightening discussions we had on ad hoccery and for his extensive comments on multiple versions of this paper.

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Ad hoc Hypothesis

Ad hoc hypothesis denotes a supplementary hypothesis given to a theory to prevent it from being refuted. According to Karl Popper’s philosophy of science, the only way that falsifiable intellectual systems like Marxism and Freudianism have been sustained is through the dependence on ad hoc hypotheses to fill gaps. Ad hoc hypotheses are used to account for abnormalities that the theory’s unaltered form could not foresee.

Explanation

Ad hoc theories are only acceptable if and only if their non-universal, precise nature can be shown, or, to put it another way, if their potential for direct generalization is disproven. It is the hypothesis that is embraced without any other justification in order to save a theory from refutations or criticism. This technique is deployed in sociological research studies.

The derivation of the particular conclusion in an issue may be deemed invalid if an ad hoc hypothesis was proven to be acceptable and non-universal; as a result, the specific example loses its scientific significance. The necessity of repeat testing is implied in the aforementioned working rule for the acceptance of ad hoc hypotheses, which makes this process seem all the more justifiable.

Notably, the system seems to be in question whenever the introduction of an ad hoc hypothesis is required until the acceptability of the ad hoc hypothesis appears to be established by the requisite falsification attempts. The restriction of ad hoc hypotheses and the continuity principle appear to guarantee the objectivity of falsification; in other words, a theory should only be regarded as falsified if its falsification is theoretically testable.

In addition, because it gives a preferential position to a critical evaluation or falsification, this principle of restriction serves as, in a sense, the second part of the working definition for the idea of a theoretical system’s falsification. Ad hoc hypotheses can be used to attempt to prevent falsification based on the continuity principle, but this can only be done if a different hypothesis, the generalized ad hoc hypothesis (which is also subject to the continuity principle), can also be refuted. Therefore, avoiding falsification depends on (yet another) deception. 

The first falsification will take effect if the second one is unsuccessful. This methodological constraint, or the concept of the restriction of ad hoc hypothesis, has effectively eliminated the “conventionalist argument to falsifiability.” The argument that this system is, in theory, not falsifiable has been demonstrated to be inconsistent (via the principle of the restriction of ad hoc hypotheses) provided that a system enables the derivation of empirically verifiable consequences in the first place.

Since the non-falsifiability of any hypothesis (even a generalized ad hoc hypothesis) would necessitate the falsifiability of other hypotheses, this principle gives a workable definition of the term “falsification” (that is, the falsification of the original axiomatic system). This is obviously inconsistent.

The ad hoc hypothesis “This (otherwise accurate) watch showed the wrong time under such and such circumstances” is only a valid ad hoc hypothesis if the universal statement “All (otherwise accurate) watches show the wrong time under such and such circumstances” can be shown to be false, or refuted, by counterexamples.

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ad hoc hypothesis

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Hypothesis adopted purely for the purpose of saving a theory from difficulty or refutation, but without any independent rationale.

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Ad Hoc Analysis

An ad hoc analysis is an extra type of hypothesis added to the results of an experiment to try to explain away contrary evidence.

This article is a part of the guide:

• Significance 2
• Sample Size
• Experimental Probability
• Cronbach’s Alpha
• Systematic Error

Browse Full Outline

• 1 Inferential Statistics
• 2.1 Bayesian Probability
• 3.1.1 Significance 2
• 3.2 Significant Results
• 3.3 Sample Size
• 3.4 Margin of Error
• 3.5.1 Random Error
• 3.5.2 Systematic Error
• 3.5.3 Data Dredging
• 3.5.4 Ad Hoc Analysis
• 3.5.5 Regression Toward the Mean
• 4.1 P-Value
• 4.2 Effect Size
• 5.1 Philosophy of Statistics
• 6.1.1 Reliability 2
• 6.2 Cronbach’s Alpha

The scientific method dictates that, if a hypothesis is rejected, then that is final. The research needs to be redesigned or refined before the hypothesis can be tested again.

Amongst pseudo-scientists, an ad hoc hypothesis is often appended, in an attempt to justify why the expected results were not obtained.

An often quoted example of an ad hoc analysis is of a paranormal investigator investigating psychic waves, under scientific conditions. Upon finding that the experiment did not give positive results, they blame the negative brain waves given out by others.

The oft-quoted example of an ad hoc analysis is of a paranormal investigator investigating psychic waves, under scientific conditions. Upon finding that the experiment did not give positive results, they blame the negative brain waves given out by others.

This is simply trying to deflect criticism and failure by throwing out other, completely random reasons. This ad hoc analysis would need the brain waves of the onlookers to be also tested and eliminated, moving the goalpost and creating a fallacy.

The idea of biorhythms, where the body and mind are affected by deep and regular cycles unrelated to biological circadian rhythms, has long been viewed with skepticism. Every time that scientific research debunks the theory, the adherents move the goal posts, inventing some other underlying reason to explain the results.

Often, astrologers presented with contrary evidence will blame the results upon some ‘unknown’ astrological phenomenon. This, of course, is impossible to prove and so the ad hoc analysis conveniently removes the pseudo-science from the debate.

The insanely stupid Water4Gas scam works along the same principles – when researchers pointed out that the whole idea revolves around the principle of perpetual motion, they invented another ad hoc hypothesis to explain where the ‘money saving’ energy came from.

Ad hoc analysis is not always a bad thing, and can often be part of the process of refining research.

Imagine, for example, that a research group was conducting an experiment into water turbulence, but kept receiving strange results, disproving their hypothesis. Whilst attempting to eliminate any potential confounding variables, they discover that the air conditioning unit is faulty, transmitting vibrations through the lab. This is switched off when the experiment is running and they retest the hypothesis.

This is part of the normal scientific process, and is part of refining the research design rather than trying to move the goalposts.

Ad hoc analysis is only a problem when a non-testable ad hoc hypothesis is added to the results to justify failure and deflect criticisms.

The air conditioning unit hypothesis can be tested very easily, simply by switching it off, and was a result of experimental flaw. Negative brainwaves cannot be easily tested, and therefore the deflection causes a fallacy.

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Martyn Shuttleworth (Nov 17, 2008). Ad Hoc Analysis. Retrieved Aug 28, 2024 from Explorable.com: https://explorable.com/ad-hoc-analysis

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Ad hoc hypothesis.

An ad hoc hypothesis is one created to explain away facts that seem to refute one’s belief or theory. Ad hoc hypotheses are common in paranormal research and in the work of pseudoscientists . For example, ESP researchers have been known to blame the hostile thoughts of onlookers for unconsciously influencing pointer readings on sensitive instruments. The hostile vibes, they say, made it impossible for them to duplicate a positive ESP experiment. Being able to duplicate an experiment is essential to confirming its validity. Of course, if this objection is taken seriously, then no experiment on ESP can ever fail. Whatever the results, one can always say they were caused by paranormal psychic forces, either the ones being tested or others not being tested.

Martin Gardner reports on this type of ad hoc hypothesizing reaching a ludicrous peak with paraphysicist Helmut Schmidt who put cockroaches in a box where they could give themselves electric shocks. One would assume that cockroaches do not like to be shocked and would give themselves shocks at a chance rate or less, if cockroaches can learn from experience. The cockroaches gave themselves more electric shocks than predicted by chance. Schmidt concluded that "because he hated cockroaches, maybe it was his pk that influenced the randomizer!" (Gardner, p. 59)

Ad hoc hypotheses are common in defense of the pseudoscientific theory known as biorhythm theory . For example, there are very many people who do not fit the predicted patterns of biorhythm theory. Rather than accept this fact as refuting evidence of the theory, a new category of people is created: the arrhythmic. In short, whenever the theory does not seem to work, the contrary evidence is systematically discounted. Advocates of biorhythm theory claimed that the theory could be used to accurately predict the sex of unborn children. However, W. S. Bainbridge, a professor of sociology at the University of Washington, demonstrated that the chance of predicting the sex of an unborn child using biorhythms was  50/50, the same as flipping a coin. An expert in biorhythms tried unsuccessfully to predict accurately the sexes of the children in Bainbridge's study based on Bainbridge's data. The expert's spouse suggested to Bainbridge an interesting ad hoc hypothesis, namely, that the cases where the theory was wrong probably included many homosexuals with indeterminate sex identities!

Astrologers are often fond of using statistical data and analysis to impress us with the scientific nature of astrology . Of course, a scientific analysis of the statistical data does not always pan out for the astrologer. In those cases, the astrologer can make the data fit the astrological paradigm by the ad hoc hypothesis that those who do not fit the mold have other, unknown influences that counteract the influence of the dominant planets.

Using ad hoc hypotheses is not limited to pseudoscientists. Another type of ad hoc hypothesis occurs in science when a new scientific theory is proposed which conflicts with an established theory and which lacks an essential explanatory mechanism. An ad hoc hypothesis is proposed to explain what the new theory cannot explain. For example, when Wegener proposed his theory of continental drift he could not explain how continents move. It was suggested that gravity was the force behind the movement of continents, though there was no scientific evidence for this notion. In fact, scientists could and did show that gravity was too weak a force to account for the movement of continents. Alexis du Toit, a defender of Wegener's theory, argued for radioactive melting of the ocean floor at continental borders as the mechanism by which continents might move. Stephen Jay Gould noted that "this ad hoc hypothesis added no increment of plausibility to Wegener's speculation." (Gould, p. 160)

Finally, rejecting explanations that require belief in occult, supernatural or paranormal forces in favor of simpler and more plausible explanations is called applying Occam's razor. It is not the same as ad hoc hypothesizing. For example, let's say I catch you stealing a watch from a shop. You say you did not steal it. I ask you to empty your pockets. You agree and pull out a watch. I say, "Aha!, I was right. You stole the watch." You reply that you did not steal the watch, but you admit that it was not in your pocket when we went into the store. I ask you to explain how the watch got into your pocket and you say that you used telekinesis: you used your thoughts to transport the watch out of a glass case into your pocket. I ask you to repeat the act with another watch and you say "ok." Try as you will, however, you cannot make a watch magically appear in your pocket. You say that there is too much pressure on you to perform or that there are too many bad vibes in the air for you to work your powers. You have offered an ad hoc hypothesis to explain away what looks like a good refutation of your claim. My hypothesis that the watch is in your pocket because you stole it, is not an ad hoc hypothesis. I have chosen to believe a plausible explanation rather than an implausible one. Likewise, given the choice between believing that my headache went away of its own accord or that it went away because some nurse waved her hands over my hand while chanting a mantra, I will opt for the former every time.

It is always more reasonable to apply Occam's razor than to offer speculative ad hoc hypotheses just to maintain the possibility of something supernatural or paranormal.

See also cold reading , communal reinforcement, control study, Occam's razor, placebo effect , post hoc fallacy , selective thinking , self-deception, subjective validation , testimonial evidence, and wishful thinking.

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Unnatural Acts: ad hoc hypothesis

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What is the Problem of Ad Hoc Hypotheses?

• Published: July 1999
• Volume 8 , pages 375–386, ( 1999 )

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The received view of an ad hochypothesis is that it accounts for only the observation(s) it was designed to account for, and so non-ad hocness is generally held to be necessary or important for an introduced hypothesis or modification to a theory. Attempts by Popper and several others to convincingly explicate this view, however, prove to be unsuccessful or of doubtful value, and familiar and firmer criteria for evaluating the hypotheses or modified theories so classified are characteristically available. These points are obscured largely because the received view fails to adequately separate psychology from methodology or to recognise ambiguities in the use of 'ad hoc_'.

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Ad Hoc Hypotheses and the Monsters Within

Bayesian inference for psychology. part i: theoretical advantages and practical ramifications.

The Replacement for Hypothesis Testing

Asimov, I.: 1975, Eyes on the Universe: A History of the Telescope , Houghton Mifflin, Boston.

Google Scholar  

Bamford, G.S.: 1989, Popper, Refutation, and 'Avoidance' of Refutation , Ph.D. thesis, The University of Queensland, Brisbane.

Bamford, G.S.: 1993, 'Popper's Explications of Ad Hoc ness: Circularity, Empirical Content, and Scientific Practice', The British Journal for the Philosophy of Science 44 , 335–55.

Bamford, G.S.: 1996, 'Popper and his Commentators on the Discovery of Neptune: A Close Shave for the Law of Gravitation?', Studies in History and Philosophy of Science 27 (2), 207–32.

