The whewell-mill controversy about the possibility of false hypotheses in accordance with facts

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1. Mill's interpretation of Whewell as a conventionalistִ

In the third, 1851 edition of his System of Logic Mill accused Whewell of a contradiction in his theory of science. On the one hand Whewell held, Mill said, that it was impossible for two contradictory scientific theories to account with equal success for all the facts. But on the other hand Whewell, versed like no one else in the details of the historical growth of science, also argued that for every case of two competing theories it was always possible to adapt them so that both will account equally well for the same set of facts, and since they are contradictory theories, this amounts to holding that such theories are in fact or can in principle be available:

To the statement that the condition of accounting for all the known phenomena is often fulfilled equally well by two conflicting hypotheses, Dr Whewell makes answer that he knows of “no such case in the history of science, where the phenomena are at all numerous and complicated"[...] Such an affirmation, by a writer of Dr Whewell's minute acquaintance with the history of science, would carry great authority, if he had not, a few pages before, taken pains to refute it, by maintaining that even the exploded scientific hypotheses might always, or almost always, have been so modified as to make them correct representations of the phenomena. (Logicִ:502 III,xiv,6, Jr:330)

According to this passage, Whewell held a vesion of what came to be called, some half a century later, conventionalistic philosophy of science: If Mill is correct in his description,Whewell held that any set of facts can always be explained by any number of theories which may be otherwise "conflicting". Moreover, given any theory which is refuted by some observational fact, it is always possible to reshape the theory so as to make it consistent with, and so explanatory of, this fact, without thereby changing it essentially. So, if Mill was correct, then Whewell was indeed the first philosopher I know of to have formulated and used, as central to his philosophy, the thesis known today as the Duhem-Quine thesis

1.2. Mill's view of explanationִ

Though added in 1851, Mill's accusation remained as a part of the last answer (1872, 8th edition), to Whewell in a dispute which started in 1843, and lasted for 29 years. It touched upon a variety of subjects, from the nature of mathematical truth and deductive reasoning, to the nature of inductive argumentation. However, the central theme, seldom attaining any explicit expression but always there as an undercurrent feeding the two conflicting views, was the nature of truth in scientific explanation.

Mill had argued, as the opening sentence of the above passage hints, that success in explanation of facts can never count as evidence for the truth of a hypothesis. The chapter's title is "Hypotheses", and Mill's leading thesis in it was that hypotheses in science describe the causes of the phenomena and so explain them, "And this explanation is the purpose of many, if not most, hypotheses (Logicִ: 332).

Explanation, in Mill's view, is always (or "mostly") the reduction of the explanandum to its causative components. Thus, where the explanandum is an observed law of regularity, its explanation is its derivation from "the laws of causation from which it results" or if the regularity is itself a law of causation, but is complex, then its explanation is its resolution "into simpler and more general [laws] from which it is capable of being deductively inferred." (Logic Jr: 332)

This view of explanation as reduction to causal components at once determines a basic condition on explanatory theories: they must be true, in the sense of describing existing causes and such as are indeed the causes of the explained fact (regularity, law.) A hypothetical explanation, then, was such that its truth was not known and as a result could turn out to be not an explanation at all. Thus in case it was a false hypothesis, describing causes which do not exist, it is not an explanation at all, even though it does entail the facts (i.e., some regularity or law).

Thus, there is a basic difference between the explanandum and the explanans in their respective referential ontology: Whereas the law of regularity which is to be explained refers to observed phenomena, the explaining causes refer to the non-observed realm, either of componential causal laws which combine to produce the observed regularity, or to componential material causes.

1.3. The Hypothetical Method as a demand of uniquenessִ

This leads to the result that, as a rule, explanations must be hypothetical and so their explanatory function is always in doubt. Thus, their success in accounting for their facts is not sufficient for their being explanations, since they might be false and so not explain.

