Part 25

§ 7. (1) The first of these may be called the _Fixity of Terms_. Syllogistic reasoning manifestly depends on the assumption that the terms occurring in it have meanings sufficiently stable to stand transplantation from one context to another; for only so can they establish connexions between one context and another. Thus a syllogism in _Barbara_ argues that because _all M is P_ and _all S is M, all S must be P_. But it can do this ‘validly’ only if _M_, its middle term, remains immutably itself, and is the same in both premisses. Doubt, dispute, or confute this assumption, and the cogency of the syllogism as a form of ‘proof’ is overthrown at once. If the sense in which _M is P_ is not the same as that in which _S is M_, the syllogism breaks in two, and its conclusion becomes precarious. Raise the question of how far reality conforms to this assumption, and you get at once a subtle problem of the applicability of the syllogistic form to the case in hand, which is precisely analogous to the question whether a theorem of pure mathematics is applicable to the behaviour of a real thing. In either case the cogency of the ‘proof’ which establishes the conclusion is impaired and ceases to be unconditional. The conclusion of a ‘valid’ syllogism will only follow _if_ the middle term can be known to be unambiguous, and if the objects designated by the terms do not change rapidly enough to defeat the inference. And that this is the case can usually be ascertained only by actual experience. The conclusion, therefore, cannot be simply deduced; it has actually to _come true_, before we can be sure that the reasoning _was_ sound. Absolutely _a priori_ proof thus becomes impossible, if the assumption of the fixity of terms is contested: all proof becomes, in a sense, empirical.

Nevertheless, experience shows that the fixity of terms, though not a ‘fact’, is _a valid ‘fiction’_: in ordinary discussion the terms may usually be taken as fixed enough to render valid syllogisms common. An ordinary debate proceeds upon the assumption that the meaning of the terms involved is fixed, and cannot be varied arbitrarily. To science, however, this assumption does not apply without restriction. In a progressive science the meaning of terms often develops so rapidly that such verbal reasoning does _not_ suffice. Hence the mere occurrence of verbal contradictions in a scientific reasoning is no proof that the argument is unsound. It may show merely that its terms are _growing_.

It should be observed further that this same assumption is implied in the fundamental ‘laws of thought’ on which the traditional logic rests. Indeed, the notorious ‘Law of Identity’ seems to be merely another statement of it. It is usually formulated as ‘_A is A_’, but in its actual logical use it is really the assumption that ‘everything _is_ what it is called’. It is, of course, anything but self-evident that ‘_A_’ _is A_, but _unless_ the _S_, _M_, and _P_ of the syllogism are _rightly_ so called, the syllogism will not hold. Similarly, the Law of Contradiction collapses at once if the terms to which it is applied are allowed to change. The inability of ‘_A_’ both to be _B_ and not to be _B_ vanishes if ‘_A_’ is not fixed and may change its habits. And of course the real things known to science all change, and are fixed only by a fiction. Hence every application of the logical convention to real things may be challenged: it involves a fiction and takes a risk, and both of these may be bad. But the traditional logic ignores both the risk and the fiction and the lack of cogency in its attitude.

§ 8. (2) It is a further presupposition of the syllogism that the meaning of its terms is _known_. When a discussion is begun the parties to it are supposed to understand each other, and not to have first to find out and form the meaning of the terms they use. This assumption also is roughly true in ordinary debate, and its convenience is manifest. If things are rightly named, and if this feat has been accomplished once for all--presumably by Adam and Eve before they were turned out of Paradise for trying to know too much--we shall escape many of the most trying difficulties of scientific inquiry. We need no longer trouble whether the best names have been given, and whether a name good for one purpose is equally good for another, nor need we inquire whether our names may not unite what is alien on account of a superficial likeness, or separate what is akin on account of a superficial difference.

In science, on the other hand, the assumption that we know what meanings our terms can convey is not made as a matter of course. We may begin with roughly labelling objects of interest, and then inquiries may be conducted into, e.g., ‘electricity’, ‘elements’, ‘life’, ‘species’, &c., in the hope of settling what these terms _shall_ mean, and of finding out _more_ about their meaning, and without making the assumption that whatever new facts are discovered about them must conform to our preconceptions and confirm our nomenclature. Thus to a man of science it will not be cogent to argue that because an ‘element’ is (by definition) an ultimate form of matter which cannot be broken up, and ‘radium’ breaks up, ‘radium’ is not an ‘element’, or that because ‘species’ are eternal forms, and the Darwinian theory claims that they are not immutable, it can be dismissed as involving the ‘contradiction’ that a ‘species’ is not a species. Thus the best syllogisms lose their cogency so soon as a question is raised whether the verbal identity of their terms is an adequate guarantee of the real identity of the things they are applied to.