Chalmers, A.F.: 1982, What is This Thing Called Science: An Assessment of the Nature and Status of Science and its Methods? (second edition), University of Queensland Press, St. Lucia, Queensland.

Drake, S.: 1957, Introduction to Discoveries and Opinions of Galileo , by Galileo, trans. S. Drake, Anchor Books, New York.

Drake, S.: 1978, Galileo at Work: His Scientific Biography , University of Chicago Press, Chicago.

Fetzer, J.H. and Almeder, R.F.: 1993, s.v. 'Ad hoc/ad hocness/ad hoc hypotheses', Glossary of Epistemology/Philosophy of Science , Paragon House, New York.

Galileo, G.: 1929–39, Le Opere di Galileo Galilei , 20 vols. in 21, vol. 11, Barbera, Firenze.

Gillies, D.: 1990, 'Bayesianism Versus Falsificationism', Ratio (New Series) III , 82–98.

Grant, R.: 1966, History of Physical Astronomy , The Sources of Science, no. 38, Johnson Reprint Corporation, New York.

Grosser, M.: 1962, The Discovery of Neptune , Harvard University Press, Cambridge, Mass.

Grünbaum, A.: 1976, ' Ad Hoc Auxiliary Hypotheses and Falsificationism', The British Journal for the Philosophy of Science 27 , 329–62.

Hempel, C.G.: 1966, Philosophy of Natural Science , Foundations of Philosophy Series, Prentice Hall, Englewood Cliffs, N.J.

Holton, G.: 1969, 'Einstein, Michelson, and the Crucial Experiment', Isis 60 (Summer), 133–97.

Howson, C. and Urbach, P.: 1989, Scientific Reasoning: The Bayesian Approach , Open Court, La Salle, Illinois.

Klüber, H. von.: 1960, 'The Determination of Einstein's Light Deflection in the Gravitational Field of the Sun', in A. Beer (ed.), Vistas in Astronomy 3 , Pergamon Press, London, 47–77.

Lakatos, I.: 1970, 'Falsification and the Methodology of Scientific Research Programmes'. In I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge , Cambridge University Press, Cambridge, 91–195.

Laudan, L.: 1977, Progress and its Problems: Towards a Theory of Scientific Growth , University of California Press, Berkeley.

Leplin, J.: 1982, 'The Assessment of Auxiliary Hypotheses', The British Journal for the Philosophy of Science 33 , 235–49.

Mason, S.F.: 1956, Main Currents of Scientific Thought: A History of the Sciences , Routledge and Kegan Paul, London.

Maxwell, G.C.: 1974, 'Corroboration without Demarcation', in Schilpp (ed.), 292–321.

Miller, D.W.: 1981, s.v. ' Ad-Hoc Hypotheses', in W. Bynum, E. Browne and R. Porter (eds.), Dictionary of the History of Science , Princeton University Press, Princeton.

Musgrave, A.E.: 1973, 'Falsification and its Critics', in P. Suppes, L. Henkin, A. Joga, and Gr. Moisil (eds.), Logic, Methodology and Philosophy of Science IV: Proceedings of the Fourth International Congress for Logic, Methodology, and Philosophy of Science, Bucharest, 1971 , North Holland Publishing Co., Amsterdam, 393–406.

Musgrave, A.E.: 1974, 'Logical versus Historical Theories of Confirmation', The British Journal for the Philosophy of Science 25 , 1–23.

Musgrave, A.E.: 1976, 'Method or Madness? Can the Methodology of Scientific Research Programmes be Rescued from Epistemological Anarchism?', in R. Cohen, P. Feyerabend, and M. Wartofsky (eds.), Essays in Memory of Imre Lakatos , Boston Studies in the Philosophy of Science, vol. 39, D. Reidel, Dordrecht, 457–91.

Musgrave, A.E.: 1978, 'Evidential Support, Falsification, Heuristics, and Anarchism'. In G. Radnitzky and G. Andersson (eds.), Progress and Rationality in Science , Boston Studies in the Philosophy of Science, vol. 58, D. Reidel, Dordrecht, 181–201.

Newcomb, S.: 1929, 'Discordances in the Secular Variations of the Inner Planets', in H. Shapely and H. Howarth (eds.), A Source Book in Astronomy , Source Books in the History of Science, McGraw Hill, New York, 330–38.

Newcomb, S.: 1911, 'Neptune', Encyclopedia Britannica (eleventh edition), vol. XIX, Cambridge University Press, Cambridge, 385–87.

Popper, K.R.: 1972, Conjectures and Refutations: The Growth of Scientific Knowledge (fourth revised edition), Routledge and Kegan Paul, London.

Popper, K.R.: 1974, 'Replies to My Critics', in Schilpp (ed.), 961–1197.

Popper, K.R.: 1975, The Logic of Scientific Discovery (eighth impression), Hutchinson and Co., London.

Popper, K.R.: 1976, Unended Quest: An Intellectual Autobiography , Fontana/Collins, London.

Quine, W.V. and Ullian, J.S.: 1980, 'Hypothesis', in E. Klemke, R. Hollinger and A. Kline (eds.), Introductory Readings in the Philosophy of Science , Prometheus Books, New York, 196–206.

Radnitzky, G.: 1981, 'Progress and Rationality in Research', in M. Grmek, R. Cohen and G. Cimino (eds.), On Scientific Discovery: The Erice Lectures 1977 , D. Reidel, Dordrecht, 43–102.

Salmon, W.C.: 1990, 'Rationality and Objectivity in Science, or Tom Kuhn Meets Tom Bayes', in C. Savage (ed.), Scientific Theories , Minnesota Studies in the Philosophy of Science, vol. 14, University of Minneapolis Press, Minneapolis, 175–204.

Schilpp, P.A. (ed.), 1974, The Philosophy of Karl Popper , The Library of Living Philosophers, vol. 14, Open Court, La Salle, Illinois.

Schlesinger, G.: 1987, 'Accommodation and Prediction', Australasian Journal of Philosophy 65 , 33–42.

Sprott, W.F.: 1936, 'Review of A Dynamical Theory of Personality ', by K. Lewin, Mind 45 , 246–51.

Sutton, C.: 1992, Spaceship Neutrino , Cambridge University Press, Cambridge.

The Shorter Oxford English Dictionary: 1973, s.v. 'ad hoc', (third revised edition).

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• Published: 28 August 2024

Structural basis of frizzled 7 activation and allosteric regulation

• Julien Bous   ORCID: orcid.org/0000-0002-3459-7592 1   na1 ,
• Julia Kinsolving   ORCID: orcid.org/0000-0002-0431-8222 1   na1 ,
• Lukas Grätz   ORCID: orcid.org/0000-0001-6755-0742 1 ,
• Magdalena M. Scharf   ORCID: orcid.org/0000-0002-3305-3956 1 ,
• Jan Hendrik Voss   ORCID: orcid.org/0000-0003-0595-4607 1 ,
• Berkay Selcuk   ORCID: orcid.org/0000-0003-3206-4749 2   nAff3 ,
• Ogün Adebali   ORCID: orcid.org/0000-0001-9213-4070 2 &
• Gunnar Schulte   ORCID: orcid.org/0000-0002-2700-7013 1  

Nature Communications volume  15 , Article number:  7422 ( 2024 ) Cite this article

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• Cryoelectron microscopy
• G protein-coupled receptors
• Receptor pharmacology

Frizzleds (ten paralogs: FZD 1-10 ) belong to the class F of G protein-coupled receptors (GPCRs), which remains poorly understood despite its crucial role in multiple key biological functions including embryonic development, stem cell regulation, and homeostasis in the adult. FZD 7 , one of the most studied members of the family, is more specifically involved in the migration of mesendoderm cells during the development and renewal of intestinal stem cells in adults. Moreover, FZD 7 has been highlighted for its involvement in tumor development predominantly in the gastrointestinal tract. This study reports the structure of inactive FZD 7 , without any stabilizing mutations, determined by cryo-electron microscopy (cryo-EM) at 1.9 Å resolution. We characterize a fluctuating water pocket in the core of the receptor important for FZD 7 dynamics. Molecular dynamics simulations are used to investigate the temporal distribution of those water molecules and their importance for potential conformational changes in FZD 7 . Moreover, we identify lipids interacting with the receptor core and a conserved cholesterol-binding site, which displays a key role in FZD 7 association with a transducer protein, Disheveled (DVL), and initiation of downstream signaling and signalosome formation.

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Structural insight into small molecule action on Frizzleds

Pathway selectivity in Frizzleds is achieved by conserved micro-switches defining pathway-determining, active conformations

Structural insights into Frizzled3 through nanobody modulators

Introduction.

G protein-coupled receptors (GPCRs) represent the main family of signaling membrane proteins in the animal reign. They are thoroughly studied given their critical involvement in multiple key biological processes, diseases, and their potential as drug targets. The most extensively studied GPCR classes, A, B, and C, contain conserved motifs, allosteric sodium binding sites, and cholesterol-binding sites as well as an intricate network of waters that define the dynamic conformational landscape of the receptor. In the case of Frizzleds (ten paralogs: FZD 1-10 ) that are class F GPCRs, these features remain to be elucidated 1 , 2 , 3 , 4 , 5 , 6 . FZDs are involved in multiple signaling pathways including heterotrimeric G protein-dependent signaling 7 , 8 , Disheveled-dependent planar cell polarity (PCP) 9 , and Wnt/β-catenin signaling pathways 10 leading to variable cellular outputs 10 .

FZD 7 in particular is involved in mesendodermal stem cell differentiation 11 , mesendoderm migration 12 , and plays a crucial role in driving the turnover of the adult intestinal epithelium 13 . In this context, it is important for mediating pathogenic effects of Clostridioides difficile toxin B (TcdB) and its entry in colonic epithelial cells, thereby relevant for therapeutic perspectives 14 . Furthermore, FZD 7 is upregulated in multiple cancers 15 and plays a central role in several aspects of oncogenesis including tumor proliferation, metastasis, maintenance of cancer stem cells, and chemoresistance 16 , 17 . In colorectal cancer, FZD 7 is highly expressed in cell lines with APC or CTNNB1 mutations, and siRNA-mediated knockdown of FZD 7 significantly decreases cell viability and invasion activity of HCT-116 cells in vitro 16 . Thus, FZD 7 is an attractive drug target for tumor therapy 18 . Nonetheless, a better overall understanding of FZDs represents a necessary step to efficiently develop potential drugs targeting those receptors preferentially with paralog-selectivity to reduce the risk for unwanted side effects.

A thorough structural understanding of FZDs and underlying mechanisms of receptor activation is directly correlated to the quantity and quality of structural information available for distinct states. Advances in membrane protein purification, cryogenic electron microscopy (cryo-EM), and data processing have notably accelerated the release of GPCR structures in recent years from the first cryo-EM structure of GPCR-G protein complexes published in 2017 19 , 20 to the current large quantity of active GPCR structures ( https://gpcrdb.org/ ). Nonetheless, there are only a few structures including information about the transmembrane domains (TM)s of FZDs 8 , 21 , 22 , 23 . The organization of FZDs spanning different conformations and complexes as well as underlying mechanisms of activation, remain to be properly understood.

Here, we apply state-of-the-art cryo-EM to elucidate the apo structure of FZD 7 with an overall resolution of 1.9 Å (FSC 0.143). We took advantage of this high-resolution structure to improve the previously published FZD 7 -Gs protein model 8 and provide a direct comparison of G protein-bound and apo state of FZD 7 . Moreover, the cryo-EM map quality of the inactive FZD 7 is sufficient to identify an internal water pocket comparable to the previously reported water pockets for class A and B GPCRs 24 , 25 , 26 , 27 . We further studied water involvement in FZD 7 dynamics and activation by molecular dynamics (MD) simulations. In addition, we identified a conserved cholesterol-binding site involving W 4.50 (Ballesteros–Weinstein numbering), which relates to recent findings reporting on the involvement of cholesterol in FZD-dependent WNT/β-catenin signaling and potential dysregulation in a pathologic context 28 , 29 .

We probed the importance of this cholesterol-binding site in signaling by employing a combination of site-directed mutagenesis and bioluminescence resonance energy transfer (BRET)-based pharmacological assays. In parallel, we used a sophisticated phylogenetic analysis highlighting the family-wide importance and conservation of regions and residues of interest unraveled by the structural analysis, and notably established that the cholesterol-binding site and the water cavity base represent conserved features in the FZD family.

