History of Western Philosophy: Collectors Edition

by Bertrand Russell

(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.