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.
(b) The principles which are said to be necessary or logical ‘presuppositions’ all turn out to be hypothetical when they are examined. They are needed, no doubt, to solve the problem in hand, if the particular way it is formulated is taken for granted. But if either the order or the formulation of problems is altered, they cease to be either ‘necessary’ or ‘presuppositions’. For example, the ‘axiom of parallels’, alias ‘Euclid’s postulate’, is a necessary presupposition of geometry, if the existence of parallels is assumed. But if we prefer it, we can just as well (with Aristotle) make it our axiomatic ‘presupposition’ that the interior angles of a triangle are equal to two right angles, and can then deduce the existence of parallels. I.e. Euclid might have deduced what he assumed, and assumed what he deduced. If, moreover, we do not desire to construct a Euclidean geometry at all, we can deny both presuppositions, and proceed from alternative postulates, which lead to the various metageometries. The only things, in short, which all scientific principles presuppose are the desire to construct a science, and the desire to construct it in a particular way, which is simplest, or easiest, or most systematic, or most in accordance with the reigning prejudices. But these desires are the very things which the logician’s account of principles always omits to mention.