Erkenntnis 79, n. 2 (2014) ), pp. 297-326, doi:10.1007/s10670-013-9495-7The final publication is available electronically on SpringerLink:

http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s10670-013-9495-7

NOVEL PREDICTIONS AND THE NO MIRACLE ARGUMENT

Mario Alai

Università di Urbino Carlo Bo - DiSBeF

Abstract

Predictivists use the no miracle argument to argue that ‘‘novel’’predictions are decisive evidence for theories, while mereaccommodation of ‘‘old’’ data cannot confirm to a significantdegree. But deductivists claim that since confirmation is alogical theory-data relationship, predicted data cannot confirmmore than merely deduced data, and cite historical cases in whichknown data confirmed theories quite strongly. On the other hand,the advantage of prediction over accommodation is needed byscientific realists to resist Laudan’s criticisms of the nomiracle argument. So, if the deductivists are right, the mostpowerful argument for realism collapses. There seems to be aninescapable contradiction between these prima facie plausiblearguments of predictivists and deductivists; but this puzzle canbe solved by understanding what exactly counts as novelty, ifnovel predictions must support the no miracle argument, i.e., ifthey must be explainable only by the truth of theories. Taking mycues from the use-novelty tradition, I argue that (1) thepredicted data must not be used essentially in building the theoryor choosing the auxiliary assumptions. This is possible if thetheory and its auxiliary assumptions are plausible independentlyof the predicted data, and I analyze the consequences of thisrequirement in terms of best explanation of diverse bodies ofdata. Moreover, the predicted data must be (2) a prioriimprobable, and (3) heterogeneous to the essentially used data. Myproposed notion of novelty, therefore, is not historical, butfunctional. Hence, deductivists are right that confirmation isindependent of time and of historical contingencies such as if thetheorist knew a datum, used it, or intended to accommodate it.Predictivists, however, are right that not all consequencesconfirm equally, and confirmation is not purely a logical theory-data relation, as it crucially involves background epistemic

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conditions and the notion of best explanation. Conditions (1)–(3)make the difference between prediction and accommodation, andaccount for the confirming power of theoretical virtues such asnon ad-hocness, non-fudging, non-overfitting, independence andconsilience. I thus show that functional novelty (a) avoids thedeductivist objections to predictivism, (b) is a gradual notion,in accordance with the common intuition that confirmation comes indegrees, and (c) supports the no miracle argument, so vindicatingscientific realism.

1. Scientific realism, predictivism, and confirmation

Against antirealists like van Fraassen (1980), scientific realistsmaintain that we can have (and in the best cases we have)compelling reasons to believe in the truth of theories. The mostpowerful support for this view is the “no miracle” argument: itwould be a miracle that our theories were as empiricallysuccessful as they are, unless they were true (Smart 1968; Putnam1975, 73; Musgrave 1988; Niiniluoto 1999, 197). But since miraclesare not a plausible explanation, this is to say that truth is notjust the best possible, but the only plausible explanation of scientificsuccess: hence, the truth of successful theories can bepractically certain.

Laudan (1981) objected that a number of theories which onceenjoyed considerable empirical success, predicting and explaininga wealth of data (like Ptolemaic cosmology, caloric theory,phlogiston theory, Newton’s gravitation theory, etc.) were laterrejected as false.

Realists replied by two qualifications: one is that asuccessful prediction can be explained without assuming the truthof the whole theory, but only of those assumptions which wereessential in deriving that prediction (Kitcher 1993, Psillos 1999,108 ff.). Hence, there can be evidence not for the exact andcomplete truth of theories, but for their at least partial and/orapproximate truth, in the sense that at least those componentsessentially involved in successful predictions must be at leastapproximately true (partial, or “deployment” realism). HenceforthI will always intend the realist claims about truth with thisimplicit qualification.

The second qualification made in reply to Laudan is based onpredictivism, the claim that prediction confirms more thanaccommodation: when a theory accounts for known phenomena, thiscan be explained just by the fact that its author knew these

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phenomena, wished to accommodate them, and patiently andingeniously engineered the theory and chose the appropriatecollateral assumptions to this purpose. No need therefore toassume that her theory is also true: the no miracle argument doesnot apply. On the contrary, if a theory predicts novel phenomena,the purposeful accommodation explanation is barred, hence truth ormiracle remains the only possible explanations (Musgrave 1985,1988; Lipton 1991, 1994; Psillos 1999; Sankey 2001). The nomiracle argument, therefore, applies only to cases of novelpredictions, and “few, arguably none, of the theories cited [byLaudan] had any novel predictive success” (Musgrave 1985, 211).Hence, they cease to be counterexamples to the realist argument.1

We shall now ask precisely what is novelty if it is to supportthe no miracle argument; but clearly it must be something whichprevents any explanation except truth (or miracle). For instance,we shall see, phenomena need not be new in any temporal sense; onthe other hand, they must not be the kind of phenomena for whichthe theory was tailored, and not so probable to be easily guessed.

But deductivists have criticized predictivism for over 150 yearsnow,2 holding that all consequences of a theory confirm it equally,no matter whether old or new;3 and if they are right, the secondrealist reply to Laudan is undermined. Therefore in § 2 I shallexamine their objections, and throughout the rest of the paper Iwill argue that they don’t refute the minimal form of predictivismrequired to support the no miracle argument, if the correct notionof novelty is identified.

Before that, however, a different basic objection must beconsidered: i.e., that there is no need to invoke the truth of atheory T to explain how it predicted a novel datum d, for there isreally nothing to explain: that d follows (deductively orinductively) from T is just a logical fact about T. Roger White

11 Lyons (2002) has countered that even particular claims which were essential in

deriving novel predictions have been shown to false. For a discussion and a replysee (Alai, forthcoming).2 The predictivism-deductivism debate has been sketched in Lakatos 1970,123-124; Musgrave 1974, 1-3; Lipton 1991, ch. 10; Barnes 2008, ch. 1, etc. 3 In fact, what is commonly called deductivism should be called moreprecisely ‘consequentialism’, for consequences can be both deductive andinductive (as was brought to my attention by an anonymous reviewer for thisJournal). This sense of ‘deductivism’ is altogether different from two others:(1) Alan Musgrave’s idea that induction is really a form of deduction with animplicit epistemic premise (its opposite being inductivism), and (2) Popper’stheory of empirical control (see Grunbaum, Salmon (eds.) 1988). I owe thisdistinction to Howard Sankey.

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(2003, 659-663) answered that the right question is not why dfollows from T, but how the theorist succeeded in choosing, amongthe various possible theories compatible with the data sheintended to accommodate, one that also predicted the unforeseen d.It cannot have happened by luck, for it would have been a“miraculously” unlikely coincidence; so, there must be analternative explanation. For Barnes (2008, 137), it is that inchoosing to endorse T the theorist relied on true backgroundtheories. But this is not enough, for true background beliefs willnot lead to further true beliefs unless coupled with soundmethods. For White the explanation is that “the theorist’sselection of her theory was reliably aimed at the truth, [i.e.]the mechanisms which led to her selection of a theory gave her agood chance of arriving at the truth” (2003, 664). These“mechanisms”, I suggest, can be interpreted as including truebackground beliefs together with sound methodology.

Yet, this answer is still incomplete, for reliability is notinfallibility: one might reliably aim at true theories, hence achievethem in a good number of cases, but fail to achieve one, or onepredicting d, in the particular case at hand. What we need istherefore:(A) The theorist actually picked a theory containing enough truthto have d as a consequence.But this explanation is utterly implausible unless it is in turnadequately explained, since among the theories saving all theknown data the true ones are infinitely fewer than the false ones,and those predicting d are even fewer. Hence, if theories wherechosen randomly, getting a theory with enough truth to predict dwould be utterly unlikely, or again, a “miracle”. So, how did thetheorist succeed in getting such a theory?

An answer is possible if theorizing is not a chance process:developing Maher’s (1988, 1993) and White’s (2003, 659-663)suggestions, the theorist got a true theory because (B) the theorist (i) aimed at a true, deep and heuristically fecund theory, and (ii) she worked skilfully, employing scientific method, which is

reliable, i.e., truth-conducive, and heuristically fecund.In turn, if reliability is not to remain an empty “virtus dormitiva”,it should be explained: for instance, (C) scientific method is reliable because it

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(i) aims at explaining observed phenomena by deep and generaltheoretical hypotheses whose consequences go beyond thosephenomena;

(ii) respects empirical constraints;(iii) assuming that nature is simple, symmetrical, consilient,

etc., it reconstructs the unobservable natural systems byanalogy, abduction and inductive extrapolation from theobservable ones;

(iv) nature actually is simple, symmetrical, consilient, etc.;(v) any background theories employed by the theorist or

presupposed by her method (see Boyd 1981) were themselves truesince derived by sound scientific method.4

So, (B) does not directly explain novel success, but its actualexplanans (A). By itself, (B) is not sufficient (or not sufficientlyexplicit) to explain novel success: first, because the actualexplanans (A) is explained, but not entailed, by (B); second,because (B) itself needs to be explained by (C). So, when claimingthat only truth can explain novel success, one should understand‘truth’ as a short for (A-B-C), as I will do henceforth.

