Part 35

[380] = A.D. 1363. The numerals which accompany the written figures are equivalent to 6,527 and are meaningless.

[381] Published by Macmillans, 1912.

[382] Cf. Mr. H. W. B. Joseph’s _Logic_^2, p. 548.

[383] Cf. §§ 10, 28.

[384] _Post. Anal._ i. 2. 71 b 20.

[385] i.e. truth-claim.

[386] Cf. _Formal Logic_, p. 173.

[387] Mr. Alfred Sidgwick has been pointing out for the past twenty years how fatal this difficulty is to the traditional notion of formal validity; nor has any logician confuted his argument, or even shown that he apprehended its meaning and scope. It would seem, therefore, that the condition of formal logic is so precarious that its only chance of survival lies in hushing up all the vital objections to its stereotyped doctrines. But is not the policy of ignoring unanswerable objections the sure mark of a pseudo-science?

[388] The latest I have noticed occurs in Abercrombie’s _Inquiries concerning the Intellectual Powers_ (1830); it reads very strangely now.

[389] Controversially the criticism of ‘self-evidence’ has been met in the same way as that of the ‘validity’ of the syllogism, i.e. by total silence.

[390] _Anal. Post._ i. 34.

[391] It may be suggested that there is a similar confusion on this question: when history is called a science, it is often forgotten that its data are essentially such that they can only occur once, while the material of the other sciences is such that cases of ‘the same’ may always be found in it. But neither need it be denied on this account that history can, and should, be written in a scientific spirit.

[392] _Science et Méthode_, ch. iii, L’Invention mathématique.

[393] _Republic_, 511 c.

[394] _Anal. Post._ i. 1.

[395] Diogenes Laertius, ix. 51.

[396] Cf. § 3.

[397] Or more difficult, if the indetermination is conceived as limited.

[398] This we saw (§ 4) is really a mistake: mathematical proofs are really hypothetical, and deduced from the initial postulates and definitions. They hold of the ideal objects of mathematics, but that they can be advantageously applied to reality is merely an empirical fact, and it is not inconceivable that the world should grow _more_ recalcitrant to mathematical treatment, though actually it has grown _less_ so.

[399] In _Republic_ vi his whole argument for the existence of metaphysical truth, culminating in a supreme ‘Idea of the Good’, depends on the assumption that the ‘hypotheses’ of the sciences, being insecure originally, remain so until they are deduced from a (self-proving) ‘unhypothetical principle’. This assumes, of course, that they cannot be confirmed empirically by the results of their working, and exhibits the _lacuna_ of logic in a typical way.

[400] _Formal Logic_, ch. xxi, § 7.

[401] e.g. the ‘accidental’ distribution of variations in biology, for which see _Humanism_, pp. 146-50, and the postulates of causality and determinism in science generally (_Formal Logic_, ch. xx, § 6, and _Studies in Humanism_, ch. xviii, § 4).

[402] Cf. § 8 and _Formal Logic_, ch. x.

[403] The ‘novelty’ which is claimed for the conclusion of a syllogism is only one case of this: in the traditional interpretation it is hopelessly at variance with the demand that it shall also follow from its premisses of necessity. Cf. _Formal Logic_, ch. xvi, §§ 8-10.

[404] Usually, but wrongly, called ‘dispassionate’ or ‘disinterested’. What is wanted is, not that the inquiring mind should take no interest in the conclusions it considers, but that, though it cares keenly and even passionately for one of them, it should yet be capable of sufficient self-control to consider fairly the case _against_ the conclusion it favours. This mental attitude is probably best secured by caring more for truth than for a party victory, and is denominated a ‘disinterested love of truth for its own sake’. But even so we love what we deem the truth, because it is the _best_ thing to believe, and better (on the whole and in the end) than anything else that is propounded.