LOGIC Triads of these diVerent kinds were, in later ages, called ‘moods’ of the syllogism Both of the given triads exemplify the pattern of a syllogism of the Wrst Wgure, but there is obviously a great diVerence between them: the Wrst is a valid argument, the second is invalid, having true premisses and a false conclusion.3 Aristotle sets himself the task of determining which of the possible moods produces a valid inference He addresses it by trying out the various possible pairs of premisses and asking whether any conclusion can be drawn from them If no conclusion can be validly drawn from a pair of premisses, he says that there is no syllogism For instance, he says that if B belongs to no C, and A belongs to some B, there cannot be a syllogism; and he gives the terms ‘white’, ‘horse’, ‘swan’ as the test instance (1 25a38) What he is doing is inviting us to consider the pair of premisses ‘No swan is a horse’ and ‘Some horses are white’ and to observe that from these premisses no conclusion can be drawn about the whiteness or otherwise of swans His procedure appears, at Wrst sight, to be both haphazard and intuitive; but in the course of his discussion he is able to produce a number of general rules which, between them, are adequate to determine which moods yield a conclusion and which not There are three rules which apply to syllogisms in all Wgures: (1) At least one premiss must be universal (2) At least one premiss must be afWrmative (3) If either premiss is negative, the conclusion must be negative These rules are of universal application, but they take more speciWc form in relation to particular Wgures The rules peculiar to the Wrst Wgure are (4) The major premiss (the one containing the major term) must be universal (5) The minor premiss (the one containing the minor term) must be afWrmative No valid argument has true premisses and a false conclusion, but of course there can be valid arguments from false premisses to false conclusions, and invalid arguments for true conclusions 120