Barnes (2008, 137-138) objects that the truth of T cannotexplain why it was endorsed, to the preference of differenttheories; hence he claims that novelty does not speak directly forthe truth of T, but only for the reliability of its author. Butthe endorsement of T is explained by the joint fact that (B) itsauthor reliably aimed at a true and fecund theory, and (A) T istrue and fecund.

2. Deductivist objections and an apparent stand-off

As said, supporters of the no miracle argument can resist Laudan’scriticism by holding that the argument applies only to novelpredictions, hence prediction confirms more than accommodation.But deductivists deny this asymmetry: confirmation, they hold, is alogical relation between data and theories, hence independent ofhistorical contingencies, such as whether a given datum had beendiscovered beforehand or not (McIntyre 2001, 309). In other words,as stressed by positivists, the context of discovery is irrelevantto the context of justification. Deductivists support their point

4 The presupposition of earlier theories by the theorist or by her methoddoes not launch an infinite regress, since the earliest, “take-off” theorieswere introduced without relying on previous theories or on theory-dependentmethods (Barnes 2008, 146-155).

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by arguing that predictivism has paradoxical consequences, and itis refuted by historic cases:

(I) Peter Lipton (1991, 166) imagines that two twin scientists(call them John and Jill) independently and unbeknownst of eachother construct the same theory T. They work in equal epistemicconditions, with the only difference that a datum d, followingfrom T, was antecedently known and accommodated by John, while itwas ignored by Jill, who predicted it on the basis of T afterconstructing it. If predictivism is right, it would seem, Jill’stheory should be better confirmed than John’s: but this isimpossible, since they are one and the same theory! Moreover, ifthey are predictivist, John (who accommodated d) should have alower confidence in T than Jill (who predicted d); but if they metand learned about each other’s work, who should rationally modifyhis or her level of confidence? John, in learning that Jill wasable to predict d, or Jill, in learning that John merelyaccommodated it?

(II) It would seem to follow from predictivism that if we knewall the phenomena in a given domain, we could never have decisiveevidence for a theory in that domain, for no genuine predictionwould be possible (Ladyman 2002, ch. 8 § 1.3). But this isparadoxical, for a greater knowledge of phenomena should offergreater evidence for (or against) theories in that domain.Similarly,

(III) for predictivists ignorance should be an advantage: we should be more confident in a theory if it was constructed ignoring part of the relevant data than by using them (Lipton 1991, 166; Hudson 2007, 6).

(IV) Predictivism appears to imply that historical research onwhich data were available to the theorist when she constructed hertheory are relevant to its confirmation: but obviously it is not,for practicing scientists never raise this problem when evaluatinga theory (Hudson 2007, 5).

Deductivists also point out that the confirmation of novelpredictions seem to have played no relevant role in theacceptation of some paradigmatic theories, and often theories areaccepted just because they explain and systematize a body of knowndata (Brush 1994; Brush 1996, 612; Ladyman 2002, ch. 8, § 1.3). Forinstance,

(V) Scerri and Worrall (2001, 417) notice that there was nomajor progress in the acceptance of Mendeleev’s Periodic Tableafter the discovery of Gallium, Germanium, Scandium, threepreviously unknown elements it had predicted, and the citation for

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the Davy Medal awarded to Mendeleev did not even mention thosepredictions. Furthermore, no particular emphasis was given tothose discoveries in contemporary literature.

(VI) Fresnel’s memory on the wave theory of light, from whichPoisson drew the white spot prediction, won the French Academyprize; but the jury assigned the prize without bothering tocontrol the prediction, and it was given no special emphasis inthe motivation of the award (which rather stressed Fresnel’s newmethod for observing and measuring diffraction fringes, and thefact that his hypothesis gave a very general account of thealready known straightedge diffraction cases, yielding veryprecise measurements for them). Furthermore the majority of thejurors, Laplace, Biot and Poisson, were corpuscularist, and didnot convert to the wave theory after the prediction was confirmed.In fact, it almost seems that Fresnel’s victory stemmed more fromthe relative weakness of the only other competitor to the contest,than from the jury’s intimate convictions (see Worrall 1989b, 139-144).

(VII) According to Stephen Brush, no theory “was acceptedprimarily because of its successful predictions of novel facts”(1994, 140). For instance, Heisenberg’s matrix mechanics andSchrödinger’s wave mechanics made just two relatively unimportantnovel predictions, and their confirmation “played essentially norole” in their acceptance (ibid., 136).

(VIII) On the other hand, the data about Mercury’s perihelionentailed by General Relativity were known to Einstein in advance,and perhaps even used by him; yet, they are considered as decisiveevidence for his theory (Gardner 1982, 5; Earman, Glymour 1978).Therefore novelty does not seem to be required for a high level ofconfirmation.

(IX) Conversely, Dirac’s relativistic quantum theory wasaccepted after predicting the existence of the positron; but itwas soon replaced by quantum electrodynamics (ibid., 139). So,novelty is not even sufficient to decisive confirmation.

Summing up, novelty would seem irrelevant to the degree ofconfirmation. But if these objections are correct we face aparadoxical contradiction5 between two apparently undeniablepoints: the predictivist idea that since the no miracle argumentapplies to prediction but not to confirmation, the former confirmsmuch strongly than the latter; and the deductivist claim thatlogically, methodologically, and historically knowledge or usage

5 Musgrave (1974, § 2) and Barnes (2008) speak of a “paradox”, and Lipton (1991, 164) of a “puzzle”.

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of data make no difference. Scientific realists must sort out thiscontradiction, if they wish to use novel predictions as acriterion for their commitments, and reply to Laudan that pastfalse theories did not have predictive success.

A solution can be found by clarifying the nature of novelty:while much has already been done to this end,6 here we should askmore precisely what is novelty if it must support the no miracleargument, so leaving truth as the only plausible explanation ofnovel success. In this way, I submit, we can save and reconcilethe sound intuitions of both predictivists and deductivists: theapparent contradiction between them depends on equivocation on themeanings of ‘novel’ and ‘prediction’, and both parties should bebrought to agree that (a) not all consequences of a theory confirmit with equal strength, but (b) the difference does not depend onhistorical contingencies, as knowledge or usage. I shall try toexplain what makes the difference, i.e., what property is requiredfor the no miracle argument. Some might question whether thatproperty should be called ‘novelty’, but I think there are goodreasons for doing so.

3. The conditions for novelty: reconciling predictivism and deductivism

3.1 The use-novelty tradition and inessentialityPredictive success confirms a theory in accordance with the nomiracle argument when its only plausible explanation is truth (inthe sense of (A-B-C) above). So, a prediction is “novel” in thesense we are seeking if it rules out all the alternativeexplanations.

The first alternative explanation to be ruled out, of course,is skilful purposeful accommodation: if a datum d was known, oreven just probable in the light of available evidence or ofaccepted background theories, the theorist might have decided topredict it, and she might have succeeded, even by using a falsetheory, through suitable modifications of the theory andappropriate choice of auxiliary assumptions. But this explanationis not possible if, as required by Popper, d “has not thus farbeen observed” (1965, 241-242), or if, as required by Lakatos, d is“improbable and even impossible in the light of previousknowledge” (1970, 118 fn. 2),

6 See Gardner 1982, 1-ff; Leplin 1997, chs. 2,3; Barnes 2008, ch. 1.

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However, the accommodation explanation is also ruled out evenif d was known in general, but not to the theorist (Gardner 1982, 10,McIntyre 2001), or, as noticed by Lakatos’ disciples Zahar (1973)and Worrall (1978, 65), if d was known to the theorist, but not partof the problems for which theory T was designed, or the theoristdid not intend to accommodate d. For instance, the precession ofMercury’s perihelion and the negative result of Michelson andMoreley’s experiments strongly confirmed the theory of relativity,even if already known to Einstein.7 So, being unknown in any formis a sufficient, but not necessary condition of the kind ofnovelty we are interested in.

But relativizing novelty to the problems tackled by theoriesmay raise a problem similar to objection (I) above: if John framesT in a problem context including d, and Jill independentlyadvances T for problems not including d, is T confirmed or not?Moreover, the intention of accommodating d, qua psychological notion,can hardly be relevant to confirmation (Musgrave 1974, 15; Leplin1997, 50). In fact, if the theorist did not intend to accommodate d,but unconsciously used it as a clue or a constraint to thesolution, this would already explain her success better than thetruth of T. So, lack of intention to accommodate d is notsufficient to the novelty of d, and to confirm T.

This is why Zahar (1973) supplemented8 the notions of problem-novelty and intention-novelty with that of use-novelty. Actually,Popper had already taken this position when he approvingly quotedfrom Schlick: “The corroboration of a prediction means nothingelse but the corroboration of a formula for those data which werenot used in setting up the formula. Whether these data had alreadybeen observed or whether they were subsequently ascertained makesno difference at all” (Schlick 1931, 149-150, in Popper 1979, 112,my italics). Subsequently also Worrall adopted a use-noveltyaccount of confirmation (1978; 1985, 318, 321, passim; 1989b, 148;Scerri, Worrall 2001, 424-427, passim; etc.).