§ 9. (3) It is a further presupposition of the logician’s conception of ‘proof’ that absolute truths exist, and that in the ideal demonstration they form the premisses from which the conclusion follows. This presupposition is not stated, and is not implied in the form of the syllogism. For a syllogism is no less ‘valid’ if its premisses are true only hypothetically, and not absolutely. Indeed, it is not thought to impair the ‘validity’ of a syllogism that its premisses should be utterly false. At any rate we can _reason_ quite as well with hypotheses and probabilities as with absolute truths, and this is in fact what we usually do, whether or not we are aware that our premisses are conditional and hypothetical. This ordinary practice, however, is resented by the traditional logic. For if our premisses are only hypothetically true, how can they lead to conclusions which can be declared absolutely true? And if our conclusions are not absolutely true, how can they be certain? Are they not bound to remain infected with the doubts which beset their premisses?[383] As we value the certainty of our conclusions, therefore, absolutely true and certain premisses must be procured. If they cannot be procured, even the best formal proofs will remain hypothetical, and all truth will become dependent on experience. For if nothing is true absolutely, and every truth has originated humbly in a guess that has grown into a successful hypothesis, it can always be suggested that after all it may benefit by a little more verification. It may be true enough psychologically and for practical purposes, but it does not realize the ideal of ‘logical certainty’.

§ 10. This ideal Logic has formulated from the first. Aristotle already was not content with merely analysing the form of reasoning; he aspired to formulate the norm of scientific demonstration. The ‘demonstrative syllogism’, which he held to be the form of truly scientific reasoning, differs from the formal syllogism in two essential respects. Its premisses are absolutely true, and its middle term states the real ‘cause’, which connects its terms and is not merely a _ratio cognoscendi_. The reasoning proceeds, therefore, from premisses which are unambiguous, true, and certain, i.e. _necessarily_ true and _absolutely_ certain. Nor does the conclusion lose any of this excellence. Logic puts on a fine air of modesty, and merely claims that the syllogistic form is a guarantee that no truth can be _lost_ on the way from the premisses to the conclusion in a ‘valid’ argument. If, therefore, our thought is properly arranged, our conclusion will be as true and certain as were its premisses, and no man will be able to gainsay it. It is the great beauty and merit of the syllogistic form that it is an arrangement which gives us this guarantee.

It was natural, therefore, that throughout the history of logic enormous importance should be attached to the acquisition of unquestionable starting-points. For the possession of ‘valid forms’ was not enough. It only insured against loss of truth, it did not provide for its acquisition. It seemed, however, to imply that truth could only be generated out of truth, and handed down from the premisses to the conclusion. Hence the insistent demand for assured starting-points, self-evident ‘principles’, which the infallible method of syllogistic deduction might conduct to equally certain conclusions.

In reality, however, this demand for certainty was extra-logical: it is not required for the purpose of analysing reasoning. For it is just as easy to reason from doubtful and probable premisses as from certainties, nor need the doubt in the reasoner’s mind affect the form of the reasoning. If, however, there is an imperative desire for certainty, it must be somehow gratified by logic. And there seemed to be no way of doing so except by ascribing absolute truth and certainty to the initial principles of science.

Of course it was covertly assumed that certainty could only be reached by _starting_ from certainty, and that no possibility of a growth of assurance in the progress of the reasoning could be entertained. In a sense this assumption was correct (cf. §§ 27, 28), because it is true that the gradual verification of scientific truths does not render them absolute; but it led to neglect of all methods which appeared to start with premisses initially doubtful and hardening into certainties by gradual confirmation. No doubt it was not strictly impossible to reason from premisses not known to be true, but such reasoning was despised as ‘dialectical’, and no inquiry was made into the frequency of its occurrence in actual science. Why, then, waste time upon so unworthy a procedure, instead of fixing one’s whole attention upon the truly logical ideal, the absolute proof of absolute truth? Let us maintain, rather, the old Aristotelian[384] conviction that the truly scientific syllogism proceeds from premisses that are true and underivative (because ‘self-evident’) and inerrant, and demonstrates its conclusion with ineluctable necessity! Thus the attainment of _absolute truth_ was unobtrusively smuggled in as the aim of reasoning, and became an integral feature of the ideal of ‘demonstration’.

§ 11. From the standpoint of the scientific inquirer, however, this whole theory of proof is open to the gravest objections. He finds first that it is impracticable, being composed throughout of counsels of perfection with which he cannot comply, and then that, even if he could, they would be perfectly useless, and destructive of his aims.

(1) It strikes him at once that the Fixity of Terms is an obvious _fiction_. He will of course be aware, from his scientific experience, that fictions have their uses and are often indispensable; but he will know also that not all fictions are useful, and that the adoption of a fiction has in each case to be justified by its usefulness. Moreover, it is not so much its immediate and prospective use which justifies it, though this yields the usual motive for its adoption, as the ulterior uses ascertained _ex post facto_ by experience.