The overall organization of FZD 7 in its inactive conformation

The sequence of wild type FZD 7 with the addition of a Hemagglutinin signal peptide and a double Strep tag was cloned in a pFastBac vector and expressed in Sf9 insect cells. The receptor was purified as described in ref.  14 . In brief, Sf9 pellets were solubilized in LMNG, and FZD 7 was further purified by a combination of Strep tag and size exclusion chromatography (SEC) (Superdex 200 increase) (Supplementary Fig.  1a ). The fractions corresponding to the FZD 7 dimer were subjected to cryo-EM analysis (Supplementary Fig.  1b–f , Supplementary Table  1 ). FZD 7 forms an artificial antiparallel dimer with C 2 symmetry (Fig.  1a–b ). The interface involves TM3-6 and is stabilized by a layer of lipidic aliphatic chains and introduced cholesterol hemisuccinate (CHS), which renders the antiparallel dimer remarkably stable (Fig.  1b , Supplementary Fig.  2 ). While the density of the aliphatic chains is of poor quality, implying variability and/or a dynamic nature, the high-quality map of CHS1 suggests the presence of a distinct high affinity cholesterol-binding site, while CHS2 displays an intermediate density quality (Supplementary Fig.  2 ). The CRD of FZD 7 , part of the linker domain (M1 CRD -A205 linker ), ICL3 (T452 5.74 -K463 6.25 ), and the C terminus (S565 8.62 -V574 C-ter ) were not visible in the density due to flexibility. The FZD 7 dimer displays features reminiscent of inactive GPCRs with an inward TM6 position and a densely packed bundle of TMs similar to previously published inactive structures of FZD 1 , FZD 3 , FZD 4 , FZD 5 and FZD 6 (Fig.  1c Supplementary Fig.  3a ) 8 , 21 , 22 , 23 . The overall position of TM6, however, is closer to TM7 than the structures containing a BRIL in ICL3 (Supplementary Fig.  3b ), suggesting that the addition of BRIL fused to TM5 and TM6 by a rigid linker distorts the bottom of TM5-6.

a Cryo-EM density map of the FZD 7 dimer with C 2 symmetry, colored by monomer, with an intermolecular layer of lipids sandwiched between the monomers, shown in red. b Atomic arrangement of the FZD 7 dimer shown with a close-up side view of the compact interface presenting with endogenous 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) and two major cholesterol hemisuccinate (CHS) molecules, which altogether mediate and stabilize the interface between the monomers. c Overall organization of the extracellular region of FZD 7 with ECL1, ECL2, ECL3, and the hinge region which altogether form a peripheral lid over the transmembrane bundle. d A top view of the helical bundle depicts the folded β-stranded structure of ECL2 with K533 7.41 and Y534 7.42 rendering blockage of the receptor core. e Map of the surface electrostatic potential of the internal cavity highlighting the bottleneck in modulating entry of water molecules.

The extracellular loop (ECL2) of FZD 7 forms a β-turn partially obstructing the access to the receptor core similarly to other class F receptors (Fig.  1d ) 21 . Furthermore, the two bulky residues K533 7.41 and Y534 7.42 contribute to obstructing access to the core cavity. Despite these structural elements forming a bottleneck, there is a clear connection between the extracellular side and the core cavity of FZD 7 allowing the exchange of water between the two compartments (Fig.  1e ). FZD 7 includes a hydrophilic internal cavity (volume 1277Å 3 calculated with CavitOmiX; v. 1.1.beta, 2024, Innophore GmbH) that adopts a bent shape, protruding deep into the receptor core, adapted to the presence of an internal water network important for receptor stability and potentially involved in conformational rearrangements and receptor dynamics (Fig.  1e ). ECL1 (E310-E334), ECL3 (V513-P525), and the hinge (F206-Y244) adopt an organized conformation forming the peripheral lid (Fig.  1c ). The overall organization of this peripheral lid is variable between the different class F GPCRs (Supplementary Fig.  3a ). FZD 1,3,6 and FZD 7 adopt a similar overall organization with (i) a long extension of TM6 above the lipid bilayer like SMO and (ii) a shorter ECL2 that points downward, compared to SMO, where the loop points upward and interacts with the SMO CRD potentially impacting the allosteric cooperation during SMO activation 21 , 30 . The downward orientation of the FZD 7 ECL3 is dictated by a disulfide bridge (C508 6.70 -C515 ECL3 ) between the top of TM6 and the ECL3, similar to FZD 1,3,6 and consistent with the previous hypothesis that the distribution of cysteine residues mediates the cap organization with potential impact on receptor cell surface expression, signaling profiles and receptor specificity 21 , 31 (Fig.  1c ). In comparison, FZD 4 features a shorter extension of the TM6 helix, and a shorter hinge that adopts a different peripheral lid organization and FZD 5 adopts an intermediate conformation with a slightly shorter TM6 extension compared to FZD 1,3,6,7 and an intermediate hinge size (Supplementary Fig.  3a ).

FZD 7 -Gs protein coupling elicits limited conformational rearrangements

A direct comparison of inactive FZD 7 and the amended FZD 7 -Gs protein structure 8 allowed us to investigate the conformational rearrangements involved in constitutive FZD 7 activation (G protein coupling) with an unprecedented level of detail generally confirming the previously proposed FZD-G protein coupling mechanism 7 , 23 , 32 . Additionally, we elaborated on a hypothesis suggesting that the limited dynamics of TM6 in FZDs explain the relatively poor G protein coupling capacity of FZDs compared to other GPCR classes.

The unliganded FZD 7 -Gs protein complex presents with a limited outward motion of TM6, a slight inward motion of TM1,2,5 and TM7/H8 upon G protein α5 helix coupling to the intracellular core of the receptor (Fig.  2d , Supplementary Movie  1 ). The extracellular side of FZD 7 maintains the same overall organization in the absence of an agonist irrespective of the receptor’s activation status. A kink of the conserved P481 6.43 occurs in TM6 (Fig.  2a ) along with a rearrangement of a set of residues previously described as the molecular switch R 6.32 -W 7.55 (Fig.  2f ) 7 and the extended molecular switch 32 W354 3.43 –Y478 6.40 (Fig.  2e ) interact by π-π stacking with W354 3.43 pointing towards TM5 in the inactive state and towards TM7 in the active state (Fig.  2e ). The FZD 7 W354 3.43 rotamer flip upon G protein coupling is not observed in the FZD 1,3,9 structures 23 . The molecular switch R470 6.32 -W547 7.55 is characterized by the combination of a cation-π interaction and a hydrogen bond (between R470 6.32 guanidine group and W547 7.55 backbone carbonyl oxygen) tightly regulating TM6 opening. In this context, G protein coupling promotes TM6 opening with a rotamer flip of W547 7.55 without fully disrupting the interaction but rather extending it (Fig.  2f ). This reorganization is accompanied by a rotamer change of nearby F474 6.36 (Fig.  2b ).

The intracellular rearrangements of conserved residue a P481 6.43 , b extended molecular switch residues, F474 6.36 - W547 6.36 , e Y478 6.40 and f molecular switch residues W547 7.55 - R470 6.32 are observed upon agonist binding. c A network of extended polar contacts in ICL3 is made between the two conformations of FZD 7 . d Comparison of the nucleotide-free Gα s -bound FZD 7 (pink, PDB: 7EVW) and inactive FZD 7 (purple) highlighting structural changes of conserved residues and regions of interest. g G protein binding rearranges residues in ICL1 involving D278 1.57 , F282, R281, R280, and M279. Scatterplot of occurring χ1 χ2 dihedral angles of residue h W354 3.43 and i W547 7.55 calculated for each frame (50 ps time steps) over the trajectory from replica 1 of FZD 7 simulations of active and inactive state.

Previously reported class F GPCRs structures display variability in terms of R/K 6.32 -W 7.55 side chain positioning in both active and inactive states resulting in great variability in R/K 6.32 -W 7.55 cation-π interaction, ranging from strong interactions to very weak or negligible interactions (Supplementary Table  2 ). Nonetheless in all structures reported so far R/K 6.32 can accommodate either cation-π interactions with W 7.55 or hydrogen bonds with W 7.55 or the carbonyl oxygen of T 7.54 , W 7.55 , W 7.57 (Supplementary Table  2 ), supporting that the molecular switch can undergo drastic conformational changes while preserving TM6/TM7 contacts, thereby regulating and limiting TM6 opening.

For FZD 7 , to investigate further the dynamics of these two sets of residues (W354 3.43 –Y478 6.40 and R470 6.32 -W547 7.55 ) and the possibility of transient rotamer switches as the main switch mechanism driving FZD activation, we subjected FZD 7 in its active and inactive conformation derived from the experimental structures to MD simulations for 300 ns with 3 replicates. Throughout the entire simulations, the respective active and inactive states remain consistent, as evidenced by the TM2-TM6 distances and the TM6 kink observed across all replicates. (Supplementary Figs.  4a–d , 5a , Supplementary Table  3 ). The dihedral angles of the rotamers W354 3.43 and W547 7.55 show a distinct monodispersed profile in the active versus inactive conformation (Fig.  2h, i , Supplementary Figs.  5b, c ), suggesting a permanent switch of the two upon heterotrimeric G protein coupling.

G protein coupling also induces rearrangement of ICL1,3, whereas ICL2 maintains the same organization (Fig.  2c, g ). ICL1 (D278 1.57 S283 12.51 ) adopts a loose conformation in the inactive FZD 7 structure and rearranges into a more compact conformation in the G protein-coupled complex (Fig.  2g ). TM5,6 are extended from R451 5.73 to D457 ICL3 and K466 6.28 to E462 6.24 in the G protein bound FZD 7 state, allowing D457 ICL3 , T459 ICL3 and, K463 ICL3 to make polar contacts with G s α 5 helix (Fig.  2c ).

The mechanisms of TM6 opening are finely regulated among GPCRs with different mechanisms for the different classes. For example, in class A GPCRs a set of shared motifs throughout the transmembrane section rearrange upon agonist stimulation notably inducing a kink of P 6.50 (25° for the β 2 adrenergic receptor (β 2 AR) PDB:3SN6 (active) PDB:6PS3 (inactive)) provoking a disruption of the ionic lock (consensus motif involving the TM3 D/ERY motif (comprising D/E 3.49 , R 3.50 , and Y 3.51 ) and TM2 (for example T68 2.39 for β 2 AR) or TM6 (A 6.34 , E 6.30 ), involved in controlling the opening of the intracellular segment of TM6 (12 Å for β 2 AR) (Fig.  3a ). The ionic lock is permanently disrupted upon receptor activation 33 . In class B1 GPCRs, sequential peptide and G protein binding induces α helix disruption in TM6 and the formation of a sharp kink (70° for the Glucagon receptor (GCGR) PDB:5XEZ (inactive) PDB:6WPW (active)) with a large outward motion (18 Å for GCGR), leading to a breakage of the conserved polar network R 2.46b , R/K 6.37b , N 7.61b and Q 8.41b (Fig.  3b ) 19 . Similarly, other GPCR classes feature their own structural mechanisms regulating TM6 opening 34 , 35 , 36 . Interestingly, the difference in TM6 dynamics between class A (β 2 AR) (Fig.  3a ) and class B1 GCGR (Fig.  3b ) GPCRs is correlated to their respective efficacy to couple to and activate the heterotrimeric G protein with GCGR exhibiting a substantially lower guanine nucleotide exchange activity 37 . This gap in efficacy is due to the higher energy barrier between the active and inactive state for GCGR.

The dynamic nature of TM6 in GPCRs between the inactive and active conformations are shown in a class A, β 2 AR (PDB: 6PS3, 3SN6), b class B, GCGR (PDB: 5XEZ and 6WPW) and c class F, FZD 7 (PDB: 9EPO, 7EVW). d The molecular switch in class F, R 6.32 -W 7.55 acts as a hinge limiter restricting the swing out of TM6.

In the case of FZDs, the molecular switch R 6.32 -W 7.55 acts as a hinge limiter (Fig.  3c, d ) permitting only a restricted TM6 opening (11°, 5.5 Å). Hence, the open conformation of FZDs remains suboptimal for G protein coupling providing a rational explanation for the limited capacity of FZDs to couple to heterotrimeric G proteins and their propensity to display selectivity towards DVL over heterotrimeric G proteins 5 . Interestingly, R/K 6.32 is frequently mutated in cancers with obvious consequences on TM6 dynamics, eventually impacting receptor signaling profiles. FZD 6 , R 6.32 A, R 6.32 Q, and W 7.55 L lose the ability to recruit DVL efficiently confirming the potential to favor a specific signaling pathway in a conformational-dependent manner in cancers 7 .

