13: On Affirmative Propositions in which There Occur Privative Terms which are not Equivalent to Infinite Terms
On Affirmative Propositions with Privative Terms neither 'A white man is a man' nor 'A white man is a non-man' is true. For if 'A white man is a-.non-man' is true, then, since it is affirmative, it is necessary that the subject supposit for something. Given that, I ask: for what does it supposit? Not for a spoken word or for a concept, since it is suppositing significatively and not materially or simply. Therefore, it supposits for something else. Consequently, the term 'white man', taken significatively, would be predicated of a pronoun referring to that for which it supposits. And, as a result, 'This is a white man' would be true—which is manifestly false. For if it is true, then either a being or a non-being is being referred to. If a being, then some being would be a white man, which is contrary to what was assumed; if a non-being, then some non-being would be a white man and would, consequently, be white—which is obviously false. And so it is clear that if no man is white, then
'A white man is a non-man' is false. And similar propositions can be proven false by the same line of reasoning.
13: On Affirmative Propositions in which There Occur Privative Terms which are not Equivalent to Infinite Terms Although propositions containing infinite terms or their equivalents have only two exponents, still affirmative propositions which contain privative terms that are not equivalent to infinite terms have more than two exponents. Hence, the proposition
'He is blind' has these exponents: 'He is something', 'By nature he should have sight', 'He will never be able to see naturally'.
But it is not possible to give firm rules for such propositions, for because of the variety of such terms the propositions in which they occur have to be expounded in different ways. Hence,
'Socrates is blind' has the exponents which have been mentioned.
But the proposition 'Socrates is foolish' has these exponents: