History of Western Philosophy - Bertrand Russell [117]
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 be also inferred from 'all men are mortal'. From 'no gods are mortal' we can infer 'no mortals are gods', but from 'some men are not Greeks' 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:
(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 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.