The structure of FZD 7 contains an internal water pocket that does not rearrange into a channel upon G protein coupling

The internal cavity of FZD 7 can be divided into two sections separated by a bottleneck (Fig.  1e ). The bottleneck is formed by a set of residues D405 ECL1 , L415 ECL1 , Y489 6.51 , K533 7.41 , Y534 7.42 (Fig.  4a, b ) leaving a sufficient opening to allow water exchange (minimum diameter 4 Å).

a Overall organization of the internal water pocket of inactive FZD 7 . b The region of the cavity referred to as the bottleneck is comprised of the following residues: L415 ECL1 , D405 ECL1 , Y489 6.51 , Y534 7.42 , and K533 7.41 . c Phylogenetic analysis of FZD 7 depicting highly conserved and interacting residue pairs involved in the internal water pocket. d , e , f The tight base of the internal water cavity facilitates a reorientation of residues W354 3.43 , Y478 6.40 , Y296 2.51 , and V540 7.48 in the d inactive conformation and e active conformation. f A top view of the transmembrane domains between the two structures highlighting residues of interest.

The different FZD structures display variable internal pockets (Supplementary Fig.  3c ). For example, the structures of inactive FZD 4,5 contain continuous cavities protruding into the receptor core to a similar depth compared to FZD 7 . FZD 4 features a straight pocket due to the less extended peripheral lid 22 and the FZD 5 pocket adopts the same overall bent shape as the one in FZD 7 .

The extracellular sections of FZD 1,3,6 display a denser packing with a disruption of the cavity preventing potential water exchange between the internal cavity and the extracellular environment. In the case of FZD 1 this is mainly due to the different positioning of the internal side chain network, notably obstructing the bottleneck section. Direct contact between the internal cavity and the extracellular side might still open up upon side-chain reorganization in a physiological context. In the case of FZD 3,6 , the side chains of the Y362 ECL2 (FZD 6 ) and Y366 ECL2 (FZD 3 ) block the pocket entrance. In FZD 7 , however, the corresponding but less bulky S407 ECL2 (FZD 7 ) does not obstruct the internal cavity. Furthermore, because of a different hinge folding compared to the one of FZD 7 , H181 hinge (FZD 3 ) and Y173 hinge (FZD 6 ) also participate in sealing the cavity entrance in FZD 3,6 .

The high-quality data of our FZD 7 structure allowed us to model and characterize an extensive, internal water network in the FZD 7 core (Fig.  4a , Supplementary Fig.  6a, b ), similar to the one that plays a crucial role in the folding and dynamics of class A GPCRs 24 , 25 . The water network in FZD 7 integrally fills the internal cavity, making a large number of polar contacts with inward-facing residues, (Fig.  4a , Supplementary Fig.  6a, b ) highlighting its importance in overall structure integrity.

To investigate whether this internal water network is indeed relevant to receptor activation as a conserved, family-wide mechanism, we used an approach combining phylogenetic and structural analyzes. We identified functionally equivalent orthologs (214 on average for each subfamily, 215 for FZD 7 ) for all human class F receptors to determine residues with high class-wide conservation (see Methods). To understand the involvement of conserved residues in receptor activation, we utilized the Residue-Residue Contact Score (RRCS) algorithm (see Methods) 25 . Changes were identified in the contact score (ΔRRCS) in the transition from inactive to G protein-coupled, active FZD 7 focusing on residue pairs that define G protein coupling-mediated reorganization. Lastly, we highlighted a subsection of the activation network that is spatially close to water molecules within the provided receptor structure, and identified C 1.43 , Y 2.51 , W 3.43 , V 3.44 , G 5.58 , Y 6.40 , P 6.43 , M 7.44 and V 7.48 at the base of the water pocket (Fig.  4c ). Additionally, this network consisting of water-interacting residues is immediately connected to the class-wide conserved switch residues W 7.55 and F 6.36 that are crucial for receptor activation as we mentioned previously. With validation from the experimental FZD 7 structures, C 1.43 , Y 2.51 , W 3.43 , V 3.44 , G 5.58 , Y 6.40 and V 7.48 form a solid base in both G protein-coupled, active and inactive FZD structures and prevent drastic reorganization of internal water networks upon G protein coupling, unlike what is observed in class A GPCRs 24 , 25 . This solid base notably includes W354 3.43 and Y478 6.40 presenting a part of the extended molecular switch involved in FZD activation 32 . Due to its tight packing this layer represents a structural hub between TM1-3,5-7 partially mediating the overall bundle organization with the potential to tolerate limited motion of the transmembrane domains while maintaining a similar organization of the extracellular side of FZD 7 (Fig.  4d–f ; Supplementary Movie  2 ).

It is also noteworthy that the structural phylogenetic analysis indicates SMO lacks the conserved molecular mechanism found in FZDs (Fig.  4c ). The difference in conservation of residues between FZDs and SMO in the receptor core creates a basis for the different activation mechanism observed between FZDs and SMO despite their evolutionary relatedness.

Dynamics of the internal water pocket in FZD 7

To further characterize the role of the internal water network in G protein coupling, we analyzed the temporal distribution of waters in the internal pocket of FZD 7 in both the active and inactive conformation by MD simulations. Most water positions attributed to the inactive structure are present in the simulation with variable occupancy (Fig.  5a ). The water density maps with an occupancy threshold of 20% show that the entire pocket is occupied and continuously filled with water (Fig.  5b,c ), without significant depth differences between active and inactive conformations in agreement with the respective internal pockets of the experimental structures. The TM6 outward motion allows intracellular water to occupy a shallow groove in the cavity normally occupied by the α5 helix of the heterotrimeric G protein, but the solid water pocket base remains tight preventing water exchange with the upper cavity (Fig.  5b, c ). To investigate the dynamics of the water pocket further, we examined how minor rearrangements in the side chain orientation could further restrict the bottleneck, as seen in the FZD 1 apo structure 23 . We investigated the distances between atoms of key residues of the bottleneck (L415 ECL2 -K533 7.41 and D405 ECL2 - L415 ECL2 ) to better understand this process and to probe the dynamics of the bottleneck (Fig.  5f , Supplementary Figs.  7a–c ). Independent of the activation state, the bottleneck adopts two major sub-conformations (Fig.  5d–f ). In the first conformation, the bottleneck forms a tight ring transiently disrupting the cavity and opening with slight side chain conformational changes (Fig.  5d ). The second conformational state shows a reorganization of the ECL2 with side chain reorientation of D405 ECL2 and L415 ECL2 , causing a pocket disruption upward towards the bottleneck position (Fig.  5e ). These two states are transient and were observed in both active G protein-bound and inactive state-derived simulations (Supplementary Figs.  7b,c ; active replicate 3 and inactive replicate 1). While these variations of the extracellular section of the receptor are not directly related to G protein coupling, they might play an important role in other signaling events, such as FZD-DVL coupling or agonist stimulation, which remain structurally characterized.

a The occupancy and location of water molecules attributed to the internal water pocket with green depicting high occupancy and red depicting low occupancy during molecular dynamics simulations of the inactive FZD 7 . Volumetric map for water molecules calculated for 20% occupancy with inactive b (blue density) and c active FZD 7 (purple density). d Key residues in the bottleneck region for the first conformation (transient bottleneck closing) with a volumetric map of the bottleneck residues computed with a threshold of 20% occupancy (blue density). e The second conformation represents a reorganization of ECL2 (disruption) with a volumetric map of the bottleneck residues that was computed with a threshold of 20% occupancy (brown density). f Distance calculations between L415 ECL2 /CD2 and K533 7.41 /NZ depict the two transient conformations shown in ( d turquoise) and ( e orange) over the course of 6000 frames of the MD simulations.

A conserved and functionally important cholesterol-binding site in FZDs

While the structural analysis revealed a well-defined cholesterol-binding site in FZD 7 , we also took a structure-independent computational approach that only utilizes the evolutionary information to determine if a cholesterol-binding pocket is conserved in this family (Fig.  6a ). Similar to the water network analysis, we calculated residue conservation for all class F receptors (Fig.  6a , Supplementary Fig.  8a, b ). We identified residues that are conserved within paralogs with no sequence variation or variation with only similar amino acids (BLOSUM80 score greater than 2). We hypothesized that a set of conserved and structurally continuous amino acids on the receptor surface is associated with cholesterol binding. We could only identify a single region strongly enriched in conserved aromatic residues (Fig.  6a ). Upon projection of those residues onto a receptor structure (Fig.  6a ), we observed that residues at the receptor surface were exclusively enriched at the structurally identified cholesterol-binding-site. This exclusive enrichment highlights the importance of cholesterol binding at this conserved site not only for FZD 7 but for all class F GPCRs. Our analysis revealed five aromatic residues constituting a binding surface for cholesterol. While residues W 4.50 , H 4.46 and F 3.35 are fully conserved, the positions F/Y 2.46 and F/Y 3.34 are conserved in their aromatic nature in all class F receptors. Thus, the results from the class-wide phylogenetic analysis are in agreement with the structural analysis pinpointing five conserved, aromatic residues at the receptor surface between TM2-4 that coincide with the cholesterol-binding site observed in the FZD 7 structure.

a A phylogenetic analysis was performed across class F GPCRs where highly conserved residues involved in cholesterol binding were identified. Fully conserved residues are colored in dark red and residues with similar conservation are colored in yellow. b Overview of the cryo-EM pipeline from data collection to model building and structural characterization of the cholesterol-binding site. c Based on the structural analysis, site-directed mutagenesis of cholesterol-interacting residues was performed and then used for analysis of functional downstream readouts of transducer coupling and signaling. Figure  6 was created with BioRender.com released under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International license.

Cholesterol-binding motifs in membrane proteins have been extensively studied 38 . Notably, the cholesterol recognition/interaction amino acid consensus sequence (CRAC) domain 39 , and cholesterol consensus motifs (CCMs) are present in class A GPCRs 40 . The class A CCMs and the highly conserved cholesterol-binding site found in FZDs share the same position when projected on the overall topology of the receptor (between TM3 and TM4). Additionally, W 4.50 , which participates in cholesterol-π stacking within the class A CCMs, is also conserved in class F GPCRs. Unlike conventional class A CCMs, the FZD cholesterol-binding site is heavily enriched in aromatic residues emphasizing a strong potential for cholesterol-π stacking compensation mechanism, suggesting a peculiar functional importance for cholesterol in FZDs. While cholesterol is important for folding and stabilization in class A GPCRs, we hypothesize that cholesterol-mediated receptor stabilization presents a conserved feature of FZDs and that cholesterol plays a role in receptor activation and signaling.

FZD 7 -binding cholesterol is critical for transducer association and signaling

Therefore, we structurally identified three residues that hydrophobically interact with cholesterol: F345 3.34 , H382 4.46 , and W386 4.50 (Figs.  6a and  7a, b ). To better understand the functional implications of these interactions, we generated mutants where two of these three interacting residues were mutated to alanine (for a disruption of cholesterol-π (CH-π) contacts) (Figs.  6c and 7a, b ). A NanoBiT-based approach was developed based on a C-terminally SmBiT-tagged receptor (FZD 7 -SmBiT or β 2 -SmBiT) and a membrane-tethered LgBiT construct (FLAG-LgBiT-CAAX), which allows to selectively detect the fraction of receptors located at the plasma membrane without assay interference originating from intracellular, potentially immature receptors (Supplementary Fig.  9b, c ). All generated mutants were validated for proper cell surface expression prior to probing function (Supplementary Fig.  9d–i ).

a Organization of the inactive FZD 7 monomer with the cholesterol (CHS; green) binding site. b Analysis of the cholesterol-binding site reveals various interacting residues of which three were mutated for functional studies; F345 3.34 , H382 4.46 , and W386 4.50 . c Gα s translocation assay showing BRET2 ratios of ΔFZD 1-10 HEK293T cells transiently transfected with rGFP-CAAX and G \({{\rm{\alpha }}}\) S −67- R lucII, with either negative control (pcDNA), wild type FZD 7 , or the indicated FZD 7 mutants normalized to conditions with pcDNA. Data are presented as means ± SEM of normalized BRET2 ratios from three independent experiments. (** p  < 0.001, one-way ANOVA followed by Tukey’s multiple comparison). d A NanoBiT-based DEP recruitment BRET assay was performed with FZD 7 -SmBiT, its respective cholesterol-binding site mutants, and β 2 AR-SmBiT as a control in HEK293A cells. For functional reconstitution of Nluc, membrane-anchored FLAG-LgBiT-CAAX was cotransfected. Data are presented in triplicates of three independent experiments with baseline-corrected BRET values based on conditions with 0% DEP-Venus. Data represent superimposed datapoints from three (FZD 7 wt and β 2 ) to four (FZD 7 mutants) independent experiments, each performed in triplicate. Error bars in both x and y directions represent SD e ΔFZD 1-10 HEK293T cells were transfected with Renilla (Rluc), the Super 8x TOPFlash reporter, and wild type FZD 7 , or the indicated mutants. Cells were stimulated with 300 ng/mL of recombinant WNT-3A overnight. Data are presented as Fluc/Rluc ratios, normalized to the respective vehicle control, from three independent experiments performed in triplicates analyzed using one-way ANOVA (Dunnett post hoc test) (** p 0.01, * p  < 0.05). Data are presented as means ± SEM (error bars) from three independent experiments performed in triplicate.

