Prior Analytics - Book I   

the universal is both negative and necessary the conclusion also

will be necessary. For if it is not possible that A should belong to

any C, but B belongs to some C, it is necessary that A should not

belong to some B. But whenever the affirmative proposition is

necessary, whether universal or particular, or the negative is

particular, the conclusion will not be necessary. The proof of this by

reduction will be the same as before; but if terms are wanted, when

the universal affirmative is necessary, take the terms

'waking'-'animal'-'man', 'man' being middle, and when the

affirmative is particular and necessary, take the terms

'waking'-'animal'-'white': for it is necessary that animal should

belong to some white thing, but it is possible that waking should

belong to none, and it is not necessary that waking should not

belong to some animal. But when the negative proposition being

particular is necessary, take the terms 'biped', 'moving', 'animal',

'animal' being middle.

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It is clear then that a simple conclusion is not reached unless both

premisses are simple assertions, but a necessary conclusion is

possible although one only of the premisses is necessary. But in

both cases, whether the syllogisms are affirmative or negative, it

is necessary that one premiss should be similar to the conclusion. I

mean by 'similar', if the conclusion is a simple assertion, the

premiss must be simple; if the conclusion is necessary, the premiss

must be necessary. Consequently this also is clear, that the

conclusion will be neither necessary nor simple unless a necessary

or simple premiss is assumed.



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Perhaps enough has been said about the proof of necessity, how it