Mill then details two ways in which this hypothetical nature, and so the doubtful status as explanation, may be surmounted. Either the explanatory cause is first logically deduced from phenomena, or it is laid down as an hypothesis which entails the phenomena but then a proofִִ is added to show that no other hypothesis can replace it. Newton's explanation of planetary motion is used as an example of both of these ways: Newton both deduces the inverse square Law from the Kepler motions of the planets, and also proves that this law not only entails these motions but also that no other law can entail them.(Logic Jr:323). This last procedure Mill calls the Hypothetic Method. He, therefore, does not include under this name the mere entailing of the phenomena from some "merely supposed" (p.322) hypothesis. His Hypothetical Method only starts with a supposed hypothesis, but it must end with a proof of its uniqueness, and so of its truth. Hence the "Hypothetical" Method explainsִ only if it succeeds in surmounting its hypothetical status, and so its name refers only to its first but not to its final state:

It appears, then, to be a condition of the most genuinely scientific hypothesis, that it be not destined always to remain an hypothesis, but be of such a nature as to be either proved or disproved by comparison with observedִ facts. (Logic Jr 325)

1.4. Three ways of saving hypothesesִ

Within this rigorous conception of explanation Mill refers to descriptive, non-causal deductive structures. These gain their certainty by either connecting via their deductive chain only observed phenomena, or in case they refer also to non-observed components their certainty is gained by declaring them to be non-referential. An example of the first is the sine law for refraction of light, and for the latter Mill uses as an example the Ptolemaic astronomy:

And, lastly, we must add to these all hypothetical modes of merely representing or describingִ, [sic], phenomena; such as the hypothesis of the ancient astronomers that the heavenly bodies move in circles; the various hypotheses of excentrics, deferents, and epicycles, which were added to that original hypothesis;...In all these cases verification is proof;ִ if the supposition accords with the phenomena there needs no other evidence of it. (ibid:325)

Thus, in addition to the previous two ways of surmounting the merely hypothetical status of the deductive structure, thereby turning it into an explanation through a proof of the uniqueness of the hypothesis (i.e. either by deducing it from some phenomena, or by proving its irreplacability for entailing the explained phenomena), Mill agrees that a third way exists: By declaring the hypothesis to be non-referential and then nothing more than an instrument for logically connecting phenomena with phenomena. But though this way at once creates a non-hypothetic deductive structure, it thereby loses its explanatory import and becomes mere description. And only because it is non- referential can it be declared that here "verification is proof", and "there needs no other evidence of it" beyond its verification.

1.5. Mill's realism: Distinction between truth and having itִ

Hence, in all other cases except these three, verificis no proof at all. We see, therefore, that because Mill is a realist in his theory of explanation, i.e., because he holds that explanation is causal and thus refers to the unobserved realm of componential laws and "agencies" (such as forces, aether vortices, etc.), he concludes that the mere verification of a hypothesis cannot be taken as its proof, and only if the hypothesis is “both”, causal and proven true,ִ can its deductive entailment of the phenomena be regarded as their explanation. His realism, which he regarded as identical with Newton's philosophy of science and by which he interpreted Newton's work, included not merely the demand for the hypothesis truely describing a vera causaִ (p.326), but also a clear theory of confirmation. According to this, verification could be attained only by deductive derivation from facts (either directly or by a reductio ad impossible), and the only definite conclusion from another procedure is the refutation of the hypothesis. Thus, Descartes' vortex hypothesis would be "perfectly legitimate" if it could be "tested" by observation. Even though it could not be proved, and thus could not be "converted...from an hypothesis into a proved fact", still "it might chance to be disִproved, [sic], ... by some want of correspondence with the phenomena".(327) Which ever way that might go, however, testing for truth and proving or disproving it, is distinct from the truth and falseness of the hypothesis:

But the hypothesis would have been false, though no such direct evidence of its falsity had been procurable. (ibid:328)

Thus, a clear-cut distinction is drawn by Mill between proofִ of truth-value and the possession of it. This is the essence of his realism in the philosophy of science. It entailed the possibility that a false hypothesis might account for all the known phenomena, and this, in its turn, entailed that neither accounting for all the known phenomena, nor the successful prediction of as yet unknown ones, should be taken as a proof of the hypothesis' truth.