The double mutants, F345 3.34 A-H382 4.46 A and F345 3.34 A-W386 4.50 A (Fig.  7a, b ) were expressed at the cell surface level and adapted to our assay sensitivity (Supplementary Figs.  9c–i ). We examined heterotrimeric G protein activation by employing the previously published Gα s translocation assay (Supplementary Fig.  9a ) 8 . Using pcDNA as control, we quantified the BRET between membrane-tethered rGFP-CAAX and Gα s -67- R luc in ΔFZD 1-10 cells expressing FZD 7 . Interestingly, the FZD 7 double mutants showed similar levels of constitutive activity towards G s compared to wild type FZD 7 highlighting the double mutant’s full capability to functionally activate G s in a ligand-independent manner (Fig.  7c ).

FZD 7 drives epithelial renewal by mediating WNT/β-catenin signaling, which is intrinsically dependent on the scaffold protein DVL. DVL interacts with FZDs through their DEP domain and serves as a hub for signalosome formation and signal initiation 13 , 41 .

To further explore the mode of action of cholesterol on FZD 7 , we tested the functionality of the mutants in a direct BRET assay monitoring Venus-DEP recruitment to FZD 7 . Here, Venus served as the BRET acceptor and the wild type or mutant FZDs were C terminally tagged with SmBiT and served as the BRET donors (Supplementary Fig.  9b ). The double mutants completely abrogated FZD 7 -DEP recruitment, suggesting that cholesterol plays a key role in constitutive DVL recruitment by FZDs (Fig.  7d ).

Furthermore, previous studies link WNT/β-catenin signaling to cholesterol 42 , and suggest a direct link between dysregulation of cholesterol in the plasma membrane and aberrant WNT signaling 28 . Based on these findings, we ran a set of luminescence-based assays probing β-catenin-mediated regulation of T-cell factor/lymphoid enhancer factor (TCF/LEF) gene transcription (TOPFlash) to validate the impact of the mutations in the cholesterol-binding site of FZD 7 on WNT/β-catenin signaling. The F345 3.34 A-H382 4.46 A and F345 3.34 A-W386 4.50 A double mutations in FZD 7 reduced the WNT-3A-induced TOPFlash signal compared to wild type FZD 7 , which is in line with their dramatically reduced ability to recruit DEP (Fig.  7e ). These findings reveal a distinct mode of interaction between G protein and DVL with FZD, where cholesterol association to FZD is crucial for FZD-DVL interaction, while it is not required for constitutive G protein coupling.

Our results present high-resolution, structural insight into FZD 7 and the combination of cryo-EM structure, MD simulations, and phylogenetic analysis allows to draw FZD family-wide conclusions on structural aspects and mechanisms of FZD activation. These data are complemented with experiments employing genetically encoded biosensors to functionally validate our structural findings. This integrative approach provides us with information to understand FZD 7 function in particular and FZDs in general. The direct comparison between G protein-coupled and unbound FZD 7 highlights that the conserved molecular switch (R/K 6.32 -W 7.55 ) reported to be important for class F GPCR activation 7 , 23 , 32 is rearranged upon G protein association acting as hinge limiter, likely governing class F signaling. P 6.43 allows the TM6 to kink similarly to what is observed in class A GPCRs where the helix bend is accomplished by P 4.50 kink mediating G protein association 23 , 32 . In that regard FZDs differ from SMO, which lacks the proline and accommodates G protein association through parallel outward shift of TM6 instead of a kink. While it is now well established that FZDs are binding and activating heterotrimeric G proteins 7 , 8 , systematic analysis of FZD mutants have unraveled that they tend to prefer DVL over G protein coupling suggesting that distinct conformational substates define transducer selectivity 5 . Interestingly, mutations affecting the molecular switch of FZD 6 , specifically R 6.32 A and R 6.32 Q/L, with R 6.32 Q/L being naturally occurring cancer mutants of FZD 6 , show impaired recruitment of DVL. However, they enhance WNT-induced recruitment of miniG proteins to FZDs. This suggests that the positioning and dynamics of TM6-7 tightly regulate selectivity in coupling to DVL versus G protein 7 .

Beyond validation of conformational changes upon transducer coupling, we shed light on two understudied receptor features, receptor-associated water molecules and cholesterol. The internal water pocket of the receptor and its plasticity highlight its potential for receptor dynamics on the extracellular side that could play a central role in agonist-induced allosteric conformational changes. This aspect is also mentioned in the reported structure of FZD 4 22 , but there are only a few structural waters identified in the electron density map, and the bottom of the pocket featured four non-attributed ions that are not present in the FZD 7 structure. Additionally, the identification of a conserved, tight layer of residues forming the base of the internal pocket that maintains the same organization upon G protein association suggests that constitutive G protein coupling is not sufficient to propagate bidirectional allostery from the bottom to the top of the receptor in the absence of an agonist. Nonetheless, agonist stimulation of FZDs triggers a conformational change on the intracellular, transducer binding site of the receptor as shown both for G proteins as well as DVL 43 indicating that WNT-CRD interaction elicits conformational dynamics that are transferred to the transducer interaction site in an allosteric manner. This concept is further supported by diverse assessments of FZD dynamics such as the WNT-induced FZD-CRD dynamics 44 as well as agonist-induced FZD conformational changes 3 , 45 . On a structural level, however, it remains to be elucidated how WNT stimulation of FZDs elicits full receptor activation and what conformational rearrangements are induced and required to promote DVL over G protein signaling.

We also identified a conserved cholesterol-binding site across class F GPCRs. In class A GPCRs cholesterol is mostly associated with structural stabilization 46 but can also be involved in signaling, as for example in the case of GPR161, where mutations that prevent cholesterol binding suppress G s -mediated signaling, whereas other pathways remain unaffected 47 .

In the case of SMO, cholesterol displays an agonist effect to mediate Hedgehog signaling. In this context, cholesterol targets internal binding sites and has been proposed to navigate in a narrow channel stretching from the bottom of TM5,6 to the receptor core/CRD to initiate receptor activation 48 , 49 .

Previously, it was shown by a cholesterol-bead pulldown assay that cholesterol interacts with FZD 5 but not with other FZDs. Based on FZD 5 deletion mutants, the linker domain between the CRD and the FZD core was suggested to be involved in cholesterol binding and to affect FZD 5 function allosterically, for example in the context of pancreatic cancer 29 . These data stand in contrast to our findings regarding both the FZD paralog selectivity and the location of the cholesterol-binding site. However, the overall functional consequences of cholesterol on FZD maturation and signaling are similar since the cholesterol-site mutants of FZD 7 present with reduced DEP recruitment, reduced TOPFlash signal and reduced surface expression, translating to reduced ability to signal along the WNT/β-catenin pathway and impaired receptor maturation.

In conclusion, we provide a high-resolution structure of FZD 7 that allows family-wide conclusions on a FZD-specific receptor activation mechanism. Receptor activation comes along with a TM6 swing out at the same time as the molecular switch mechanism involving R/K 6.32 and W 7.55 acts as a hinge limiter dependent on the rotamer flip of W 7.55 . This discovery defines a common mechanism of FZD activation providing a molecular explanation for the transducer selectivity of FZDs preferring DVL over G protein coupling. Furthermore, the high quality of our cryo-EM structure provided deeper insight into the dynamics of receptor-associated water molecules and a conserved, allosteric cholesterol-binding site that regulates DVL over G protein coupling. Both receptor-associated waters and the allosteric cholesterol site might open avenues for targeting FZDs pharmacologically by allosteric, small molecule compounds.

Figure preparation

Figures were designed using Pymol Molecular Graphics System (Schrödinger LLC) (v. 2.5) including the plugin CavitOmiX (v. 1.1.beta, 2024, Innophore GmbH); matplotlib (3.8.3), GraphPad Prism 10 (GraphPad Prism Software Inc.); ChimeraX (v. 1.5); VMD (v1.9.4.a55); biorender.com.

Cells lines

HEK293A, (Thermofisher scientific)/R70507. ΔFZD 1-10 HEK293T cells were kindly provided by Benoit Vanhollebeke. Spodoptera frugiperda (Sf9) insect cells (#11496015) are from Thermo Scientific.

FZD 7 expression & purification

The full-length sequence of human FZD 7 was prepared from a HiBiT-FZD 7 construct (Addgene #195845) and cloned into a pFastBac1 vector containing a FLAG tag at the N-terminal, a 3 C cleavage site, and a Twin-Strep-tag® inserted on the C-terminal via Gibson cloning 50 . FZD 7 was expressed in Spodoptera frugiperda (Sf9) insect cells using the Bac-to-Bac baculovirus expression system (Thermo Fisher Scientific). Insect cells were grown in suspension in EX-CELL 420 Serum-free medium to a density of 2 × 10 6 cells/ml and infected with recombinant baculovirus at a 1:50 v/v ratio. After culturing for approximately 48–54 h at 28 °C, cells were harvested by centrifugation and pellets were stored at −80 °C until use.

For the purification of FZD 7 , cell pellets were thawed and lysed in buffer containing 10 mM TRIS-HCl pH 7.5, 100 mM NaCl, 1 mM EDTA, and protease inhibitors [leupeptin (5 µg/mL) (Sigma Aldrich), benzamidine (10 µg/mL) (Sigma) and phenylmethylsulfonyl (PMSF) (10 µg/mL) (Sigma Aldrich)]. After centrifugation (15 min at 3000 g), the pellet containing crude membranes was homogenized using a glass Dounce tissue grinder (10 strokes using A pestle then 20 strokes using B pestle) in a solubilization buffer containing 50 mM TRIS-HCl pH 8, 200 mM NaCl, 1% LMNG (Anatrace), 0.1% CHS (Sigma Aldrich), 0.1% GDN (Anatrace), iodacetamide (2 mg/mL) (Anatrace), and protease inhibitors. The mixture was stirred for 1.25 h at 4 °C and centrifuged (20 min at 38,400 g). The cleared supernatant was incubated with Strep-Tactin resin (IBA) for 2 h at 4 °C. The resin was washed with 10 column volumes (CV) of a buffer containing 50 mM TRIS-HCl pH 7.5, 500 mM NaCl, 0.02% lauryl maltose neopentyl glycol (LMNG), 0.002% cholesterol hemisuccinate tris salt (CHS), and 0.002% glycol-diosgenin (GDN). The resin was then washed with 15 column volumes (CV) of 50 mM TRIS-HCl pH 7.5, 100 mM NaCl, 0.02% LMNG, 0.002% CHS, and 0.002% GDN. FZD 7 was eluted in the same buffer supplemented with 2.5 mM desthiobiotin (IBA) and samples corresponding to the dimeric protein peaks ( ~ 8 mL) were concentrated in a 50-kDa molecular weight cutoff (MWCO) concentrator (Millipore) to 3.68 mg/mL.

After concentration, FZD 7 was loaded onto a size-exclusion chromatography column (SEC) (Superdex 200 Increase 10/300 GL, GE Healthcare) equilibrated with a buffer containing 10 mM TRIS-HCl pH 7.5, 100 mM NaCl, 0.002% LMNG, 0.0002% CHS, and 0.0002% GDN. Peak fractions corresponding to the dimeric receptor were flash-frozen and stored at −80 °C until further use.