He will ask, therefore, for evidence that an _absolute_ fixity of terms is the vital necessity for logic it is declared to be. He will admit, of course, the familiar arguments for a certain _stability_ of meanings which have come down from the days of Plato, but he will suggest that a _relative_ fixity of terms is quite sufficient to content them. He will point out that in a progressive science any absolute fixity in its terms is precluded by the very progress of the science. For the terms in use must somehow manage to convey the _growing_ knowledge they are employed to ‘fix’. The term ‘gas’, for example, must not be tied down to the meaning Van Helmont desired to convey when he invented it; it must incorporate all that physics has discovered about ‘gases’ ever since. Similarly, when Darwinism transforms the notion of ‘species’, and the discovery of radio-activity that of ‘atom’, these developments of meaning must be recognized as perfectly proper. To object to these conceptions as modern science uses them, on the ground that, because to Plato and Aristotle species were eternal and immutable, a ‘species’ that changes cannot be truly a species, or that because an ‘atom’ is etymologically ‘indivisible’, it becomes an impossible self-contradiction when it is made up out of ‘electrons’, will seem to him to reveal only the fatuous pedantry of an utterly unscientific mind.

§ 12. (2) If he is acquainted with psychology, he will perceive also that the fiction of the fixity of terms is subject to a further restriction. It is not only in science as such--for all sciences must be conceived as progressive--that the fixity of terms cannot be made absolute: a real fixity is strictly inconceivable for and in every human mind. For every term that is actually used to convey a meaning must be held to form part of a _new_ truth,[385] i.e. of a truth that was not previously in being. It is not a question of principle whether the truth is supposed to be new only to the person to whom it is addressed, or claims to be new to all, i.e. to science. For no judgement would be made unless it had something new to say.[386] Hence _every real judgement_, as opposed to the verbal formulas which are called judgements in the logic-books, _more or less modifies the meaning of its terms_. If it succeeds in being a real judgement and a new truth, it establishes a new and previously unknown relation between its subject and its predicate. ‘_S_’ is henceforth an _S_-which-can-have-_P_-predicated-of-it, and ‘_P_’ a _P_-which-can-be-predicated-of-_S_. Thus both the psychological associations and the logical associates of _S_ and _P_ are changed. That logicians should not have noticed so obvious a fact can be attributed only to their inveterate habit of not using in their illustrations real judgements intended to cope with actual problems, but operating with their verbal skeletons, which are not being used by any one to convey his meaning, and so do not have any _actual_ meaning.

Clearly, then, no science can interpret the fixity of terms quite literally. Or rather, it can only interpret it literally--as a matter of the literal integrity of the _words_ that _may_ convey a meaning. But in a scientific inquiry the convention of formal logic must be reversed; the fixity of terms must be _understood_ not to be absolute, but to be merely _ad hoc_ and sufficient to convey a definite meaning, which it is desired to develop. Accordingly it must always be assumed that the results of an inquiry are to modify its terms, and that it is permissible, and indeed inevitable, to develop their meaning, so long as they remain capable of expressing and conveying the new truth. We must come to every inquiry with a willingness to learn and to expand our terms. The Fixity of Terms, as it is tacitly presupposed in the traditional logic, is a scientific blunder of the gravest kind.

§ 13. (3) To renounce it, however, entails further consequences. It appears to undermine the whole notion of _formal validity_. For if we admit in principle that the meaning of terms depends vitally on that of the judgement in which they occur, how can we continue to rely absolutely on the mere verbal identity of its terms to hold together a syllogism? In any syllogism the middle term, _M_, may have one shade of meaning in relation to _P_, another in relation to _S_. It may be quite right to call _M_ _P_ in one connexion, and to call _S_ _M_ in another; and yet, when the two assertions are put together, they may lead to a conclusion which is an error or an absurdity. The man who (in his laboratory) would rightly declare that ‘all salt is soluble in water’ and (at his dinner table) as properly hold that ‘all Cerebos is salt’, could not combine these assertions to draw the conclusion that ‘all Cerebos is soluble in water’, without finding that the facts confuted his anticipation.

