Prior Analytics - Book I   

Clearly then from what has been said a syllogism results or not from

similar relations of the terms whether we are dealing with simple

existence or necessity, with this exception, that if the negative

premiss is assertoric the conclusion is problematic, but if the

negative premiss is necessary the conclusion is both problematic and

negative assertoric. [It is clear also that all the syllogisms are

imperfect and are perfected by means of the figures above mentioned.]



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In the second figure whenever both premisses are problematic, no

syllogism is possible, whether the premisses are affirmative or

negative, universal or particular. But when one premiss is assertoric,

the other problematic, if the affirmative is assertoric no syllogism

is possible, but if the universal negative is assertoric a

conclusion can always be drawn. Similarly when one premiss is

necessary, the other problematic. Here also we must understand the

term 'possible' in the conclusion, in the same sense as before.

First we must point out that the negative problematic proposition is

not convertible, e.g. if A may belong to no B, it does not follow that

B may belong to no A. For suppose it to follow and assume that B may

belong to no A. Since then problematic affirmations are convertible

with negations, whether they are contraries or contradictories, and

since B may belong to no A, it is clear that B may belong to all A.

But this is false: for if all this can be that, it does not follow

that all that can be this: consequently the negative proposition is

not convertible. Further, these propositions are not incompatible,

'A may belong to no B', 'B necessarily does not belong to some of

the As'; e.g. it is possible that no man should be white (for it is

also possible that every man should be white), but it is not true to

say that it is possible that no white thing should be a man: for

many white things are necessarily not men, and the necessary (as we