Cryo-EM sample preparation and image acquisition

The purified FZD 7 -dimer fractions from the SEC were pooled and concentrated to 3.08 mg/mL (45 µM) in a 100-kDa MWCO concentrator. Montelukast was added at a molar ratio of 1:2 prior to grid freezing, however no small molecule was observed in the dataset. Next, a 3 µL sample was applied on glow-discharged (20 mA, 40 s.) UltrAuFoil R 1.2/1.3 300-mesh copper holey carbon grids (QuantiFoil, Micro Tools GmbH, Germany), blotted for 3.5 s, then flash-frozen in liquid ethane using Vitrobot Mark IV (Thermo Fisher Scientific). Images were collected on a Titan Krios G3i operating at 300 kV at the 3D-EM facility at Karolinska Institutet. Micrographs were recorded using a Gatan K3 detector in super-resolution mode using EPU software (v. 2.14.0). A total of 21,081 movies were obtained at a magnification of 165,000 corresponding to a 0.5076 Å calibrated pixel size and exposure dose of 80 e/Å 2 with defocus ranging from −0.6 µm to 2.0 µm (Supplementary Fig.  1 ).

Cryo-EM data processing

Data processing for FZD 7 -dimer was processed using cryoSPARC (v4.2-v4.4) 51 , 52 . Movie frames were aligned using Patch Motion Correction and Contrast Transfer Function (CTF) parameters were estimated by Patch CTF correction. Particle picking was performed by automatic Gaussian blob detection (mask diameter = 160 with elliptical and circular blob) yielding particles that were then subjected to reference-free 2D classifications (classes = 100, mask diameter = 160). Particles were extracted in a box size of 162 Å and downscaled to 2 Å/pixel. Iterative 2D classifications allowed the selection of 1,555,782 particles that were used as references to train a model with Topaz, a positive-unlabeled convolutional neural network for particle picking 53 . Topaz picked 7,332,734 particles that were used for further 2D classification. Particles were selected from the best 2D class averages (3,268,658 particles) and launched into 2 rounds of ab-initio model reconstructions (C 1 ) with 6 classes. Particles from the best class were reextracted with a pixel size of 0.6768 Å for further refinement. After NU-refinement with C 2 symmetry, the subset was subjected to global CTF refinement corrections for high order aberrations iterative refinement followed by two rounds of ab-initio model reconstructions (C 1 ) with two classes, ending up with a curated set of 105,380 particles. After NU-refinement, the final set was subjected to global CTF refinement corrections, reference-based motion correction, and then to a final NU-Refinement (C 2 ) yielding a map with 1.94 Å overall resolution (FSC 0.143) (Supplementary Fig.  1 ).

Model building

Initially, the FZD 7 –mG s (PDB: 7EVW) complex was used as a starting point for modeling. We first corrected the initial deposited model. To correct the model, we used the following tools including manual inspection and adjustments in Coot (0.9); global model refinement and relaxation in Rosetta (2022.45+release.20a5bfe), and global minimization with Phenix (1.20.1-4487) real-space refinement.

To build the inactive FZD 7 model, we started from the model of the FZD 7 –mG s complex, extracted the receptor chain and applied the same strategy combining manual inspection and adjustments in Coot (0.9); global model refinement and relaxation in Rosetta, and global minimization with Phenix real space refinement. Overall statistics of the two final models are summarized (Supplementary Table  1 ).

Plasmids and molecular cloning

The plasmid encoding DEP-Venus has been described previously 43 . Plasmids encoding Gα s −67- R lucII and rGFP-CAAX were kindly provided by Prof. Michel Bouvier (IRIC, Université de Montréal, Canada). The TOPFlash reporter gene plasmid was from Addgene (#12456) and the plasmid for the constitutively expressed Renilla luciferase (pRL-TK) was from Promega.

C-terminally SmBiT-tagged receptor constructs (FZD 7 -SmBiT, β 2 -SmBiT) were generated in multiple steps. In the first step, the C-terminal Nluc tag in HA-FZD 5 -Nluc 5 was exchanged with a SmBiT tag (resulting in HA-FZD 5 -SmBiT) using the Q5 Site-Directed Mutagenesis Kit (New England Biolabs) according to the manufacturer’s instructions. In a second step, the sequence for FZD 5 in HA-FZD 5 -SmBiT was replaced with the nucleotide sequence for FZD 7 (amplified from HiBiT-FZD 7 50 and the β 2 -adrenergic receptor (amplified from FLAG-SNAP-β 2 (kind gift from Davide Calebiro, University of Birmingham) via Gibson Assembly. Receptor mutants for FZD 7 were generated in the FZD 7 -SmBiT backbone using the GeneArt Site-Directed Mutagenesis Kit (ThermoFisher) according to the manufacturer’s instructions.

The membrane-anchored LgBiT construct (FLAG-LgBiT-CAAX) was generated based on DEP-Venus-kRas 43 via Gibson Assembly. The N-terminal FLAG tag was attached during the PCR by being implemented in the oligo design.

Generated plasmids were verified by Sanger Sequencing (Eurofins Genomics). A list containing all primers used to generate plasmids can be found in (Supplementary Table  4 ).

Cell culture and transfection

HEK293A (human embryonic kidney cells) and ΔFZD 1-10 HEK293T cells were used to functionally assess FZD 7 and the respective mutants with a various panel of biosensors. Cells were grown in Dulbecco’s Modified Eagle’s Medium (DMEM) supplemented with 2 mM glutamine, 10% fetal calf serum, 0.1 mg/mL streptomycin, and 100 units/mL penicillin and stored at 37 °C with 5% CO 2 . Whenever indicated, cells were transfected in suspension with 1 µg of total DNA per mL cell suspension using linear polyethyleneimine (PEI Max, Polysciences Inc., stock concentration: 1 mg/mL) at a PEI:DNA ratio of 3:1. Transfected plasmid amounts indicated below always refer to the amount of transfected DNA per mL cell suspension.

Confocal microscopy

HEK293A cells were seeded on a four-chamber 35 mm dish (ibidi, #80416) precoated with poly-D-lysine (PDL, Sigma Aldrich, #A3890401) at a density of 35,000 cells per quarter. The following day, cells were transfected with either FLAG-LgBiT-CAAX or empty pcDNA3.1 (negative control). After 24 h of incubation, cells were washed with PBS ( + MgCl 2 , CaCl 2 , Gibco #14080048, from now on only “PBS”), fixed with 4% paraformaldehyde (in PBS) and permeabilized using 0.25% Triton X-100 (ThermoFisher, #T8787) in PBS. After three washing steps with PBS, samples were blocked for 2 h with PBTA (1% bovine serum albumin (BSA), 0.05% Triton X-100 and 0.02% NaN 3 in PBS) and incubated overnight with anti-FLAG M2 antibody (Sigma Aldrich, #F1804, 1:1000 in PBTA) at 4 °C. After four washing steps with PBS and another blocking step for 30 min using PBTA, samples were incubated with a polyclonal goat anti-mouse secondary antibody (Alexa Fluor 488-conjugated, Invitrogen, #A28175, 1:1000 in PBTA) for 2 h at room temperature. Cells were washed four times with PBS, nuclei were counterstained with Hoechst 33342 (1 µg/mL) and cells were imaged in 0.1% BSA/HBSS using a Zeiss LSM800 confocal microscope.

DEP recruitment assay

For DEP recruitment assays, 20 ng of FZD 7 -SmBiT or 40 ng of FZD 7 -SmBiT (mutants) or 20 ng of β 2 -SmBiT (negative control) were transfected together with 300 ng of FLAG-LgBiT-CAAX and varying amounts of DEP-Venus (between 0 ng and 400 ng) into HEK293A cells (300,000 cells/mL, ad 1 µg DNA per mL cell suspension with pcDNA3.1). To assess the robustness of the assay setup with respect to variation in receptor membrane expression, a different set of experiments was performed using FZD 7 -SmBiT wt in a range between 1 ng and 20 ng (Supplementary Figs.  8e-i ). 100 μL/well of the transfected cells were seeded into PDL-coated, white 96-well plates. Cells were incubated for 48 h at 37 °C (with 5% CO 2 ) in a humidified incubator. Experiments were carried out using a TECAN Spark microplate reader. Cells were washed once with HBSS and maintained in 90 µL of HBSS. First, Venus fluorescence was measured (excitation 485/20 nm; emission 535/25 nm) followed by the addition of 10 μl of coelenterazine h (Biosynth, C-7004, final concentration: 5 μM final). After five minutes of incubation, Nanoluc (Nluc) luminescence (filtered between 445 and 485 nm) and the sensitized Venus emission (filtered between 520 and 560 nm) were detected. At least three independent experiments were conducted, and all conditions were run in triplicates. For data analysis, raw BRET/fluorescence was corrected by subtraction of the average value of the corresponding titration with 0% DEP-Venus. Net BRET data from the DEP recruitment assay were fitted using a one-site-specific binding equation that yielded BRET 50 and BRET max values. The corresponding BRET 50 values were log normalized to indicate a normal distribution. The plot of BRET max values over luminescence was fit using linear regression. Titration experiments were plotted and analyzed using GraphPad Prism 10 (GraphPad Prism Software Inc.).

Gα s translocation assay

For the Gα s translocation assay, cells were transfected with 500 ng of the control plasmid, pcDNA3.1 (pcDNA) or FZD 7 -wt (SmBiT-FZD 7 ) and its respective mutants, 25 ng Gα s −67- R lucII, 300 ng rGFP-CAAX, and supplemented with pcDNA to yield 1 ug total DNA/mL cell suspension. Cells were mixed with the transfection reagent and 100 µL were seeded onto PDL-coated 96-well plates. Transfected cells were grown for 48 h at 37 °C with 5% CO 2 and washed once with HBSS. The substrate, coelenterazine 400a, was prepared at a final concentration of 2.5 µM and added to each well. Following incubation for 5 min, constitutive receptor activity was measured in a Tecan spark plate reader. R lucII emission intensity was quantified using a 400/40 monochromator and rGFP emission using a 540/35 monochromator with an integration time of 50 ms in both channels. The BRET2 ratio was defined as acceptor emission/donor emission or rGFP/ R lucII and fitted using a simple linear regression in Prism 5.0 software (GraphPad, San Diego, CA, USA). The BRET2 ratio was normalized to pcDNA levels and analyzed with one-way ANOVA and Tukey’s multiple comparison post hoc test. Data are represented as means ± SEM from three independent experiments performed in triplicates (** p  < 0.001).

TOPFlash luciferase assay

ΔFZD 1-10 cells HEK293 (450,000 cells/mL) were transfected in suspension with 100 ng of Nluc-FZD 7 , 250 ng of the M50 Super 8x TOPFlash reporter (Addgene #12456) and 50 ng of Renilla luciferase control plasmid (pRL-TK, Promega) per mL cell suspension. The control plasmid, pcDNA, was used to adjust the total transfected DNA amount of 1 µg per mL cell suspension. Cells were seeded (40,000 cells/well) onto a PDL-precoated, white-wall, white-bottomed 96-well microtiter plate (Thermo Fisher Scientific). After 24 h, cells were stimulated with either 300 ng/mL WNT-3A or vehicle control prepared in serum-free DMEM containing 10 nM of the porcupine inhibitor C59 (2-[4-(2-Methylpyridin-4-yl)phenyl]-N-[4-pyridin-3-yl)phenyl]acetamide, Abcam) to block secretion of endogenous WNTs.

About 24 h after stimulation, the Dual Luciferase Assay Kit (Promega, #E1910) was used for the readout. Briefly, cells were lysed with 20 µL of 1× Passive Lysis Buffer for 20 min at room temperature under shaking. Then 20 µL of LARII reagent was added to each well and β-catenin-dependent Fluc bioluminescence was detected using a Spark multimode microplate reader (Tecan, 550–620 nm, integration time: 2 s). Next, 20 µL of 1× Stop-and-Glo reagent was added to each well and Rluc bioluminescence was recorded (445-530 nm, integration time: 2 s) to account for differences in transfection efficiency. TOPFlash ratios were calculated by dividing the Fluc emission (β-catenin-dependent transcriptional activity) by the Rluc emission (indicator for transfection efficiency). Data are presented as means ± SEM from three independent experiments performed in triplicate. The significance level between wt FZD 7 and mutant FZD 7 was assessed by a one-way ANOVA, followed up by Dunnett’s post-hoc test comparing all means to wt FZD 7 , as implemented in GraphPad Prism10.

