Both for good and evil, therefore, the day of the cultured gentleman is past.
CHAPTER XXII Aristotle’s Logic
ARISTOTLE’S influence, which was very great in many different fields, was greatest of all in logic. In late antiquity, when Plato was still supreme in metaphysics, Aristotle was the recognized authority in logic, and he retained this position throughout the Middle Ages. It was not till the thirteenth century that Christian philosophers accorded him supremacy in the field of metaphysics. This supremacy was largely lost after the Renaissance, but his supremacy in logic survived. Even at the present day, all Catholic teachers of philosophy and many others still obstinately reject the discoveries of modern logic, and adhere with a strange tenacity to a system which is as definitely antiquated as Ptolemaic astronomy. This makes it difficult to do historical justice to Aristotle. His present-day influence is so inimical to clear thinking that it is hard to remember how great an advance he made upon all his predecessors (including Plato), or how admirable his logical work would still seem if it had been a stage in a continual progress, instead of being (as in fact it was) a dead end, followed by over two thousand years of stagnation. In dealing with the predecessors of Aristotle, it is not necessary to remind the reader that they are not verbally inspired; one can therefore praise them for their ability without being supposed to subscribe to all their doctrines. Aristotle, on the contrary, is still, especially in logic, a battle-ground, and cannot be treated in a purely historical spirit.
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Aristotle’s most important work in logic is the doctrine of the syllogism. A syllogism is an argument consisting of three parts, a major premiss, a minor premiss, and a conclusion. Syllogisms are of a number of different kinds, each of which has a name, given by the scholastics. The most familiar is the kind called «Barbara»:
All men are mortal (Major premiss). Socrates is a man (Minor premiss). Therefore: Socrates is mortal (Conclusion). Or: All men are mortal. All Greeks are men. Therefore: All Greeks are mortal.
( Aristotle does not distinguish between these two forms; this, as we shall see later, is a mistake.)
Other forms are: No fishes are rational, all sharks are fishes, therefore no sharks are rational. (This is called «Celarent.»)
All men are rational, some animals are men, therefore some animals are rational. (This is called «Darii.»)
No Greeks are black, some men are Greeks, therefore some men are not black. (This is called «Ferio.»)
These four make up the «first figure»; Aristotle adds a second and third figure, and the schoolmen added a fourth. It is shown that the three later figures can be reduced to the first by various devices.
There are some inferences that can be made from a single premiss. From «some men are mortal» we can infer that «some mortals are men.» According to Aristotle, this can also be inferred from «all men are mortal.» From «no gods are mortal» we can infer «no mortals are gods,» but from «some men are not Greeke» it does not follow that «some Greeks are not men.»
Apart from such inferences as the above, Aristotle and his followers thought that all deductive inference, when strictly stated, is syllogistic. By setting forth all the valid kinds of syllogism, and setting out any suggested argument in syllogistic form, it should therefore be possible to avoid all fallacies.
This system was the beginning of formal logic, and, as such, was both important and admirable. But considered as the end, not the beginning, of formal logic, it is open to three kinds of criticism:
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(1) Formal defects within the system itself.
(2) Over-estimation of the syllogism, as compared to other forms of deductive argument.
(3) Over-estimation of deduction as a form of argument.
On each of these three, something must be said.
(1) Formal defects . Let us begin with the two statements «Socrates is a man» and «all Greeks are men.» It is necessary to make a sharp distinction between these two, which is not done in Aristotelian logic. The statement «all Greeks are men» is commonly interpreted as implying that there are Greeks; without this implication, some of Aristotle’s syllogisms are not valid. Take for instance:
«All Greeks are men, all Greeks are white, therefore some men are white.» This is valid if there are Greeks, but not otherwise. If I were to say:
«All golden mountains are mountains, all golden mountains are golden, therefore some mountains are golden,» my conclusion would be false, though in some sense my premisses would be true. If we are to be explicit, we must therefore divide the one statement «all Greeks are men» into two, one saying «there are Greeks,» and the other saying «if anything is a Greek, it is a man.» The latter statement is purely hypothetical, and does not imply that there are Greeks.
The statement «all Greeks are men» is thus much more complex in form than the statement «Socrates is a man.» «Socrates is a man» has «Socrates» for its subject, but «all Greeks are men» does not have «all Greeks» for its subject, for there is nothing about «all Greeks» either in the statement «there are Greeks» or in the statement «if anything is a Greek it is a man.»
This purely formal error was a source of errors in metaphysics and theory of knowledge. Consider the state of our knowledge in regard to the two propositions «Socrates is mortal» and «all men are mortal.» In order to know the truth of «Socrates is mortal,» most of us are content to rely upon testimony; but if testimony is to be reliable, it must lead us back to some one who knew Socrates and saw him dead. The one perceived fact—the dead body of Socrates—together with the knowledge that this was called «Socrates,» was enough to assure us of the mortality of Socrates. But when it comes to «all men are mortal,» the matter is different. The question of our knowledge of such general propositions is a very difficult one. Sometimes
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they are merely verbal: «all Greeks are men» is known because nothing is called «a Greek» unless it is a man. Such general statements can be ascertained from the dictionary; they tell us nothing about the world except how words are used. But «all men are mortal» is not of this sort; there is nothing logically self-contradictory about an immortal man. We believe the proposition on the basis of induction, because there is no well-authenticated case of a man living more than (say) 150 years; but this only makes the proposition probable, not certain. It cannot be certain so long as living men exist.
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 $4.63, and tender a $5 bill 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, there-
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fore 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