1.6. Prediction as merely unexpected accordance with facts and the clash with Whewell

This is one of Mill's most interesting arguments. For though it was well accepted in the Baconian-Newtonian realistic tradition both that no amount of positive confirmation could be regarded as absolute proof of truth, and also that only refutation was a deductively feasible way of reasoning, it was also well accepted in that tradition that the ampliative prediction of unexpected facts has some verificatory weight, beyond that of mere accordance with previously known facts. Mill's argument attacked this instinctive belief and destroyed its validity.

This argument is that the surprise-effect in the true prediction of unknown facts does not change anything in the confirmative situation, which is still only and strictly accordance with facts, and so cannot escape the power of the previous argument about the possibility of false hypotheses being in full accordance with the facts:

But it seems to be thought that an hypothesis of the sort in question [such as the Cartesian vortices, Z.B.] is entitled to a more favourable reception, if, besides accounting for all the facts previously known, it has led to the anticipation and prediction of others which experience afterwards verified. (328)... But it is strange that any considerable stress should be laid upon such a coincidence by persons of scientific attainments...(329)... Though twenty such coincidences [of the predictions of the undulatory theory of light with the facts, Z.B.] should occur, they would not prove the reality of the undulatory ether.(329)

ֶThis is the point where clash with Whewell was inevitable. Whewell's whole philosophy of science evolved around the notion that it was exactly the absolute truth of a scientific hypothesis that emerged through the history of its better and better accord with facts. In this respect, it was Whewell who actually represented the philosophical spiritִ of the Baconian-Newtonian tradition, even though the philosophy of Bacon and of Newton were represented by Mill. Thus, Bacon based his "new induction" on the demand for nothing less than a direct proof of the uniqueness of the hypothesis (through a method of successive elimination of all its alternatives by experimental refutation, (see his Novum Organum.)

The same was the case of Newton's own philosophy of method. He rejected full accord with facts as a truth-criterion as early as 1672, in his dispute with Hooke over his Optics. In the same breath he also went even further than Bacon, and rejected Bacon's uniqueness proof by elimination of alternative hypotheses. His argument for his theory of gravitation as expounded in the Principiaִ was executed by "analysis", in which he derived the law of gravitation from the phenomena of Kepler planetary motions (corresponding to Mill's first way of direct proof of the hypothesis) and then by an inverse "synthesis" in which he derived Kepler motions from the law and proved that any alternative to that would inevitably be refuted by the facts (of the stationary aphelia points of the orbits).

2. The disputeִ

2.1. The chipher metaphor for predictionִ

Whewell, on the other hand, declared that full and complete confirmation of a hypothesis, through the future accord of its predictions (including its derived laws) with as yet non-available facts, is a conclusive proof of its truth. This was no mere slip of the Whewell pen since the facts of the matter are that in his 1849 paper "Of Induction", Whewell declared the following:

If I copy a long series of letters, of which the last half-dozen are concealed, and if I guess these aright, ... this mustִ be because I have made out the import of the inscription. (OI Butts: 294-5)

To Mill this was a clear case of market-place logic, and he referred to the inference from confirmation by predictions to the truth of a hypothesis as an argument "well calculated to strike the ignorant vulgar" in his edition. In view of Whewell's indignant protest, Mill changed it in the next edition to: "well calculated to impress the uninformed whose faith in science rested solely on similar coincidences between its prophecies and what comes to pass". (Lo Jr, p.329)

Whewell's response to the original wording was that the "ignorant vulgar" who actually were "struck" with the success in prediction in history were, as a rule, men of science. And his own logic then is clearly proposed as a justification of this historical rule which controls the assent of the scientific community:

If we can predict new facts which we have not seen as well as explain those which we have seen it must beִ because our explanation is not a mere formula of observed facts, but a truth of a deeper kind. (OI Butts, 294)