Molecular dynamic simulations

FZD 7 (G protein bound (PDB:7EVW) and inactive) structures were used as a starting point for initial model generation. For inactive FZD 7 , the sequence between residues 206-563 was used, the ICL3 (452-463) was added and refined in Coot with geometry restraints and without map restraints. For the FZD 7 -mG s model, the sequence between residues 206-563 was used, while the sequence between residues 509 and 525 was added on the base of FZD 7 apo structure and refined in the same manner. A CHS molecule found in the conserved cholesterol-binding site was maintained in the system for both active and inactive FZD 7 and was parametrized using the CHARMM General Force Field and the CHARMM-GUI ligand reader.

The simulation system was generated in CHARMM-GUI bilayer builder from the online server ( CHARMM-GUI ) 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 . CHARMM36 is a standard force field used in molecular dynamics (MD) simulations to model the behavior of biological macromolecules, such as proteins, and is particularly well-suited for simulating membrane protein systems. It has been optimized to work with the TIP3P water model, a simple and widely used model in MD simulations, which represents a water molecule with three interaction sites: one for the oxygen and one for each hydrogen atom. While the simplicity of TIP3P can limit the accuracy of hydrogen bonding representation, more sophisticated models like TIP4P and TIP5P, which offer better representations of water’s dielectric properties and hydrogen-bonding networks, can negatively affect protein behavior by altering the helix/coil equilibrium. Therefore, to ensure optimal simulation of the protein and observe water occupancy in the internal cavity without speculating on potential water-mediated hydrogen bonds, we adopted a conservative approach using the CHARMM36 force field with the TIP3P water model.

The receptors were pre-aligned in pymol (v. 2.5) on 7EVW (reference from Orientations of Proteins in Membranes (OPM) database ( OPM (umich.edu) ) and histidine protonations assignation was done manually in UCSF Chimera (v.1.13). The disulfide bonds: C210-C230; C234-C315; C336-C411; C508-515 were defined in CHARMM-GUI bilayer builder 56 , 64 . The receptors were capped with N-terminal acetyl and C-terminal CT3. A lipid bilayer with 100% palmitoyl-oleoyl-phosphatidylcholine (POPC) was generated and the system was solvated with TIP3 model and completed with 0.15 M Na + and Cl - . Minimization, equilibration and productions runs were performed with the CHARMM36 and CHARMM36m force field in GROMACS(2023-2) 65 .

The systems were first subjected to 5000-step minimization with the steepest descent algorithm integrator. The systems were further equilibrated in six successive steps with an iteratively decreasing force constant for the positional restraints for a total equilibration time of 22 ns and starting from randomly assigned velocities. The first initial two equilibration steps were run as NVT ensemble, before switching to the NPT ensemble for the remainder of the equilibration as well as production runs. Temperature coupling at 310 K was achieved using the v-rescale thermostat, while pressure coupling was achieved using the c-rescale barostat.

For the production runs, without positional restraints, random velocities based on the Boltzmann distribution were assigned to each of the 3 replicates for both systems and unbiased simulations were run for 300 ns with a time step of 2 fs. Hydrogen bonds were constrained using Linear constraints solver (LINCS) 66 and long-range electrostatic interactions were computed using Particle-Mesh Ewald (PME) 67 with 1.2 nm cutoff.

The full production trajectories were analyzed with both AMBER tool CPPTRAJ (V6.4.4) 68 calculating RMSD, dihedral angles and distances, and VMD (v1.9.4.a55) 69 using Volmap tool to compute volumetric maps based on water or residues occupancy. Prior to analysis, the trajectories were centered and aligned on the TMs with the respective software.

All trajectories are deposited on GPCRmd 70 . This simulation investigates fast dynamic events that donʼt require enhanced sampling as supported in similar studies 24 , 71 .

Identification of orthologs of human class F GPCRs

To be able to identify orthologous protein sequences we employed a multi-step pipeline. We used BLAST 72 (BLAST+ version 2.9.0) using the query human sequence of class F GPCRs against the UniProt database (retrieved at 14.07.2021). We fetched all sequences up until the 3 rd human sequence hit and aligned them by using MAFFT FFTNS algorithm 73 . We trimmed the alignment by using clipkit-m kpic-gappy option 74 and generated a quick first tree by using FastTree with default parameters 74 . We retrieved the clade of the query protein by excluding the clades containing the other two human sequences. We realigned the identified subset of sequences and built multiple sequence alignment by using mafft linsi algorithm with maxiterate 1000 option. For tree reconstruction, we performed model selection with IQ-Tree 2 75 . We built trees with RaxML-NG 1.0.3 with the selected model, having removed diverged paralogs by using a previous algorithm described by ref. 76 . The same paralogs were also removed from the multiple sequence alignment to calculate the residue conservation.

Calculation of the residue conservation within orthologs

The most frequently observed amino acid was identified in a certain position with the following considerations: (i) If there is a gap, the residue is labeled as 0 conservation (ii) if it is not a gap, we continue our calculations. We calculated the total count of the most frequent amino acids with the total number of similar amino acid groups defined as the ones having a BLOSUM 80 score of >1. We divided the total number of identical and similar matches by the total number of non-gap positions to calculate the percentage. If the percentage is equal to or greater than 90%, we labeled that position conserved.

Alignment of human class F GPCRs sequences

We clustered the set of unfiltered sequences obtained using 0.65 identity by using cd-hit 77 . For each human receptor, we retrieved 5 representative sequences representing the largest calculated clusters. We aligned human and representative sequences of class F receptors by using mafft linsi algorithm. We removed the representative sequences and all gapped positions.

Calculation of class-wide conservation and sequence variation in class F GPCRs

For each aligned position from the multiple sequence alignment of human sequences, we investigated if the homologous positions were previously labeled as conserved. To calculate the conservation of the position across paralogs we used the percentage of receptors having a conserved amino acid as was previously described above. For example, if 8 out of 11 receptors are identified as conserved at a specific residue, we calculate the conservation as 8/11 or 72.7% Residue divergence is calculated by comparing the most frequently observed residues for each receptor to each other. We retrieved this information from all 11 class F GPCRs and used entropy as a measure of sequence divergence. For the conserved water network analysis, positions with 0 entropy were used (all identical residues in class F GPCRs) and 0.44 entropy (one of the receptors in the class is different). For the cholesterol analysis, positions with 0 entropy and positions that only showed strict similarity based on BLOSUM 80 score were used.

Calculation of the residue-residue contact score change network

We applied the previously published residue-residue contact score (RRCS) 78 algorithm to inactive and active state FZD 7 structures using a custom Python script to subtract RRCS inactive from RRCS active to identify the changes observed during the activation of the receptor.

Reporting summary

Further information on research design is available in the  Nature Portfolio Reporting Summary linked to this article.

Data availability

The cryo-EM density maps for FZD 7 dimer have been deposited in the Electron Microscopy Data Bank (EMDB) under accession codes EMD-19881 . The coordinates for the models of the amended FZD 7 -Gs and for FZD 7 dimer have been respectively deposited in the PDB under accession numbers 9EW2 and 9EPO . All molecular dynamic trajectories were deposited on GPCRmd (inactive FZD 7 ID: 2064 and active FZD 7 ID: 2065 ).  Source data are provided with this paper.

Code availability

Multiple sequence alignments of paralogs and orthologs used for evolutionary analysis, and code and input files used for residue-residue contact analysis are provided at https://github.com/CompGenomeLab/fzd7_evolution_and_structure . https://doi.org/10.5281/zenodo.13175921 .

Scharf, M. M. et al. The dark sides of the GPCR tree - research progress on understudied GPCRs. Br J Pharmacol , 1–26 (2024).

Schulte, G. International Union of Basic and Clinical LXXX. the class frizzled receptors. Pharm. Rev. 62 , 632–667 (2010).

Article   CAS   PubMed   Google Scholar  

Kozielewicz, P. et al. Structural insight into small molecule action on Frizzleds. Nat. Commun. 11 , 414 (2020).

Article   ADS   CAS   PubMed   PubMed Central   Google Scholar  

Schulte, G. et al. Frizzleds act as dynamic pharmacological entities. Trends Pharm. Sci. 45 , 419–429 (2024).

Grätz, L. et al. Pathway selectivity in Frizzleds is achieved by conserved micro-switches defining pathway-determining, active conformations. Nat. Commun. 14 , 4573 (2023).

Article   ADS   PubMed   PubMed Central   Google Scholar  

Schulte G. 75th Anniversary Celebration Collection International Union of Basic and Clinical Pharmacology. CXIV: The Class F of G Protein-Coupled Receptors. Pharmacol Rev . 76 (2024).

Wright, S. C. et al. A conserved molecular switch in Class F receptors regulates receptor activation and pathway selection. Nat. Commun. 10 , 667 (2019).

Xu, L. et al. Cryo-EM structure of constitutively active human Frizzled 7 in complex with heterotrimeric Gs. Cell Res . 31 , 1311–1314 (2021).

Article   CAS   PubMed   PubMed Central   Google Scholar  

Seifert, J. R. K. & Mlodzik, M. Frizzled/PCP signalling: a conserved mechanism regulating cell polarity and directed motility. Nat. Rev. Genet 8 , 126–138 (2007).

Gao, C. & Chen, Y. G. Dishevelled: the hub of Wnt signaling. Cell Signal 22 , 717–727 (2010).

Gumber, D. et al. Selective activation of FZD7 promotes mesendodermal differentiation of human pluripotent stem cells. Elife 9 , 1–28 (2020).

Article   Google Scholar  

Čapek, D. et al. Light-activated Frizzled7 reveals a permissive role of non-canonical wnt signaling in mesendoderm cell migration. Elife 8 , 1–24 (2019).

Flanagan, D. J. et al. Frizzled7 functions as a Wnt receptor in intestinal epithelial Lgr5+ stem cells. Stem Cell Rep. 4 , 759–767 (2015).

Article   CAS   Google Scholar  

Kinsolving, J. et al. Structural and functional insight into the interaction of Clostridioides difficile toxin B and FZD7. Cell Rep. 43 , 113727 (2024).

King, D. T., Zhang, W., Suto, J. M. & Li, Y. Frizzled7 as an emerging target for cancer therapy. Cell Signal 24 , 846–851 (2012).

Ueno, K. et al. Frizzled-7 as a potential therapeutic target in colorectal cancer. Neoplasia 10 , 697–705 (2008).

Yang, L. et al. FZD7 has a critical role in cell proliferation in triple negative breast cancer. Oncogene 30 , 4437–4446 (2011).

Larasati, Y., Boudou, C., Koval, A. & Katanaev, V. L. Unlocking the WNT pathway: Therapeutic potential of selective targeting FZD7 in cancer. Drug Discov. Today 27 , 777–792 (2022).

Liang, Y. L. et al. Phase-plate cryo-EM structure of a class B GPCR-G-protein complex. Nature 546 , 118–123 (2017).

Zhang, Y. et al. Cryo-EM structure of the activated GLP-1 receptor in complex with G protein. Nature 546 , 248–253 (2017).

Tsutsumi, N. et al. Structure of human frizzled5 by fiducial-assisted cryo-em supports a heterodimeric mechanism of canonical wnt signaling. Elife 9 , 1–20 (2020).

Yang, S. et al. Crystal structure of the Frizzled 4 receptor in a ligand-free state. Nature 560 , 666–670 (2018).

Article   ADS   CAS   PubMed   Google Scholar  

Zhang, Z. et al. A framework for Frizzled-G protein coupling and implications to the Wnt-PCP signaling pathways. Cell Discov. 10 , 3 (2024).

Venkatakrishnan, A. J. et al. Diverse GPCRs exhibit conserved water networks for stabilization and activation. Proc. Natl Acad. Sci. USA 116 , 3288–3293 (2019).

Yuan, S., Filipek, S., Palczewski, K. & Vogel, H. Activation of G-protein-coupled receptors correlates with the formation of a continuous internal water pathway. Nat. Commun. 5 , 4733 (2014).

Bertalan, É., Lešnik, S., Bren, U. & Bondar, A. N. Protein-water hydrogen-bond networks of G protein-coupled receptors: Graph-based analyses of static structures and molecular dynamics. J. Struct. Biol. 212 , 107634 (2020).

Wootten, D. et al. A hydrogen-bonded polar network in the core of the glucagon-like peptide-1 receptor is a fulcrum for biased agonism: Lessons from class B crystal structuress. Mol. Pharm. 89 , 335–347 (2016).

Erazo-Oliveras, A. et al. Mutant APC reshapes Wnt signaling plasma membrane nanodomains by altering cholesterol levels via oncogenic β-catenin. Nat. Commun. 14 , 4342 (2023).