But it can be objected that even being used is a contingent,historico-pragmatic property, like being known and being intended, andas such irrelevant to the logic of confirmation. Moreover, if T’sdegree of confirmation depends on the reasoning process which ledto T, it may be very hard to evaluate: for often we don’t have anyknowledge of this process, and even if we have the scientist’snotebooks, memories, diaries, and letters, we cannot be certain

7 Zahar 1973 §1.1. See Gardner 1982, p.2, Maher 1993, p. 339.8 Tacitly and perhaps unconsciously: see Gardner 1982, p. 3, Leplin 1997,p.50.

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that they are complete and reliable (Gardner 1982, 7). Finally,examples like John and Jill’s again show that confirmation cannotdepend on what was used or intended, for the very same theory Tmight have been conceived by John using d, and by Jill not usingd: but surely T cannot be both confirmed (in Jill’s case) and notconfirmed (in John’s case) by d (Musgrave 1974, 14). In such acircumstance John would have used d unnecessarily, in the sense that hecould have predicted d (precisely as Jill did) instead of merelyaccommodating it; so, one can explain why John actually managed toconceive T and accommodate d by citing his desire to accommodate it,ingenuity and patience; but this cannot explain how John could havedone that without using d (just as it cannot explain how Jill didfind a theory predicting d without using it). Jill’s predictivesuccess is explainable only by assuming her reliability and thetruth of T in the above sense (A-B-C). Likewise, that John couldhave predicted d rather than accommodating it (i.e., that his useof d was inessential) can only be explained by the fact that he couldhave found a sufficiently deep and true theory, plus the necessaryauxiliary assumptions, without using d. In § 4 I’ll discuss why andhow he could have found it.

Hence, even not being used is not necessary (though sufficient)to novelty, and to support the no miracle argument. Not havingbeen used essentially is also sufficient. This has been recognized byLeplin, for whom d is novel for T even if it was used, if (Independence): “There is a minimally adequate reconstruction of the

reasoning leading to T that does not cite any qualitativegeneralization of d”;

(Uniqueness): at the time T predicts d, no other theory usingdifferent mechanisms does (1997, 77, 64). These conditions are designed to implement, among others, the

constraints that if d was used in framing T, it was onlyinessentially, and d is “significantly different” from the datathat were used essentially (1997, 63). For this consequence tofollow, of course, the reasoning mentioned in (Independence) mustnot be understood as an actual psychological process, but as alogically possible rational path. (Uniqueness) generalizes an ideaof Lakatos’ (1968, 375-390) developed by Musgrave (1974, 15 ff.),according to which d is novel and confirms a new theory T just incase it is excluded, or at least not predicted, by the old theoryT’ challenged by T.

But even before Leplin, the inessential-use idea emerged inWorrall as a specification or development of his use-noveltyconception, although not explicitly distinguished from it (1978,

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68; 1985, 319, 321; 1989b, 149-151; etc.). Over the years, thisidea has become more elaborate and pervasive (e.g., in Worrall2005, 818; Worrall 2006, 40, 50-51, etc.), although occasionally hestill talked as if the ultimate criterion were actual use withoutfurther specification.9

In a nutshell, the scheme he has been proposing in many papersis: a general theory or research programme T (say wave theory oflight, General Relativity, etc.) does not entail an empiricalprediction d directly, but only through collateral assumptionswhich lead to a specialization T’, entailing d. Now, if only byusing d one can pick T’ as the right specialization of T, dconfirms T’, but only provided T is accepted, and it does not confirm T.If instead T’ (hence d) already follows from T directly, or bymeans of very natural assumptions, then d confirms T. So, whatmatters is if T gave the theoretician “independent reasons” for T’and d, or instead d had to be ‘read off’ from some observations;while it doesn’t matter if she had d in mind when developing T(1978, 68); it doesn’t matter “what Einstein was worrying about atthe time he produced his theory [but] whether he needed to use someresult about Mercury in order to tie down some part of his theory”( 1985, 319, my emphasis; 321, etc.); Fresnel’s wave hypothesisaccounted for various known phenomena of diffraction, but theycounted as novel because he could have predicted them in advance(1989b, 149-151); d is novel when “there was a heuristic path to[T] that did not presuppose its existence” (Scerri, Worrall 2001,418). The inessential use conception is clearly implicit in thesepassages: if d confirms T because it “drops naturally out of T”(2006, 51), or because there exists a heuristic path to Tindependent of d, and T gives independent reasons for d, all thismakes it irrelevant whether nonetheless d has been (unnecessarily)used or not (and a fortiori, which were the motivations, beliefs,etc. of T’s author).

Since this conception detaches novelty from historicalcontingencies like being known or not, intended or not, used ornot, Worrall considers his own viewpoint as “at root a logical theoryof confirmation”, based on logical relations between d, thegeneral theory T, and its specialization T’ (2005, 819; 2006, 56).This is very important, since, as we shall see, the above9 “So long as e was not used in constructing … theory T, then … there is no question ofany reduction of support …” Worrall 2005, 818; see also ibid., 819, etc.); “… thecrucial difference is that in cases of little or no support, certain aspects ofthe theory were fixed precisely to yield the phenomenon at issue” (Scerri,Worrall 2001, 423); predictions give little support when “the fact was both knownand used in the construction of the theory” (ibid., 424; also 426, etc.).

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objections (I)-(IX) to predictivism basically presuppose ahistorical notion of novelty, hence they are ineffective against anon-historical notion.

But Worrall’s account can still be improved. First, stressingmore explicitly the difference between inessential-use-novelty (a non-historical notion) and use-novelty (a historical notion), wouldhelp to show how objections (I)-(IX) can be answered (see §§ 3.4-3.5 below); moreover, it would prevent commentators frommisunderstanding Worrall’s notion of novelty as relative to theindividual scientist or her motivations (like Gardner 1982) or asmere use-novelty (like Barnes 2005).

Secondly, why does evidence confirm so strongly, when not usedessentially? Worrall can see no better justification than the nomiracle argument (“surely it would be a miracle if the theorycould have such evidence in its favour, and yet be entirely off-beam”). Yet, this justification does not fully satisfy him: “Ialways thought [it] was an overly flattering description” (2006,50). In fact, if we ask how can T have such evidence in its favourif it is not true, we are just begging the question “why is devidence for T?” If instead ask how could T “naturally” predict din advance of any observation, one can simply answer (as noticedin § 1) that it is a logical fact about T that it entails d. Whatwe need to ask, then, is why T was (or could have been) chosen amongcountless others independently of d. In § 4 I shall argue that itis because T was plausible independently of d, and precisely byanalyzing what this means I will explain why d confirms, and whyperhaps the no miracle argument might be more convincing toWorrall. I will also argue that, contrary to Worrall’s claim,confirmation is not just a relation among T, its specialization T’and d, and it is not a purely logical relation, since it partlydepends on background assumptions, conceptual schemes, and on thenotion of best explanation.

My account will also differ from Leplin’s: for he grants thathis conditions (Independence) and (Uniqueness) are merely sufficient,not necessary, to novelty (1997, 78); but understanding a conceptis finding how it differs from others, its differentia specifica, hence,its necessary conditions. Moreover, both the requirement that T bethe first theory to predict d (Uniqueness), and the Lakatos-Musgraverequirement that d is not predicted by T’s rival, bring theseconception back among the historically contingent notions, withthe related problems: for instance, they have the implausibleconsequence that if T1 and T2 are arrived at independently, eachpredicts d in an equally natural way and is otherwise equally

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plausible, but T1 happens to have been conceived (or completed? orpublished?) earlier, then d is novel for T1 but not for T2, and T1

is more confirmed (Ladyman 2002, 8 § 1.3). Per se, that T1 predicts something not predicted by T2, as

required by Lakatos and Musgrave, does not show that T1 is true, ormore nearly true than T2 (for instance, if the prediction were adhoc T1 might well be false). Leplin requires (Uniqueness) because iftwo incompatible theories predicted d, then at least one of thesesuccesses could not be explained by truth, but by chance; but ifchance is a viable explanation, then it can be used in all cases,and truth is no longer the only possible explanation in any case(1997, 64-65). But this problem cannot be solved simply byintroducing (Uniqueness) as a constraint on novelty, so that d nolonger classifies as novel for T2: even if d does not count as“novel” for T2, still we must explain how T2 predicted it, since byhypothesis d was not used essentially in constructing T2. But iftruth is assumed to explain the success of T1, it cannot alsoexplain that of T2. Therefore there must be a differentexplanation, but then it could also apply to T1, and we can’t anylonger assume that it is true: the no miracle argument andpredictivism fail anyhow.

So, if really incompatible theories can predict the samephenomenon without using it essentially, there must possibleexplanations of success other than accommodation (i.e., essentialuse) and truth; therefore we have no choice but to identify themand restrict the no miracle argument to cases where they arebarred. Once done this, however, (Uniqueness) becomes superfluous.This shows that inessentiality is necessary but not sufficient toa notion of novelty which can support the no miracle argument:further conditions, excluding any possible explanation of successother than truth, are required (thus, historical conditions, likenot having been known or used, are neither necessary norsufficient). In §§ 3 and 4 I will try to find and elucidate thosefurther conditions.