That the "must"s I underlined both here and in the previous passage are meant in their strict, rather colloquial, sense can be seen in his further retort. Mill, as we saw, refused to see anything "strange" (meaning "surprising") in the confirmation of a hypothesis’ predictions and Whewell now insists:

Nothing strange, if the theory be true; but quite unaccountable if it be notִ) ִ.ibid emphasis added)

And he then goes straightly to expound the cipher metaphor, cited above. Thus, on his view it was logically impossible to explain the predictive success of a theory except by its truth, and so a predictive confirmation is a full proof of truth, or as Mill put it,

According to Dr Whewell, the coincidence of results predicted from an hypothesis with facts afterwards observed amounts to a conclusiveִ proof of the truth of the theory. (Logic JR:329 emphasis added(

And as a proof of this interpretation, Mill quotes Whewell's cipher metaphor. Now, Whewell, who read Descartes’ Principiaִ, and amply quoted from it, must have been well acquainted with Descartes' resort to the same metaphor in the concluding paragraphs of the Principiaִ ִ.This is of the utmost significance for an adequate interpretation of Whewell, for Descartes executes in these fateful paragraphs a set of astonishing apologetics maneouvers whose incoherence only reflects his despair on recognizingthe logical invalidity of his "moral" conviction. Descartes declares that (a) success at a coherent deciphering does not entail the truth of the guessed code since (b) the code could be false and yet by chance give the text a coherent meaning, but nevertheless (c) it is unbelievable that this could be reallyִ the case, and so we are morally (though not logically) justified in our belief in the truth of the code.

2.2. The apologetics of Whewell - Logical as moral proofִ

Descartes thus formulated two distinct criteria of justification, the logical and the moral. These conflicted in this case, and so we must hold a contradictory belief: we must believe both that the code is (certainly - Whewell's "must be") true and also that it may be false. Whewell, who gives no hint of having borrowed the metaphor from Descartes, makes in it one crucial change: He silently ignores the difference in the kind of justification allotted to the two beliefs. Thus, what he does in fact is adopt Descartes’ moral criterion and call it logical. In this step he goes according to a plan which will become more evident in the following account. It consists in conflating, or rather intentionally identifying the belief-behaviour of the scientific community with the logicִ of discovery and acceptance of scientific theories. I shall argue that Whewell's whole dispute with Mill is in fact a dispute over this identification, and that Whewell had to adopt it since he was constructing something which Mill was not, namely, a grand apologetic justification for the scientific community. It is the essence of apology to posit the actual as necessary in some sense, and the identification for this purpose of the logically, the physically and the morally necessary is a standard step in modern philosophy from Leibniz through Kant to Poincaré.

2.3. The argument from equivalence, (Mill's attack)ִ

The standard argument against the inference to truth from successful prediction is from the equivalence of theories, or in another formulation, from the logical fact that the truth of the consequence does not in general entail that of the hypothesis, and so a false hypothesis can entail a true consequence. This is the single crucial stonewall against which the whole tradition of Western scientific and philosophic thought mounts an attack after attack. Whewell's attack consists in ignoring it completely.

Mill raised of course this standard argument, and alluding to the contemporary undulatory optics, stated that the ether whose vibrations constitute light cannot be regarded as more than "a conjecture" in spite of the verification of all the (observable) consequences derivable from the assumption of its existence, “because this evidence I cannot regard as conclusive because we cannot have in the case of such a hypothesis, the assurance that if the hypothesis be false it must lead to results at variance with the true facts”.

