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.