To begin with, a possible explanation of novel success short ofthe truth of the theory is the truth of only some of its tenets, thosenecessary to derive the successful prediction, in accordance withdeployment realism (Psillos 1999, 108 ff.) and the first realistqualification in reply to Laudan: the no miracle argument does notwarrant belief in whole theories, but only in the componentsessentially deployed in deriving novel predictions. This explainshow incompatible theories can predict the same datum d: this ispossible if they share those true tenets from which d follows.

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Hence, pace Musgrave and Leplin, d might contemporarily confirm boththeories, showing that they are both at least partially true. Yet,Lyons (2002) cites cases of novel predictions derived not justfrom false theories, but from particular false claims. So, there arestill other possible explanations of success, which must excludedby our notion of novelty.

3.2 A priori improbabilityOne of them is chance. A false theory may casually happen to makea true prediction when the latter is a priori probable becausescarcely informative: the less informative and the more a prioriprobable a prediction is, the more are the possible theories(including false ones) from which it follows. The most a prioriprobable consequences, tautologies, follow from any theory. So,false theories can have true, although uninformative, empiricalconsequences (see Alai, forthcoming, § 4).

For instance, either answer to a yes/no question concerning abasic constituent of the space of possibilities has equalinformation content and a priori probability; so, in the absence ofprevailing evidence in either sense, it does not surprise if evenfalse theories get the right answer about ½ of the times.Existential claims become more and more probable in proportion tohow weakly their subject is characterized. For instance, if T isan astronomical theory, successfully predicting

(a) the existence of a hitherto unknown planet somewhere in theuniverse,

it receives very little support from this prediction: for, beingscarcely informative, it follows from a host of possible theories,including false ones, and being a priori probable it is likely to betrue anyhow. So the truth of T is not the only plausibleexplanation of this success. On the other hand, if T predicts

(b) the existence of a hitherto unknown planet in the solarsystem,

this, if true, confirms it much better, since the chanceexplanation is much less plausible. But if T successfully predicts

(c) the existence of a hitherto unknown planet, together withits exact mass and orbit

(as Newton’s gravitation theory did with Neptune), it gets highlyconfirmed. The reason is that prediction (c) is very informative,hence a priori improbable; so it very unlikely that, among theinfinite false theories compatible with known data, by sheer luck

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the theorist has picked one that in addition predicts such rich,precise and improbable new datum. It’s more likely that T is true.Thus, only a priori improbable predictions are strongly confirming.An example of predictive success which cannot be plausiblyexplained by chance is the value predicted by quantumelectrodynamics for the magnetic moment of the electron:1159652359x10-12, where the value obtained by experiment is1159652410x10-12. On some admittedly questionable but reasonableassumptions John Wright (2002, 143-144) figures that the a prioriprobability of such an agreement is as small as 5x10-8.

The information content of a prediction can be conceived in ausual way as the class of possibilities it excludes. If we aredealing with a space of infinite possibilities, it can be measuredby the class inclusion relation; if instead we model a space offinite possibilities (for instance through the basic vocabulary ofour chosen language, or through the minimal differences detectableby instruments, etc.), information can be measured by counting theexcluded possibilities or, as in information theory, the number ofbinary decisions needed to exclude them. In any case, informationcontent and a priori probability can be evaluated only relativelyto a language or conceptual scheme providing a partition of thespace of possibilities, and to background information on therelative weights of these possibilities. Nonetheless, as shown bythe above examples, often the comparison of predictions forinformation content and a priori probability has a clear sense and afairly definite result for any partition of the space ofpossibilities acceptable in the light of our independent acceptedtheories.

The need of an a priori improbability constraint on novelty isillustrated for instance by Hutchison’s (2002) criticism of the nomiracle argument: he points out that even Rankine’sthermodynamics, a radically wrong theory, made a novel prediction,the existence of an entropy function. So, he claims, this was a“lucky guess – the sort of things the no-miracle realists tend todeny” (2002, 113): even radically false theories can make novelpredictions. But that guess was not so lucky, after all: asexplained by Hutchison himself, Rankine arrived to that predictionby considering that “it is trivially true that there is a state-function S* that satisfies the relationship characterizing entropy(viz., ΔH=∫T.dS*) for adiabatic changes. For in such changes ΔH=0(by definition), so any constant S* mimics the entropy!” (ibid.).From this premise, Rankine hazardously inferred that such afunction existed also for non-adiabatic changes. So, knowing that

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there was an entropy function for adiabatic changes, Rankine facedthe existential question if such a function existed also for thenon-adiabatic ones, and the yes/no question whether adiabaticchanges are like non-adiabatic ones, in this respect; but neitheranswer to these questions was so a priori improbable, and neitherwas particularly favoured by antecedent evidence. So, hisprediction was enough a priori probable to succeed by chance, hencenot really novel. Rankine also made a much more informative andless probable prediction, the numerical value of the function: ifsuccessful, it would have supported a no miracle argument. But, tonobody's surprise, he did not get it right, thus confirming acontrario the cogency of the no miracle argument when based on a prioriimprobable predictions.

According to Lyons (2002) another counterexample to the nomiracle argument is provided by caloric theory, which in spite ofits falsity predicted that the rate of expansion is the same forall gases. But if the state of the art faced caloric theoristswith a question on the sameness of the expansion rate for allgases, they could only answer yes or no. So, in the absence ofevidence to the contrary, it was not too improbable that areasoning from false premises concluded to the right answer ratherthan to the wrong one. So, that prediction was no counterexampleto the no miracle argument.

3.3 HeterogeneityAnother condition for novelty, needed to exclude explanationsalternative to accommodation and truth, has to do with theuniformity and graduality of nature and the general scope of lawsand theories: when a theory is conceived to account for a body ofold data, typically it will have much wider consequences: it willalso license predictions about a wide body of putative “new”empirical phenomena, different but similar to the earlier ones.Moreover, because of the uniformity of nature, it is probable thatthese predictions of phenomena resembling the old ones come outtrue. So, even a false theory is likely to make true predictionsabout phenomena similar to those it has been engineered toaccommodate. Hence, these predictions cannot confirm much.

For instance, suppose T is a chemical theory, whose author madean essential use of old data ODT, consisting in the melting pointsof copper, iron and aluminium observed in a number of pastoccasions; most likely T will predict that

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(sf): these metals will have the same melting points in thefuture. Strictly speaking, (sf) is new, but only in a pickwickian sense,and it adds little or no confirmation to T. One might think that(sf) does not confirm much, because it is not really unknown,since it is made very probable by induction over ODT. Lakatosseemed to suggest so:

If I already know P1 ‘Swan A is white’, Pω ‘All swans are white’represents no progress, because it may only lead to thediscovery of such further similar facts as P2 ‘Swan B iswhite’. So-called ‘empirical generalizations’ constitute noprogress. A new fact must be improbable or even impossible inthe light of previous knowledge (Lakatos 1970, 118 fn. 2).

But the problem is not that (sf) is practically known: for we haveseen that a prediction can be novel and support the no miracleargument even if the datum was plainly known, as long as it wasnot used essentially. The problem is rather that (sf) ishomogeneous to the essentially used data ODT. In science phenomenaare normally considered not as single events, but as types ofrepeatable events, which can be observed over and over. In thissense, (sf) is the same phenomenon as the old ones, it belongs tothe same set ODT on which T is based, so in a sense it has alreadybeen used any theory accounting for ODT is likely to predict (sf),independently of being true or no.

But our chemical theory T might predict more than just ODT and(sf): for instance, it might include assumptions on the atomicstructure of elements, from which the melting point of differentmetals could be derived. These predictions would differ from ODT

more than (sf), so if born out they would confirm T to a greaterextent. Still, they would concern, if not the same phenomenon, atleast a phenomenon of the same type (the melting point of metals).But if T also predicted radically different phenomena (e.g.,different properties of metals, or different properties ofdifferent elements) it would be much more confirmed. So, only theprediction of data which are heterogeneous with respect to thoseessentially used decisively confirms theories, and the moredifferent are the predicted data, the stronger they confirm.

Although heterogeneity (like similarity) is an intuitivelyclear notion, it is not easily characterizable, since it isgradual and relative. But our criterion can be that a datum d isheterogeneous to the essentially used data ODT when it is notinferable from ODT by some standard generalization procedure,without essentially involving the theoretical (unobservable)

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mechanisms of T. This is because the no miracle argument appliesonly to the assumptions of T which are necessary to the derivationof d. So, if d could be derived independently of such assumptions,it wouldn’t be decisive evidence for T.

This criterion yields at least the following three conditionsfor heterogeneity: first, d should differ from ODT qualitatively,and not just quantitatively. For instance, Leplin (1997, 77-78)requires that d is not derivable from ODT just by supplyingquantitative measurements to effects which are only qualitativelydescribed in ODT: this is clearly to avoid that the successfulprediction could be explainable just by the use of old data andtrial and error and standard mathematical corrections. Forinstance, Hutchison (2002, 112) holds that in spite of holding aradically wrong theory, Rankine was able to predict the “new”result of the specific heat of saturate steam by a method “veryclose to trial and error”. That prediction, therefore, was notnovel in the sense we are looking for.