This is the standard, traditional way of putting the equivalence argument, but Mill was tough enough to put it also in a more daring and explicit form: It is not merely that the confirming evidence is not "conclusive", rather it does not even raise the probability of the hypothesis being true at all. Addressing himself to "persons of scientific attainment" (L.329), he retorts to Whewell's evidence from the scientific tradition (by which Whewell answered Mill's reference to the "ignorant vulgar"), and declares that

most thinkers of any degree of sobriety allow, that an hypothesis of this kind is not to be received as probably trueִ because it accounts for all the known phenomena, since this is a condition sometimes fulfilled tolerably well by two conflicting hypotheses; while there are probably many others which are equally possible, but which, for want of anything analogous in our experience, our minds are unfitted "to conceive” .(Logic: 285)

Mill had also an original explanation for the source of the equivalence possibility, or the fact that a hypothesis could entail true consequence and yet be false. This explanation became eventually the fundamental tenet of various conventionalistic philosophies, namely, that a hypothesis, mainly a material one, could be false in its reference yet true in its logical structure (what Poincaré named "relations"). In virtue of this logical skeleton it succeeded in its predictions, but this true logical skeleton does not have to be embedded in that or this material medium. It is this difference between the material reference and the logical sense, or between the matter and the form of the hypothesis, that is the explanation of the equivalence phenomenon

.Accordingly, if there exists a partial formal analogy between the hypothetical model and the real unobserved mechanism at work, it is nothing strange that they should accord with each other in one respect more. Though twenty such coincidences should occur, they would not prove the reality of the undulatory ether; it would not follow that the phenomena of light were results of the laws of elastic fluids, but at most that they are governed by laws partially identicalִִ with these; which, we may observe, is already certainִ, from the fact that the hypothesis in question could be for a moment tenable. (Loִ Jr 329)

ֶThe clauses which I underlined catch the essential argument: On the one hand, it is an obvious triviality that if the hypothesis works, it does this only because it must be partially true, since this is what is meant by being partially true. But given this, it also follows that the hypothesis need not be anything more than partially true for doing its work.

2.4. The non actuality of equivalence - (Whewell's answer)ִ

ֱWhewell had no logical answer either for the equivalence argument itself (in its weak version against proof of the hypothesis, or strong version against its increased probability or for the explanation Mill provided for the possible success of false hypotheses. He had, however, a combined historical and emotive argument, namely, that there were no actual cases of equivalent theories or of false but well confirmed theories in the history of science, and this is as it should be since it is inconceivable that there should be such cases. Reiterating the cipher metaphor and adopting it to his conception of proof by "consilience of inductions", he argued that such consilience

was a striking and surprising coincidence which gave the theory a stamp of truth beyond the power of ingenuity to counterfeit. I may compare such occurrences to a case of interpreting an unknown character, in which two different inscriptions, deciphered by different persons, had given the same alphabet. We should, in such a case, believe with great confidence that the alphabet was the true one; and I will add, that I believe the history of science offers no example in which a theory supported by such consiliences had been afterwards proved falseִ. (Butts 295(

ֶ Thus, it was "inconceivable" that a false theory would be well confirmed, and conveniently enough no historical case existed to refute this inconceivability, just as was the case with the equivalence case:

Thus when he [Mill] says that the condition of a hypothesis accounting for all the known phenomena is "often fulfilled equally well by two conflicting hypotheses", I can only say that I know of no such case in the history of science, where the phenomena are at all numerous and complicated; and that if such a case were to occur one of the hypotheses might always be resolved into the other. (Butts p.292)

The lines I underlined hold the key to Whewell's conception. Here he declares an obviously aprioriִִ law of history, since he admits that no actual cases ever came to his knowledge. It follows therefore that his view that no equivalence case could occur is a logical consequence of his more basic tenets, by which he classified and interpreted the history of science, so that such cases did not occur because it was a logical impossibility that they should. His apologetic technique gloriously reaps here its fruits.

2.5 . Resolvabilityִ

Let me begin at the end-result, namely, all equivalent theories are "resolvable" into each other. The aim of assertion is to show that equivalent theories are not distinct theories at all but, on the contrary, they constitute different verbal formulations of one single theory, and so they are in fact identical with each other. That Whewell actually held this view of the identity of all equivalent theories can be gathered from several pieces of evidence, apart from the above quoted assertion about their necessary mutual resolvability, to the exact interpretation of which I shall return later.

