History of Western Philosophy - Bertrand Russell [118]
Metaphysical errors arose through supposing that 'all men' is the subject of 'all men are mortal' in the same sense as that in which 'Socrates' is the subject of 'Socrates is mortal'. It made it possible to hold that, in some sense, 'all men' denotes an entity of the same sort as that denoted by 'Socrates'. This led Aristotle to say that in a sense a species is a substance. He is careful to qualify this statement, but his followers, especially Porphyry, showed less caution.
Another error into which Aristotle falls through this mistake is to think that a predicate of a predicate can be a predicate of the original subject. If I say 'Socrates is Greek, all Greeks are human', Aristotle thinks that 'human' is a predicate of 'Greek', while 'Greek' is a predicate of 'Socrates', and obviously 'human' is a predicate of 'Socrates'. But in fact 'human' is not a predicate of 'Greek'. The distinction between names and predicates, or in metaphysical language, between particulars and universals, is thus blurred, with disastrous consequences to philosophy. One of the resulting confusions was to suppose that a class with only one member is identical with that one member. This made it impossible to have a correct theory of the number one, and led to endless bad metaphysics about unity.
(2) Over-estimation of the syllogism. The syllogism is only one kind of deductive argument. In mathematics, which is wholly deductive, syllogisms hardly ever occur. Of course, it would be possible to re-write mathematical arguments in syllogistic form, but this would be very artificial and would not make them any more cogent. Take arithmetic, for example. If I buy goods worth 16s. 3d., and tender a £1 note in payment, how much change is due to me? To put this simple sum in the form of a syllogism would be absurd, and would tend to conceal the real nature of the argument. Again, within logic there are non-syllogistic inferences such as: 'A horse is an animal, therefore a horse's head is an animal's head.' Valid syllogisms, in fact, are only some among valid deductions, and have no logical priority over others. The attempt to give pre-eminence to the syllogism in deduction misled philosophers as to the nature of mathematical reasoning. Kant, who perceived that mathematics is not syllogistic, inferred that it uses extra-logical principles, which, however, he supposed to be as certain as those of logic. He, like his predecessors, though in a different way, was misled by respect for Aristotle.
(3) Over-estimation of deduction. The Greeks in general attached more importance to deduction as a source of knowledge than modern philosophers do. In this respect, Aristotle was less at fault than Plato; he repeatedly admitted the importance of induction, and he devoted considerable attention to the question: how do we know the first premisses from which deduction must start? Nevertheless, he, like other Greeks, gave undue prominence to deduction in his theory of knowledge. We shall agree that Mr Smith (say) is mortal, and we may, loosely, say that we know this because we know that all men are mortal. But what we really know is not 'all men are mortal'; we know rather something like 'all men born more than one hundred and fifty years ago are mortal, and so are almost all men born more than one hundred years ago'. This is our reason for thinking that Mr Smith will die. But this argument is an induction, not a deduction. It has less cogency than a deduction, and yields only a probability, not a certainty; but on the other hand it gives new knowledge, which deduction does not. All the important inferences outside logic and pure mathematics are inductive, not deductive; the only exceptions are law and theology, each of which derives its first principles from an unquestionable text, viz. the statute books or the scriptures.
Apart from The Prior Analytics, which deals with the syllogism, there are other logical writings of Aristotle which have considerable importance in the history of philosophy. One of these is the short work