Zheng, S. et al. Aberrant Cholesterol Metabolism and Wnt/β-Catenin Signaling Coalesce via Frizzled5 in Supporting Cancer Growth. Adv. Sci. 9 , 1–22 (2022).

Zhang, X. et al. Crystal structure of a multi-domain human smoothened receptor in complex with a super stabilizing ligand. Nat. Commun. 8 , 1–10 (2017).

ADS   Google Scholar  

Valnohova, J., Kowalski-Jahn, M., Sunahara, R. K. & Schulte, G. Functional dissection of the N-terminal extracellular domains of Frizzled 6 reveals their roles for receptor localization and Dishevelled recruitment. J. Biol. Chem. 293 , 17875–17887 (2018).

Turku, A., Schihada, H., Kozielewicz, P., Bowin, C. F. & Schulte, G. Residue 6.43 defines receptor function in class F GPCRs. Nat. Commun. 12 , 1–14 (2021).

Filipek, S. Molecular switches in GPCRs. Curr. Opin. Struct. Biol. 55 , 114–120 (2019).

Ping, Y.-Q. et al. Structural basis for the tethered peptide activation of adhesion GPCRs. Nature , https://doi.org/10.1038/s41586-022-04619-y (2022).

Shaye, H. et al. Structural basis of the activation of a metabotropic GABA receptor. Nature 584 , 298–303 (2020).

Velazhahan V., Ma N., Vaidehi, N. & Tate C. G. Activation mechanism of the class D fungal GPCR dimer Ste2. 2 (2022).

Hilger, D. et al. Structural insights into differences in G protein activation by family A and family B GPCRs. 369 , 1–40 (2021).

Fantini, J. & Barrantes, F. J. How cholesterol interacts with membrane proteins: An exploration of cholesterol-binding sites including CRAC, CARC, and tilted domains. Front Physiol. 4 , 1–9 (2013).

Li, H. & Papadopoulos, V. Peripheral-type benzodiazepine receptor function in cholesterol transport. Identification of a putative cholesterol recognition/interaction amino acid sequence and consensus pattern. Endocrinology 139 , 4991–4997 (1998).

Hanson, M. A. et al. A specific cholesterol binding site is established by the 2.8 Å structure of the human β2-adrenergic receptor. Structure 16 , 897–905 (2008).

Gammons, M. V., Rutherford, T. J., Steinhart, Z., Angers, S. & Bienz, M. Essential role of the Dishevelled DEP domain in a WNT-dependent human-cell-based complementation assay. J. Cell Sci. 129 , 3892–3902 (2016).

Sheng, R. et al. Cholesterol selectively activates canonical Wnt signalling over non-canonical Wnt signalling. Nat. Commun. 5 , 4393 (2014).

Bowin, C. F. et al. WNT stimulation induces dynamic conformational changes in the frizzled-dishevelled interaction. Sci. Signal 16 , 1–18 (2023).

Kowalski-Jahn, M. et al. Frizzled BRET sensors based on bioorthogonal labeling of unnatural amino acids reveal WNT-induced dynamics of the cysteine-rich domain. Sci. Adv. 7 , 1–15 (2021).

Schihada, H., Kowalski-Jahn, M., Turku, A. & Schulte, G. Deconvolution of WNT-induced frizzled conformational dynamics with fluorescent biosensors. Biosens. Bioelectron. 177 , 112948 (2021).

Oates, J. et al. The role of cholesterol on the activity and stability of neurotensin receptor 1. Biochim Biophys. Acta Biomembr. 1818 , 2228–2233 (2012).

Hoppe N. et al. GPR161 structure uncovers the redundant role of sterol-regulated ciliary cAMP signaling in the Hedgehog pathway. Nat. Struct. Mol. Biol. (2024).

Huang, P. et al. The structural basis of smoothened activation in hedgehog signaling. Physiol. Behav. 176 , 139–148 (2016).

Google Scholar  

Huang, P. et al. Structural basis of smoothened activation in hedgehog signaling. Cell 174 , 312–324.e16 (2018).

Kozielewicz, P. et al. Quantitative profiling of WNT-3A binding to all human frizzled paralogues in HEK293 cells by NanoBiT/BRET assessments. ACS Pharm. Transl. Sci. 4 , 1235–1245 (2021).

Punjani, A., Rubinstein, J. L., Fleet, D. J. & Brubaker, M. A. CryoSPARC: algorithms for rapid unsupervised cryo-EM structure determination. Nat. Methods 14 , 290–296 (2017).

Punjani, A., Zhang, H. & Fleet, D. J. Non-uniform refinement: adaptive regularization improves single-particle cryo-EM reconstruction. Nat. Methods 17 , 1214–1221 (2020).

Bepler, T. et al. Positive-unlabeled convolutional neural networks for particle picking in cryo-electron micrographs. Nat. Methods 16 , 1153–1160 (2019).

Jo, S., Kim, T., Iyer, V. G. & Im, W. Software News and Updates CHARMM-GUI: A Web-Based Graphical User Interface for CHARMM. J. Comput. Chem. 29 , 1859–1865 (2008).

Wu, E. L. et al. Charmm-gui membrane builder toward realistic biological membrane simulations. J. Comput Chem. 35 , 1997–2004 (2014).

Lee, J. et al. CHARMM-GUI Input Generator for NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM Simulations Using the CHARMM36 Additive Force Field. J. Chem. Theory Comput . 12 , 405–413 (2016).

Jo, S., Lim, J. B., Klauda, J. B. & Im, W. CHARMM-GUI membrane builder for mixed bilayers and its application to yeast membranes. Biophys. J. 97 , 50–58 (2009).

Park, S., Choi, Y. K., Kim, S., Lee, J. & Im, W. CHARMM-GUI membrane builder for lipid nanoparticles with ionizable cationic lipids and PEGylated lipids. J. Chem. Inf. Model 61 , 5192–5202 (2021).

Brooks, B. R. et al. CHARMM: The Biomolecular Simulation Program. J. Comput. Chem. 30 , 1545–1614 (2009).

Kim, S. et al. CHARMM-GUI ligand reader and modeler for CHARMM force field generation of small molecules. J. Comput. Chem. 38 , 1879–1886 (2017).

Jo, S., Kim, T. & Im, W. Automated builder and database of protein/membrane complexes for molecular dynamics simulations. PLoS One 2 , e880 (2007).

Lee, J. et al. CHARMM-GUI membrane builder for complex biological membrane simulations with glycolipids and lipoglycans. J. Chem. Theory Comput . 15 , 775–786 (2019).

Kim, S. et al. CHARMM-GUI free energy calculator for absolute and relative ligand solvation and binding free energy simulations. J. Chem. Theory Comput . 16 , 7207–7218 (2020).

Wu, E. L. et al. Charmm-Gui membrane builder toward realistic biological membrane simulations emilia. 35 , 1997–2004 (2015).

Abraham, M. J. et al. Gromacs: high performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX 1–2 , 19–25 (2015).

Article   ADS   Google Scholar  

Hess, B. et al. LINCS: a linear constraint solver for molecular simulations. J. Comput. Chem. 18 , 1463–1472 (1997).

Abraham, M. & Gready, J. Optimization of parameters for molecular dynamics simulation using smooth particle-mesh ewald in GROMACS 4.5 MARK. J. Comput. Chem. 32 , 2031–2040 (2011).

Roe, D. R. & Cheatham, T. E. PTRAJ and CPPTRAJ: software for processing and analysis of molecular dynamics trajectory data. J. Chem. Theory Comput . 9 , 3084–3095 (2013).

Humphrey, W., Dalke, A. & Schulten, K. VMD: visual molecular dynamics. J. Mol. Graph 14 , 33–38 (1996).

Rodríguez-Espigares, I. et al. GPCRmd uncovers the dynamics of the 3D-GPCRome. Nat. Methods 17 , 777–787 (2020).

Article   PubMed   Google Scholar  

Tošović, J., Fijan, D., Jukič, M. & Bren, U. Conserved water networks identification for drug design using density clustering approaches on positional and orientational data. J. Chem. Inf. Model 62 , 6105–6117 (2022).

Article   PubMed   PubMed Central   Google Scholar  

Altschul, S. F., Gish, W., Miller, W., Myers, E. W. & Lipman, D. J. Basic local alignment search tool. J. Mol. Biol. 215 , 403–410 (1990).

Katoh, K., Rozewicki, J. & Yamada, K. D. MAFFT online service: multiple sequence alignment, interactive sequence choice and visualization. Brief. Bioinform 20 , 1160–1166 (2018).

Steenwyk, J. L., Buida, T. J., Li, Y., Shen, X. X. & Rokas, A. ClipKIT: a multiple sequence alignment trimming software for accurate phylogenomic inference. PLoS Biol. 18 , 1–17 (2020).

Minh, B. Q. et al. IQ-TREE 2: new models and efficient methods for phylogenetic inference in the genomic era. Mol. Biol. Evol. 37 , 1530–1534 (2020).

Selçuk, B., Erol, I., Durdağı, S. & Adebali, O. Evolutionary association of receptor-wide amino acids with G protein-coupling selectivity in aminergic GPCRs. Life Sci. Alliance 5 , 1–13 (2022).

Li, W. & Godzik, A. Cd-hit: a fast program for clustering and comparing large sets of protein or nucleotide sequences. Bioinformatics 22 , 1658–1659 (2006).

Zhou, Q. et al. Common activation mechanism of class a GPCRs. Elife 8 , 1–31 (2019).

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Acknowledgements

We thank Pankonin Maik for his advice and discussions regarding the analysis of the molecular dynamics simulations. We thank Rémy Sounier for his contribution to figure design. Thanks to Prof Michel Bouvier for sharing relevant plasmids. EM data were collected at the Karolinska Institutet 3D-EM facility https://ki.se/cmb/3d-em . Samples were screened in SciLifeLab for access to the cryo-EM Swedish National Facility. The work was supported by grants from Karolinska Institutet, the partial funding to doctoral students at Karolinska Institutet (2021-00430), the Swedish Research Council (GS: 2019-01190), the Swedish Cancer Society (GS: 20 1102 PjF, 23 2825 Pj), the Novo Nordisk Foundation (GS: NNF22OC0078104), The German Research Foundation (DFG; LG: 504098926; JHV: 520506488), Svenska Sällskapet för Medicinsk Forskning, SSMF (MMS: PG-22-0379; JB: PG-23-0321) and the Wenner Gren Foundations (UPD2021-0029). The MD simulations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS; NAISS 2023/5-419), partially funded by the Swedish Research Council through grant agreement no. 2022-06725.

Open access funding provided by Karolinska Institute.

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Berkay Selcuk

Present address: Department of Microbiology, The Ohio State University, Columbus, Ohio, USA

These authors contributed equally: Julien Bous, Julia Kinsolving.

Authors and Affiliations

Section of Receptor Biology & Signaling, Department of Physiology & Pharmacology, Karolinska Institutet, Stockholm, Sweden

Julien Bous, Julia Kinsolving, Lukas Grätz, Magdalena M. Scharf, Jan Hendrik Voss & Gunnar Schulte

Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey

Berkay Selcuk & Ogün Adebali

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Contributions

G.S., J.B., and J.K. initiated and designed the project. J.B., and J.K. carried out the FZD 7 purification and cryo-EM acquisition and analysis. J.B., and J.K. built the model and interpreted it. J.B., and M.S., ran the molecular dynamic analysis and interpreted the results. B.S., and O.A. Designed a strategy for the phylogenetic analysis of class F GPCRs and ran the analysis. L.G., and J.B. designed a rational strategy for cholesterol-binding site mutations. L.G., J.K., JV., and J.B. performed the wet lab experiments. J.B., L.G., J.K., B.S., O.A., and G.S. designed and prepared the figures. J.B., J.K., and G.S. wrote the manuscript. B.S., and O.A. wrote the phylogenetic analysis sections L.G., J.V., B.S., and O.A. commented and contributed to the manuscript writing. G.S. supervised and coordinated the project.

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Correspondence to Julien Bous or Gunnar Schulte .

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Bous, J., Kinsolving, J., Grätz, L. et al. Structural basis of frizzled 7 activation and allosteric regulation. Nat Commun 15 , 7422 (2024). https://doi.org/10.1038/s41467-024-51664-4

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Received : 03 May 2024

Accepted : 15 August 2024

Published : 28 August 2024

DOI : https://doi.org/10.1038/s41467-024-51664-4

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