But secondly, d should not be deducible from any mathematicalgeneralization which could be warranted just on the basis of ODT

and standard statistical techniques, such as regressive methods.10

That is, d should not be a phenomenon of the same type as ODT, onlyin a different range of the values of certain quantitativeparameters. For instance, in 1884 Le Châtelier, working byregressive techniques on the concentrations observed in a numberof chemical reactions OR, found there is a characteristicequilibrium constant for each reaction. This principle can also bederived (by suitable approximations) from Gibbs and Boltzmannstatistical mechanics, and so confirms it. All subsequentlydiscovered reactions have been found to obey the same principle,but these data do not provide any novel confirmation, since they areinstances of the same mathematical generalization of the old dataOR. A decisive confirmation of statistical mechanics, instead, isprovided by its ability to explain also totally differentphenomena, as the increase of entropy.

Or again, in 1896 Wilhelm Wien produced a formula for theblackbody radiation which was based on the data available at thetime, collected in the range of low cavity temperatures and highradiation frequencies. In 1899 Planck proposed a “classical”blackbody theory, from which Wien’s formula could be derived.Later on new experiments provided data for higher temperatures andlower frequencies: if they had obeyed Wien’s formula, they wouldhave been different, but deducible from a mathematical10 I owe this suggestion to Vincenzo Fano.

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generalization of the earlier ones, and so homogeneous to them;hence, although in accordance with Planck’s 1899 theory, theywouldn’t have confirmed it as novel predictions are supposed to do.Instead, they didn’t fit Wien’s formula, but a different formulaby Heinrich Rubens. So in October 1900 Planck tried to interpolatebetween Wien’s and Rubens’ formulas by mathematical techniques andby his assumption of quantum oscillators, thus coming up withPlanck’s law. Obviously neither the earlier data nor the recentones were novel with respect to it, and this explains why Planckhimself didn’t believe that his quantum assumption was physicallytrue. That hypothesis was only accepted five years later, whenEinstein showed that it could also account for a heterogeneousphenomenon, the photoelectric effect.

Thirdly, in the case of qualitative theories, d should not bederivable from ODT by simple induction, or by inductivegeneralization and deduction: if T is based on the observation ofa variety of elements S1, S2, …Sm of kind S statistically sufficientto warrant the generalization that all S are P, d should not bethe fact that a yet unobserved further element Sn of S is P. Or ifT is based on the observation that each member of S has one of theproperties P1, P2…Pm which are statistically representative of thetype P, d should not be the fact that a member of S has a furtherproperty Pn of type S.

Of course, deciding whether an item is inductively derivablefrom a given body of data presupposes a number of backgroundassumptions: e.g., what counts as the same property, or the samekind of entity or property, depends on the conceptual scheme bywhich one “slices up” the world; and if a sample is sufficientlyrepresentative of a certain kind depends on a large quantity ofbackground beliefs. So, judgements on heterogeneity, hence on thenovelty of d, must necessarily be relative to one’s epistemic andconceptual background.

Moreover, although heterogeneity is a qualitative difference,it still admits of different degrees, just like improbability,since kinds come in hierarchies, and items of different kinds atone level may still be part of the same kind at one or moresuperior levels. For instance, dogs and wolfs are differentspecies, but both canids; canids and felines are differentfamilies, but both are carnivores; etc. So, a cat is heterogeneousto a dog, but an ape is more heterogeneous, etc.

The heterogeneity requirement is recognized as a constraint fornovelty by Leplin (1997, 63), and it closely resembles theinductive principle that the probability of a generalization

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increases with the number of observed instances only if they are“so far distinct that they are not inferable one from the other”(Keynes 1921/2007, XX, § 6, p. 238; see also XVIII, § 4; XX, § 1),or that the more a sample of A’s reflects all the differencesamong A’s, the more it supports the generalization that all A’sare B. Of course a theory is not a mere empirical generalization;but both typically unify a class of phenomena much larger thanthat for which they were originally conceived. Hence, in bothcases, any new instance confirms the extra-content of thehypothesis in proportion to its difference from the originalbasis.

Summing up, prediction of a datum d can be considered novel inthe sense of warranting a theory T in accordance with the nomiracle argument if at least the following conditions aresatisfied: (1) d was not used essentially in constructing T, (2) dis not a priori probable, and (3) d is heterogeneous in comparisonwith the essentially used data.

3.4 Functional vs. historical novelty It follows from this account that being novel in this sense ismatter of degree, for both heterogeneity and a priori improbabilityare gradual. In § 4 we shall see that also inessentiality isgradual. Therefore novel predictions do not warrant theoriesequally, and only the most markedly novel predictions can make atheory practically certain. This agrees with a common intuitionthat confirmation comes in degrees. Another consequence is thatnovelty is relative in various respects: first of all to theories,for a datum may have been used essentially in the construction ofa theory but not of another; but then also to conceptual schemes,spaces of possibilities, and background beliefs, for it in onlyfrom the standpoint of these variables that improbability andheterogeneity can be evaluated. So, in any case, it cannot be apurely logical concept. This is confirmed by the history ofscience, showing that confirmation is sensitive to the epistemicstandpoint from which theories are evaluated.

The historical novelty of d (i.e., not having been known, intendedor used) per se is neither necessary (as we have seen) norsufficient: for if d is a priori probable or homogeneous to the olddata, even if not known or not used, it confirms little. Butshould a datum fulfilling conditions (1)-(3) be called ‘new’? Insome important sense yes, since, being heterogeneous, it is“qualitatively new” with respect to “old” data; being a prioriimprobable it is “epistemically new” with respect to a priori odds;

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and being inessential it is “new” with respect to a narrower fieldof data essential to the construction of the theory. In thissense, one might speak of “functional” novelty (as opposed topurely temporal, psychological or historical novelty), and claimthat functionally novel predictions confirm more than otherpredictions, and the more functionally novel they are, the morethey warrant belief in theories, up to practically certainty. Onthe other hand, if one feels that the term ‘new’ has a temporal,psychological or historical connotation, and wishes to preserveit, s/he may call “qualified” the data fulfilling conditions (1)-(3), and claim that the predictions of qualified data confirm morethan other predictions, and the more qualified they are, the morethey warrant belief.

Analogous terminological alternatives are to be faced for otherrelevant terms: the etymology of ‘prediction’ has a temporalconnotation, but in philosophy of science the term is mostly usedas a temporally neutral synonym of ‘consequence” (e.g., Lakatos1970, 116, fn. 4). Scerri and Worrall (2001, 424) distinguishbetween ‘accommodation1’ (non ad hoc retrodiction of knownphenomena, which has confirming power), and ‘accommodation2’ (an adhoc account, not confirming). Similarly, Brush has remarked that‘accommodation’ “with its connotations of adjustment, compromise,and low level empirical curve-fitting” is not “the onlyalternative to ‘prediction’… In modern physics a theory may beaccepted because it gives the best explanation, or at least aconvincing logical deduction from simple postulates …” (2007, 258;1994, 135).

3.5 What is right in predictivism and in deductivismThat predictions can be functionally new and support theories verystrongly, even if not historically new, accounts for the deductivistpoint (widely supported by the history of science) that not only(historically) novel consequences confirm theories (for example,the anomalies of Mercury’s perihelion strongly confirmed GeneralRelativity even if known well before, because they werefunctionally new). But also the counterpart predictivist intuitionis correct, namely that not all consequences confirm equally, forthe functionally novel ones confirm to a higher degree.

Yet, a historically novel datum is also a fortiori inessential(since it was not used); hence, if in addition it is a prioriimprobable and heterogeneous, it counts as functionally new. Sincein paradigmatic cases the predicted data in fact are a prioriimprobable and heterogeneous, and these properties are so obvious

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to be overlooked in the analysis, this may explain why some havesimply identified the condition for a higher level of confirmationwith historical novelty. Historical novelty is also important fromthe point of view of our subjective assessment of how a predictionsupports a theory, as opposed to how it objectively supports it:11 it maybe difficult to appreciate whether a datum was used essentially ornot, but in general it is much easier to see that it was not knownor used, and this (together with heterogeneity and a prioriimprobability) is enough to establish functional novelty. I shallsay more on this in § 6.

These considerations dispel the paradoxical air of deductivistobjection (I): while Jill did not use datum d, John did not use itessentially: the very fact that Jill did not use it shows that alsoJohn, who by hypothesis is in an equal epistemic situation, couldhave done without using it. So, d is inessential for both:inessentiality is relative to theories and epistemic situations,but independent of theorists. Moreover, if d is also heterogeneousand a priori improbable, it is for both, since heterogeneity is arelation between d and the old data, and a priori improbability is alogical property of d. Hence, if d is functionally new, it has thisproperty for both John and Jill, and confirms T for both of them:functional novelty is a theorist-independent notion. John, havingused d, might not be aware that d confirms T in this way, but ifhe met Jill and learned that she predicted it, he would adequatehis own level of confidence in T to hers. Jill, on the other hand,would not change her level of confidence in learning about John’swork, for d was functionally new for him, too.12 To this extent,deductivists are right: confirmation is independent of suchhistorically contingent facts about theorists as their intentions,knowledge or usage of the datum: “the time-order of theory andevidence is of no significance in itself”.13 But predictivists arealso right, as functionally novel data confirm more than theothers.