Mill argued, as we saw, that even when no equivalent theories appeared in history, this could not be regarded as anything but an accidental fact, since such theories were always logically possibleִִ. Thus, in order to explain a given set of observaštion laws, it is always possible to assume a set of subvisible entities E which interact according to subvisible laws W such that E W ְU O. Since in this entailment only one member is fixed, no reason can be given why the complete freedom as to the rest of the members should not enable us to construct any number of such theories which are distinct from each other in all their members except O. And so, in the first two editions Mill argued that

if we give ourselves the license of inventing the causes as well as their laws, a person of fertile imagination might devise a hundred modes of accounting for any given fact. (CW: 500)

To this argument Whewell answered

that the question is about accounting for a large and complex series of facts of which the laws have been ascerštained. (Butts: 292(

Clearly, Whewell rejects here a central tenet of Mill, namely, the difference between visible and invisible laws of nature. To Mill this was one fundamental proposition of his realism, enabling him mainly to maintain a rigid determinism in the face of the well-known Comtian thesis that causality looks strict only as long as no more precise measurements are undertaken. Taking this collapse of determinism as the real situation on the observational phenomenal level, Mill retreats and maintains his rigid determinism as fully existing in the invisible, strictly componential level of physical events. On that level, a full Laplacean determinism holds, such that it is

certain that whatever happens is the result of some law, is an effect of causes, and could have been predicted from a knowledge of the existence of those causes and from their laws. (Logicִ, p.345 l)

To this end Mill introduced the basic distinction between empirical or derivative laws, and ultimate causes and laws. A derivative law is merely an "empiric regularity" and has an essential limitation in its lawfulness, being as it is the resultant of several ultimate causes acting according to their ultimate laws. This derivatory, or resultant nature of an empiric law entails that it would change if the situation and combination of the ultimate causes will change (even though not their laws). This constitutes the justification of the limited degree of reliance which scientific inquirers are accustomed to place in empirical laws. (340 r;)... they are not only, as the nature of the case implies, less general, but even less certain... and not to be relied upon universally (. (344

Thus, the rigid determinism can be kept if we agree that derivative laws "do not depend solely on the ultimate laws into which they are resolvable: they mostly depend on those ultimate laws and an ultimate fact, namely, the mode of co-existence of some of the component elements of the universe". (399,R)*

(* see Mill's Auguste Comte and Positivismִִ p. 59-62, his critique of Comte's conventionalistic POS; to p.35, note, for the realism of his own ultimate laws, as against the ideality of Spencer's, and the origin of this in Comte's abstract-concrete classification of laws and sciences.

This is what is implied in Mill's argument from the possibility of explaining any observed, that is, derived or empiric law by any arbitrary ultimate causes and their ultimate laws. What is implied is his realism, holding that even though we cannot never be certain as to the nature and combination of the ultimate causes, it is they which determine the observed laws. Whatever reduction of derived laws to their ultimate components we effect, it is either true or false, irrespective of our ability to prove this. In short, our hypotheses, models, and theories, are descriptive statements which take ultimate causes and laws as their referents, and as such are either true or false.

This whole conception of a theory was rejected by Whewell, and the echo of this rejection is his short retort, that

the question is about accounting for a large and complex series of facts, of which the laws have been ascertained (Butts: 292)

How can one interpret this answer to Mill? Why does Whewell assume that pointing out this fact would refute Mill's argument from the possibility of infinitely many different yet equivalently explanatory theories ? Obviously, the point of the answer is that, contrary to Mill's suggestion that there is no limit to the ways of inventing explanatory laws, no such "licence" can be at all imagined, since the laws are already given, "already have been ascertained". So, Whewell regards this as an answer to Mill because he identifies Mill's explanatory laws, which belong to the hypothesis, with the observed laws, which are about to be explained.

Now, if this is the true meaning of Whewell's answer, then this raises a further problem. What was Whewell's theory of scientific explanation which led him to disregard Mill's intent, namely, that an `explanatory hypothesis' uses hypothetical laws to explain observation laws ?

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