No doubt, when this had happened, he might explain it, _ex post facto_ (if he knew logic), by alleging a hidden ‘ambiguity of the middle term’. We need not here discuss whether it is fair to treat as an inherent ambiguity what is really a juxtaposition of shades of meaning which were relative to different purposes and right in their original contexts, thus manufacturing a fallacy by selecting the premisses: the important thing is that the logician should be driven to admit that _any_ middle term may become ambiguous in this way when a syllogism is constructed, and that this completely stultifies his assumption that the _verbal_ identity of the middle guarantees the _real_ identity of the objects to which it refers.[387] If we call two things, which are and must be different if they are to be two, both ‘_M_’, we necessarily take the risk that the differences are irrelevant for the purpose of our argument. We may legitimately assume this, but if we do, our hypothesis has to be confirmed in fact; it is naïve to think that the verbal identity of the terms is quite enough. If, then, actual identity cannot be absolutely guaranteed, if there is _always_ a possibility that the same term when put into a syllogism and used in reasoning may develop an ambiguity and become effectively two, it is evident that no amount of formal validity will safeguard the truth of a conclusion, even when the premisses are in themselves severally true. The syllogistic form is convicted of _losing_ truth which it started from, and this is the very thing it boasted it could never do. Moreover, its coercive ‘cogency’ is exploded: whoever wishes to deny a ‘valid’ conclusion after admitting its premisses, has merely to suggest that by putting the premisses together a fatal ambiguity has been generated in the middle term.

§ 14. (4) The assumption that everything has been named rightly, and is what it is called, will scarcely commend itself to the scientific researcher. He will know from much painful experience that language only embodies the knowledge which has been acquired up to date, and too often is only a compendium of popular errors. Hence in any research which really breaks new ground the existing terminology will always prove inadequate, and new technical terms have usually to be devised in order to embody the new knowledge. The reason is obvious. _Ex hypothesi_ we are inquiring _farther_ into the subject, because our knowledge is felt to be insufficient. Accordingly the probable defects of the terminology we are initially forced to use must be borne in mind: we may expect it to omit what is unknown, to misdescribe and to classify wrongly what is partially known, putting together what does not belong together and separating what does, emphasizing the unimportant and slurring over the important, and generally failing to provide the mind with words that give it a real apprehension of the objects under inquiry. Hence the tacit assumption of Aristotelian logic that the terms reasoned with are fully known, that adequate notions are already extant, that truth has merely to be _disentangled_ by a verbal criticism of existing opinions, and has not to be discovered outright, is false; nor can any argument from a verbal identity be taken as final.

§ 15. (5) But of all the assumptions lurking in the theory of proof, the belief that reasoning can and should start from certainty will seem the falsest and most pernicious to the man of science. For it means that we are committed to a search for absolutely certain premisses as a preliminary to every inquiry, and proscribes consciously hypothetical, i.e. truly experimental, reasoning altogether, or at least condemns it as incapable of leading to certainty. This search, however, will either be perfunctory and uncritical, if it accepts false claims to certainty; or else vain, if it is conscientious. For every attempt to prove a conclusion absolutely demands _two_ absolutely true premisses; hence the more we try to prove, the more we have to prove, and our search grows the more endless and futile, the longer it is continued. An immutable basis of absolutely certain truths, therefore, for reasoning to start from, is nowhere to be found. In no science is it possible to _start_ with truths that are absolutely certain. In every science the initial ‘facts’ are doubtful; they are alleged, but not yet approved. They embody only unsystematic observation and prescientific experience of the subject, and so are probably the products of inaccurate observation, bad interpretation, false preconceptions, and popular superstitions. To acquire any considerable scientific value, such material has to be thoroughly revised and refined.

The validity of methods and the certainty of ‘principles’ are no more assured than the ‘facts’, initially. Every science has to work out its own appropriate methods experimentally; even if it borrows methods from another, it has to find out how and how far they apply to a new subject. Neither does a science acquire its principles by divine revelation; even if they fell from heaven ready-made, it would insist on testing the authenticity of the revelation. But philosophers have been extremely reluctant to admit that the certainty of principles is a gradual growth: for over 2,000 years they have been endeavouring to discover some way of securing an infallibility to principles which would render them independent of the working of the sciences which use them. But if their labours have proved anything, it is that no such way can be found.

(_a_) They have recognized many principles as ‘_self-evident_’, and equipped the mind with a variety of ‘faculties’, expressly invented to enable it to apprehend the ‘self-evident’ inerrantly. But they have not been able to agree upon a list of self-evident principles,[388] nor even to find any truth whose claims to self-evidence have not been denied by competent critics. Nor have they been able to define their notion of ‘self-evidence’ itself; they cannot discriminate between the sound ‘logical’ self-evidence, which they conceived to guarantee truth, and its merely ‘psychological’ ‘mimic’, which is certainly much commoner, and becomes more intense and extensive the more unsound is the mind that ‘apprehends’ it.[389] Hence an unprejudiced observer has no reason to put the ‘intuitions’ of philosophers and the ‘faculties’ which apprehend them on a higher cognitive level than those of women or even lunatics. They all impose themselves psychologically; but this proves nothing as to their logical value, and science has to test them just the same.