In § 2 we noticed a paradoxical contradiction between thepredictivist (and realist) point that(PR) the no miracle argument applies to prediction but not to

confirmation; therefore prediction, but not accommodation, canconfirm up to practical certainty.

11 For this distinction and the related problems, see Lipton 1991, 177-183.12 This solution of the twin scientists paradox is similar, althoughstanding on a more complete basis, to that proposed by Lipton himself: (1991),182.13 As conceded by Scerri and Worrall (2001, 423); see also Worrall (1978),50-51, 68.

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and the deductivist point that (DE) there is no advantage of prediction, and accommodation can

also confirm quite strongly, up to practical certainty. Now we see why in fact both (PR) and (DE) can be true, but not inthe same sense: (DE) is true only when ‘accommodating’ meansaccounting for historically old, but functionally new data; and inthis sense the no miracle argument does apply to accommodation,for truth is the only plausible explanation for predictionsfulfilling my conditions (1), (2) and (3), even if historicallyold; so (PR) is false. But if ‘accommodating’ means accounting fordata that are not even functionally new, the no miracle argumentdoes not apply to it, so (PR) is true, and (DE) is false.

Since (historical) novelty is not necessary to high degrees ofconfirmation, also the deductivist objections (II) and (III),while correct against a historical version of predictivism, areineffective toward “functional” predictivism: for the latter doesnot imply that if we knew all the phenomena in a given domain wecouldn’t have decisive evidence for theories in that domain(objection II), since known phenomena can still be functionallynew, and so highly confirming. Moreover, functional predictivismdoes not imply that ignoring some of the phenomena in one’s fielddoes not, per se, make a theorist more reliable (objection III):ceteris paribus, if we are told that T’s author ignored some of therelevant data, our confidence in T should be weaker. Only if itturns out that the ignored data are predicted by T, our confidenceshould increase: for knowing the data is epistemically desirablejust in order to be able to account for them, a goal that in thishypothesis has already been achieved.

4. The nature of novelty: non ad-hocness, independence and consilience

In order to get clearer about the conditions for novelty, and toaccount for the remaining deductivist objections, we must now askwhat exactly is inessentiality, so carrying out my earlier purposeto further analyze Worrall’s and Leplin’s idea that a datum d wasnot used essentially when it could have been predicted without beingused. It is not enough to explain that d could have been predictedin advance of being observed because it already followed from Tdirectly, or with very natural collateral assumptions, as Worralldoes: for this would be a purely logical fact about T, requiringno explanation, in particular no explanation in terms of truth.

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Rather, we need to explain what allowed (or could have allowed) tochoose T (rather than any theory not predicting d) without thehelp of d.

Now, while some predictions may be a direct mathematicalconsequence of a theory, in general a theory predicts a givenphenomenon only when supplemented by a series of auxiliaryassumptions {…Ai…}.14 Hence, one could have predicted d without usingit, if and only if without using d as an input one could have foundboth a theory T and the auxiliary assumptions {…Ai…} from whoseconjunction d follows.

This, in turn, is possible if (and, except for miraculouscoincidences, only if) both T and {…Ai…} are plausible independently of d,so that a rational theorist could have adopted them even withoutknowing d. Now, to spell out this condition, (i) T is plausible independently of d iff there exists a set of old

data ODT not including d, such that T is the best account of ODT.(ii) Each auxiliary assumption Ai is plausible independently of d

iff it is either an empirical datum, or a plain inductiveextrapolation from empirical data,15 or it is derivable fromanother theory Ti and a further series of auxiliary assumptions{…Aj…}, both plausible independently of d.

But Ti and {…Aj…}, are both plausible independently of d iff (iia) there exists a set of data ODi not including d such that Ti isthe best account of ODi, and (iib) each Aj is either an empirical datum, or a plain inductive

extrapolation from empirical data, or it is derivable from afurther theory Tj and a further series of auxiliary assumptions{…Ak…}, all of them plausible independently of d.

The recursive nature of this characterization launches a regresswhich ends only when all the auxiliary assumptions involved areempirical data or inductive extrapolations from them. So, jumpingdirectly at that point, d could be predicted without being used iffit is inferred from T together with {…Ai…}, where both T and {…Ai…}are plausible in the light of the vast set VD (not including d) ofall the empirical data involved in that regress; in other words,iff they could be inferred from VD, either directly by induction

14 Scerri, Worrall (2001), 440. Instead Leplin (1997) ignores the role ofauxiliary assumptions.15 Like the melting point of a metal in future occasions is extrapolatedfrom the same value in observed occasions.

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or indirectly via further collateral theories {…Ti…} and assumptions{…Aj…}) inferred from them.16

Thus, saying that d is functionally novel (or, if one prefers,qualified) entails that neither T nor {…Ai…} have been fudged (Lipton1991, 168-177) or tinkered with in order to accommodate d, and thatT genuinely explains d, rather than just fitting it by an account adhoc (Worrall 1989b, 148; Scerri, Worrall 2001, 423), or that d hasnot been overfitted (Hitchcok and Sober 2004). Functional novelty,however, does not reduce to non-fudging or non-overfitting: forthey are just features of good scientific methodology, but goodmethodology does not warrant practical certainty, as functionalnovelty does in the best instances. Thus, here I am not justsaying that functionally novel predictions confirm more becausethey are not ad hoc:17 rather, non ad-hocness is crucial forconfirmation because only by excluding ad hoc accommodations truthcan remain the only plausible explanation of success. Moreover,this analysis of novelty agrees with classical accounts the methodof hypothesis, like Whewell's, requiring that after being madeinitially plausible by explaining old data (ODT), theories arefurther confirmed by predictions about new kinds of data (d).18

Besides, since a novel prediction d is heterogeneous to theessentially used data ODT, T contemporarily offers the best accountof at least two unrelated fields of phenomena: ODT, since it mustbe plausible independently of d; and d itself, since the derivationof d must not be ad hoc, but independently plausible. So, we have aninstance of what Whewell calls the “consilience of inductions”(Whewell 1847, 1: xxxix; 2: 65 ff., 77-78), which according to himmakes the truth of an hypothesis practically certain.

In fact, we just saw that there is more: d was predicted by theconjunction of T with the auxiliary assumptions {…Ai…}, each ofwhich follows from a different theory Ti, which supplies the bestaccount of an unrelated field of phenomena. But this involvesfurther assumptions, and so on. So, we have a number ofindependent theories (T and all the theories {…Ti…} involved inderiving {…Ai…}) converging on a risky (a priori improbable)prediction, which proves to be correct: it would be a miraculouscoincidence if T or some of the theories {…Ti…} were completelyfalse, but jointly had a correct consequence d, totally unrelated to16 It might be suggested that given the holistic nature of confirmation,this regress will eventually involve all the available empirical data. I don’tknow if this must necessarily be the case.17 As Worrall suggests in 2006, 39.18 (1858), 86-88. This was brought to my attention by an anonymous reviewerfor this Journal.

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the data they were originally intended to account for. So, theconfirmation of just a novel prediction reverberates also on manybackground theories. Notice that while the conjunction of truehypotheses has only true consequences, there is no guarantee thatthe conjunction of empirically adequate (or predictively similar,etc.) theories has only true consequences (Friedman 1983, 244-247;Psillos 1999, 205 ff.). So, antirealists cannot explain thisfeature of novel success by empirical properties weaker thantruth, like empirical adequacy (van Fraassen 1980), empiricalequivalence (Stanford 2000), modest surrealism (Lyons 2002, 78),etc.

This reasoning is schematized in the following pictures.Picture 1 highlights a question: the novel prediction of d (forinstance, the precise value for the magnetic moment of theelectron) is the joint consequence of T and auxiliary assumptionsA1…An, in turn consequences of theories T1…Tn. But T, T1…Tn haveoriginally been designed to account for bodies of old data OD, OD1…ODn very different, hence apparently unrelated, to d. So, can it bea coincidence that they have as a joint consequence the correct d(e.g., the precise value for the magnetic moment of the electron),rather than any of the infinite other potential data potd1…potd∞

(for instance, any different value for the same parameter; or evenany other totally unrelated prediction)?

Picture 2 schematizes the only non miraculous answer to thispuzzle: theories T, T1…Tn are not just empirically adequate (savingthe old data OD, OD1…ODn, plus d), but true descriptions of as manyunobservable systems, of which OD, OD1…ODn are the observableeffects. Moreover, while each unobservable system i causes the setof phenomena ODi, they jointly cause d. Only this can explain whyT, T1…Tn have as a joint consequence precisely d, rather than anyother possible prediction.

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Peter Kosso emphasises the confirming power of independence whenthe convergence of various independent theories on the sameprediction testifies the otherwise unknown truth of thatprediction: for instance, as when Perrin found the same value forAvogadro’s number using theories from different disciplines:chemical, thermodynamic, and electrical; or when independentmethods, such as carbon 14, geological theories, or evolutionarytheories, attribute the same age to a fossil (1992, VIII.4, IX.4).But here we see that confirmation works also backwards: theempirically ascertained truth of the joint consequence of variousindependent theories testifies the truth of each of them.

