Prior Analytics - Book I   

the particular premiss is assertoric and negative, there cannot be a

syllogism. As instances of the positive relation we may take the terms

white-animal-snow; of the negative, white-animal-pitch. For the

demonstration must be made through the indefinite nature of the

particular premiss. But if the minor premiss is universal, and the

major particular, whether either premiss is negative or affirmative,

problematic or assertoric, nohow is a syllogism possible. Nor is a

syllogism possible when the premisses are particular or indefinite,

whether problematic or assertoric, or the one problematic, the other

assertoric. The demonstration is the same as above. As instances of

the necessary and positive relation we may take the terms

animal-white-man; of the necessary and negative relation,

animal-white-garment. It is evident then that if the major premiss

is universal, a syllogism always results, but if the minor is

universal nothing at all can ever be proved.



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Whenever one premiss is necessary, the other problematic, there will

be a syllogism when the terms are related as before; and a perfect

syllogism when the minor premiss is necessary. If the premisses are

affirmative the conclusion will be problematic, not assertoric,

whether the premisses are universal or not: but if one is affirmative,

the other negative, when the affirmative is necessary the conclusion

will be problematic, not negative assertoric; but when the negative is

necessary the conclusion will be problematic negative, and

assertoric negative, whether the premisses are universal or not.

Possibility in the conclusion must be understood in the same manner as

before. There cannot be an inference to the necessary negative

proposition: for 'not necessarily to belong' is different from

'necessarily not to belong'.

If the premisses are affirmative, clearly the conclusion which