So, the advantage of functional novelty encompasses theadvantages, widely discussed in the literature, of non fudging,non overfitting, non ad-hocness, consilience of inductions,convergence of independent theories, and Keynes’ distinction ofconfirming instances. Indeed, this agrees with a standard realistanswer to the empirical underdetermination objection, according towhich no amount of empirical data in accordance with a theory canwarrant its truth, since from a logical point of view there can beinfinitely many theories compatible with any body of data. Inresponse, realists grant that merely saving certain phenomena isnot enough, but claim that a theory must also explain them, i.e.,provide a non ad-hoc account which is simple, plausible, complete,coherent with other accepted theories, unifying, consilient, etc.;and it is far from obvious that there is more than one theoryfulfilling all of these requirements (Psillos 1999, 171-176;

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Doppelt 2005). But this is to say, in our terms, that theories canbe significantly warranted only by phenomena which arefunctionally new for them. Antirealists typically reply that whilenon-empirical virtues may pragmatically motivate our preferencefor one theory over another, they have nothing to do with truth.Moreover Laudan holds that for any theory supported by evidenceand ampliative inference rules, there might by other incompatibletheories equally well supported (1996, 33, 53). But if explaininga phenomenon in a virtuous way amounts to the prediction of afunctionally new phenomenon, save for a miracle it is extremelyunlikely that a theory virtuously explains certain phenomenawithout being true (more precisely, without the assumptions (A-B-C) holding for it). So both antirealist replies can be countered.

In § 3.4 I noticed that functional novelty is matter of degree,for both heterogeneity and a priori improbability are gradual. Now wesee that also inessentiality is gradual, since it depends on thehow plausible are the theory T and the assumptions {…Ai…},independently of d, and this in turn depends on how good are theexplanations provided by the theories T and {…Ti…} to theirrespective data (if d is inessential they are the best possibleexplanations, but even the best ones may be more or less good).So, the better they are, the more plausible are T and {…Ai…}, andthe less essential is d.

We can now deal with the deductivist objection (IV) topredictivism: if novelty is relevant to confirmation, historicalresearch on which data the theorist knew when she constructed atheory T should be relevant to our assessment of T; but obviouslyit is not, for practicing scientists never resort to suchresearches when evaluating a theory. In response, it should benoticed that

1) historical research would apply to theories of the past; but bynow the great majority of those theories have been convincinglyeither confirmed or disconfirmed by other means, so the novelty ofthis or that original prediction is no longer crucial to ourassessment, and the issue is not even raised. For instance, it hasbeen raised the doubt that the white spot had been observed evenbefore Fresnel, Poisson and Arago’s experiment (Worrall 1989b,152); but since our assessment of the wave theory of light is nowsettled on the basis of subsequent theoretical developments,inquiries on that question may interest only the history ofphysics, not physics itself.

2) Even supposing scientists were still seriously wondering onthe confirmation degree of the past theory T, historical research

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could help to solve these doubts only by discovering whether asome datum d predicted by T was unknown, or not used, or at leastinessential in the epistemic conditions of the time (forinessentiality in present or future epistemic conditions could notbe established by historical research). But such an inquiry can bea hopeless enterprise for lack of documents; and if one needs toevaluate inessentiality, that involves deciding whether T and theassumptions {…Ai…} were independently plausible in the epistemicsituation of the time; but this is more complex than justevaluating the process through which T was introduced, and itmight be too difficult to accomplish. Therefore a much moreefficient strategy would be investing energies in directly lookingfor new empirical tests.

On the other hand, in a large number of cases historicalresearch may not be needed for it is obvious that d was utterlyunknown (as the existence of Uranus, Gallium, Germanium, andScandium, the bending of light, or the background radiation), ornot used, or not used essentially; for instance, it is notcompletely certain that Einstein did not use the data aboutMercury’s perihelion in constructing General Relativity (Gardner1982, 5; Earman, Glymour 1978), but we don’t need to find thisout, for it is obvious that the theory was independently plausibleon the basis of many other empirical and theoretical reasons; so,even if those data were used, they were not essential.

3) In other cases, of course, it is plainly known that dwas used essentially, so again no historical research is calledfor.

4)Even when it is not clear whether a prediction was novel ornot, the purely historical question (whether it was unknown, ornot used, or not essential in the theorist’s epistemic situation)may be easily and usefully bypassed by asking the theoreticalquestion: if its use would be essential by our present lights. In fact,a negative answer to this question would be enough to establishthe functional novelty of the prediction, hence to confirm thetheory. I will come back on this in § 6.

5) Of course, confirmation is a much more live issue for recentand currently discussed theories, for which the functional novelty ofpredictions is of the utmost relevance. But clearly, it is notassessed by historical research, but by directly analyzing whetherthe prediction is a priori improbable and heterogeneous, andwhether the theory is independently plausible in the light ofcurrent background knowledge.

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6) For all these reasons it is unlikely that historicalresearch be relevant to our assessment of functional novelty.

5. Confronting the putative historic counterexamples

Also the purported historic counterexamples to predictivism cannow be assessed more clearly: they show that historical novelty per sedoes not make a difference to confirmation, but say nothingagainst the epistemic asymmetry between the functionally novelconsequences and all the others.

For instance, the case of Mendeleev’s Periodic Table (putativecounterexample (V) above) is historically very complex:predictions were not straightforward, there were various wrongpredictions, etc. Scerri and Worrall (2001) claim that thediscovery of the newly predicted elements Gallium, Germanium andScandium as such did not enhance much the acceptation of theTable, while Brush (1996) argues that it did, at least in Americaand Britain. But even if it did not, it can be noticed thatalthough the Table accommodated various properties of the 62previously known elements, very likely it had been conceived (orat least it could have been conceived) by considering only a subsetof those properties and those 62 elements (say, some 30? or 40? or50?) (Worrall 2005, 824). Hence, all the other data, even if used,were inessential; besides, they were very informative andheterogeneous (given the wide diversity among elements and theircharacteristics). Hence, many of those data, even if previouslyknown and used, were functionally novel: so there were alreadyplenty of reasons to believe in the Table, and the previouslyunknown elements were just three more on the top of a large number(say, 32, or 22, or 12?) of historically old but functionally newelements predicted; so, quite naturally their marginal confirmingpower was not very high. (Actually, each of the 62 known elementsmight probably have been member of a subset of elements sufficientto make the Periodic Table plausible: so each of them wasinessential, hence functionally new).

In fact, the motivation for the Davy Medal remarked thegenerality of the classification system offered by the PeriodicTable, and the “marvellous regularity” with which the propertiesof various elements followed from it (Brush 1994, 139-140); inother words, it acknowledged that the Table was contemporarily thebest account of different heterogeneous sets of data (indeed, ofall the heterogeneous data available at the time); so, it could be

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accepted because many of its data were functionally, even if nothistorically, new.

I already commented on the data about Mercury’s perihelion:objection (VIII) is that they counted as strong evidence forGeneral Relativity, although they were known to Einstein, andperhaps even used by him; so, it is at least questionable thatthey were historically new. But clearly they constituted afunctionally new prediction, since even at the time it was obviousthat they were a priori improbable, since they were very detailed andprecise; inessential, since the theory was, quite independently ofthem, by far the best available account both on empirical andtheoretical grounds, and it entailed them without ad hocassumptions; and they were heterogeneous to what Einstein hadessentially used (mainly, the contradictions between Newton’sgravitation theory and Special Relativity.

So, in general, it is explainable why Brush doesn’t know of anycase in which novel predictions were crucial in theory acceptance:for he thinks of historical novelty, which is neither sufficient nornecessary to confirmation. Typically, in fact, theories are noteven proposed unless there are some known but non trivial (i.e., apriori improbable) phenomena, in at least a few heterogeneous areas,for which they account in a detailed and non ad hoc way. So, atheory is usually put forward with its endowment of functionallyeven if not historically novel evidence, which ensures it is takenin serious consideration. More functionally new predictions can bederived after its appearance, as it is discussed and developed,and finally even historically new predictions may (but need not)come along. So, it may well be that in fact historically newpredictions are seldom crucial.

It seems also clear that Heisenberg’s matrix mechanics andSchrodinger’s wave mechanics (putative counterexample VII) werereadily accepted in spite of the fact that they licensed only twominor historically new predictions, and not thanks to them, because theyprovided the best account of a very wide field of heterogeneousphenomena, explaining anomalies of predecessor theories andoffering a single consistent method of calculation instead ofvarious ad hoc rules (Brush 1994, 137): so, they were confirmed bya wealth of functionally novel evidence.

As for Fresnel’s prediction of the white spot (objection VI),there is no question that it was historically novel (probably notknown, certainly not used, a fortiori not essential); hence, since itwas highly improbable and heterogeneous, it was functionallynovel. But then, why the French Academy commission did not wait to

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control the prediction, and did not stress it in the motivation ofthe award? And why after its confirmation the corpuscularistmembers of the commission did not convert to the wave theory?

First, it should be noticed that the commission was not,primarily, to decide whether Fresnel’s theory was to be acceptedor not, but which memory was better, Fresnel’s or his opponent’s.Now, to make this decision, they did not need to take into accountmore than what was acknowledged by Arago, i.e. that Fresnel’stheory nicely explained a number of different phenomena (cited inWorrall 1989b, 143); in fact, the second competitor’s memory wasrather weak anyhow. Much the less the commissioners needed to beconvinced of the wave theory to the point of questioning their owntheoretical commitments.

Secondly, the jury acknowledged that Fresnel’s hypothesisaccounted for many different known phenomena of diffractionpredicting very precise measures, and in a very general way,moving from abstract theoretical considerations, with no need ofspecial assumptions for particular cases. Hence, Fresnel could havepredicted those known phenomena in advance, and it doesn’t matterwhen they were actually discovered (Worrall 1989b, 150-151). So,the commission actually motivated the prize by acknowledging thatFresnel’s memory had a number of what I am calling functionallynew predictions, even aside from the white spot.

But then, shouldn’t the corpuscularist members of the jury haveconverted to the wave theory, even before the white spotprediction was confirmed (and a fortiori after that)? This would seemto refute my claim that novel predictions offer sufficient reasonsto believe a theory is true.

However, although we may generally assume that a strategyfollowed by a majority of scientists is rational, in thisparticular case we are considering the behaviour of just threepeople in a single circumstance: statistically not a significantnumber, with respect to which an important role may be played byidiosyncratic factors, such as conservatism, sociologicalallegiances, lack of proper attention, etc. Moreover, it wasnatural for them to be very cautious in the circumstance: both thecorpuscular and the wave theory had been discussed for centuries,both had some predictive successes, but various unsolvedproblems;19 hence, the jury members interpreted Fresnel’s theory

19 One juror, Poisson, wrote: “The theory of emission and that of waves bothencounter great difficulties; time and the future work of physicists andmathematicians will perhaps end by settling these doubts …” (cited in Worrall1989b, 140).

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“positivistically”, avoiding any statement on the wave hypothesis(Worrall 1989b, 140, 144). Probably they implicitly adhered to asort of reversed “partial” or “structural” (Worrall 1989a) realismwith respect to the wave theory: they may have thought it had sometrue components, something hooking up to some real structure,while still remaining convinced that its overall picture wasfalse, and the corpuscular theory, as a whole, was closer totruth.

This may also explain the rejection of Dirac’s relativisticquantum theory, in spite of its successfully predicting thepositron (putative counterexample IX): no doubt, a theory may havesome true claims, hence issue some novel predictions, yet beconsidered as false overall, and so rejected as soon another,supposedly better, is found.

6. The epistemic and counterfactual character of novelty

For Worrall novelty and confirmation are not historical, sincethey are independent of the theoretician’s psychology and(especially in the latest writings, and in spite of some passagessuggesting the contrary) of actual use. Thus far I agree with him,but then he claims novelty is a logical property, for it is just arelation of d with T and its specialization T’ which predicts d(2005, 819, 2006, 56). My account has been more complex, instead.Not only I required improbability and heterogeneity, besideinessentiality; but in characterizing inessentiality, in the placeof T’ I introduced the collateral assumptions {…Ai…}, which addedto T produce T’, hence the specific prediction d.

In itself, this is a minor difference; but more importantly, Inoticed that d is inessential if both T and {…Ai…} areindependently plausible, and this means that T and {…Ai…} couldhave been ultimately inferred, inductively or by inference to thebest explanation, from a vast set of data VD not including d(namely, they could have been inferred through a recursive processinvolving the theories {…Ti…} from which the assumptions {…Ai…} arederived, further assumptions {…Aj…} needed to derive {…Ai…} from {…Ti…}, further theories {…Tj…} from which {…Aj…} are derived, etc.).Therefore, I depart from Worrall two respects: first, novelty isnot a relation holding only among T, T’ and d, but among T, {…An…},{…Tn…}, VD, I, F, and d (where I is the function assigning eachassumption An involved in the regress to the theory Tn from whichit is derived, and F assigns to T and to each Tn a subset of VD as

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its empirical basis). Second, this is more an epistemic than alogical relation, since inessentiality involves the notion of bestexplanation, while judgements of improbability and heterogeneityare relative to one’s epistemic background, including at leastconceptual schemes, partitions of spaces of possibilities, andbackground beliefs, which are not logical notions.

But it might be asked whether another element should beincluded in my novelty relation: for the plausibility of ahypothesis depends on which data, background beliefs, scientificmethods are available, in a word, on the epistemic situation,which varies over time. Isn’t then novelty also relative to times,and more precisely to epistemic situations? That is, how are we tointerpret the counterfactual ‘could’ which defines theinessentiality of d: are we saying that even if the theorist couldhave done without d (i.e., T and each Ai used to derive d wereindependently plausible) (1) in her own epistemic situation (i.e.,given her own scientific methods, available data, and backgroundknowledge)? Or (2) only if she had been situated in our, morefavourable, epistemic situation? Or (3) in some more advancedepistemic situation, perhaps only at the “ideal limit ofresearch”? Should the set of data VD (in whose light T and {…Ai…}are plausible) have been available when T was proposed, or evenjust now, or even only at some future time?

We shall now see that (with a minor proviso) it is sufficientthat d is inessential in any of these three senses, for in each ofthese cases the convergence of independent theories andassumptions in jointly producing a true and intrinsically newconsequence could not be plausibly explained except by the theirtruth.

In fact, empirical knowledge increases and research methodsimprove with time (for there are periods in history when scienceregresses, but they are relatively short exceptions to an oppositewell marked trend). Hence, in general, if a true theory orassumption is plausible at one time, typically it will also beplausible at later times. On the contrary, even if a (completely)false theory or assumption is plausible at one time, it may (andoften will) be no longer plausible at a later time. But if atheory T and assumptions {…Ai…} allow the functionally novelprediction of d, they are most probably true; hence they willremain independently plausible, hence confirmed, at later times.

On the other hand, what is plausible at a certain time may havenot been plausible at an earlier time, when fewer data and worsemethods were available. So, it can happen that T and {…Ai…}

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predicting d were introduced at t by essentially using d, and yetone could at a later time t’ introduce them without using d, forthey have become independently plausible. In a case like this dwould objectively count as novel and strongly confirming T already att, because it would be a miraculous coincidence if T and {…Ai…}were not true, and yet on the one hand they jointly entailed d,and at the same time they were the most plausible hypotheses inthe light of methods and data having nothing to do with d, even ifnot available at t. From a subjective point of view, however, T’sauthor could not appreciate this, because, lacking many relevantdata, she had to use d. We might be able appreciate this, but onlyif we live at t’ or after; otherwise, the novelty of d could only beacknowledged in the future.20

In fact, many theories which originally were proposedessentially to account for certain data today would be perfectlyplausible even independently of them. For instance, atomic theorywas originally introduced to account for the chemical regularitiesdescribed by Proust’s law of definite proportions and Dalton’s lawof multiple proportions. Nowadays, however, it would be definitelyaccepted even without them, thanks to data gathered in manydifferent ways, like Rutherford’s scattering experiments,spectroscopy, X-ray crystallography, etc. So, Proust’s andDalton’s laws originally were only objectively inessential, but noware also subjectively so.

Considering them novel might seem odd, since the theory wastailored on them; in fact, it was considered a mere hypothesisuntil it was definitely confirmed by Perrin’s experiments onBrownian motions and Millikan’s experiments with charged oildroplets in an electric field. But supposing Proust’s and Dalton’slaws had not been known earlier, and the theory had beenintroduced just to account for Perrin’s and Millikan’s results, itwould again have been considered a mere hypothesis, untilconfirmed by new heterogeneous data (e.g., Proust’s and Dalton’s).So, no evidence is in itself functionally novel and definitelyconfirming, but only relationally and symmetrically. As we noticedfor the Periodic Table, if each of different sets of data issufficient to make T plausible, each counts as (objectively)novel; the respective time order is unimportant, except for oursubjective assessment of confirmation: whichever comes first, onlyafter the second the novelty of both can be appreciated, and T isdefinitely accepted.

20 The gap between the objective support of d to T, and our subjectiveassessment of it has been discussed by Lipton (1991, 177-183).

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Summing up, if we are asking about objective functionalnovelty, it is sufficient that d is inessential (i.e., T and {…Ai…}are independently plausible) in any of these three senses: at thetime T was proposed, now, or in the future; the only necessarycondition is inessentiality at the ideal limit of research (for itis implied by inessentiality at any other time). If we are askingabout subjective assessment, instead, there must be inessentialityand independent plausibility in the epistemic situation of theassessing subject. Therefore, since the degree of confirmationdepends on the degree of functional novelty, predictivists areright that it is not a logical relation; but deductivists are rightthat it is independent not just of the theorist, but also of theepistemic situation in which the theory is proposed, and of thatin which it is evaluated. Its subjective appreciation, however,depends on the current epistemic situation.

Acnowledgements: I have greatly benefited from comments andsuggestions by Anjan Chakravartty, Vincenzo Crupi, Dennis Dieks,Michel Ghins, F.A. Muller, Howard Sankey and two Referees forthis Journal. I am particularly grateful to my colleagues VincenzoFano and Gino Tarozzi for frequent discussions and useful advices.

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