18: On Exceptive Propositions
18: On Exceptive Propositions As far as exceptive propositions are concerned we must examine, first, which propositions are exceptive; second, what is required for the truth of exceptive propositions; third, the supposition of the terms in exceptive propositions; fourth, certain rules which should be given for exceptive propositions.
On the first point it should be noted that such syncategorematic expressions as 'except' and 'unless' make the propositions in which they occur exceptive propositions.
But it should first be understood that sometimes 'unless' is used as a conjunction, in which case it renders the proposition hypothetical, as is clear from the proposition 'Socrates cannot run unless he has feet'. Sometimes, however, it is used exceptively, in which case it does not make the proposition hypothetical, as is clear from the proposition 'No man is running unless
Socrates'. In such a case the expression 'unless' has the same function as the expression 'except', when the latter is taken exceptively.
Moreover, it should also be noted that the expression 'except' is sometimes used exceptively and sometimes diminutively. It is used exceptively, for instance, in 'Every man except Socrates is running'. It is used diminutively, for example, in 'Ten except five is five'.
With respect to the second principal point it should be noted that for the truth of an exceptive proposition it is required that the predicate be denied of the excepted thing and that it inhere. in everything else contained under the subject—if the proposition is affirmative. If the proposition is negative, then the converse is required. Thus, every exceptive proposition has two exponents, namely, one affirmative and one negative. For example, 'Every man except Socrates is running' has these exponents: 'Socrates is not running' and 'Every man other than Socrates is running'.
And the proposition 'No man except Socrates is running' has these exponents: 'Socrates is running' and 'No man other than
Socrates is running'. Thus it is impossible for an exceptive proposition to be true unless each of its exponents is true. Therefore,
On Exceptive Propositions the falsity of the exceptive follows from the falsity of a given exponent, but not conversely.
With respect to the third principal point it should be noted that the predicate in an affirmative exceptive proposition has merely confused supposition, since it is not possible to descend to the inferiors by either a disjunctive or a conjunctive proposition. The subject, however, has confused and distributive supposition.
Still, a distinction must be made with regard to confused and distributive supposition. For sometimes it is absolute, namely, when the term is equally distributed over each of the things contained under it in such a way that it is distributed over one no more than over another. Now the subject in an exceptive proposition does not have this sort of confused and distributive supposition. The other sort is, as it were, limited and circumscribed, namely, when the term is distributed over some of the things contained under it but, in virtue of something added to it, is not distributed over others of them. This does not happen except when the categorical proposition in question is equivalent to a conjunctive proposition composed of one affirmative part and one negative part. This is the case with an exceptive proposition, as has been pointed out.
Now if an exceptive proposition is negative, then both the subject and the predicate have confused and distributive supposition of the limited type.
From what has been said it is clear that rules such as the following are not universally true: 'There is a valid consequence from a distributed superior to its inferior' and 'There is a valid consequence from a universal proposition to its singular'. Rather, it must be added that the inferior in question is not an excepted term or that the universal proposition in question is not equivalent to a conjunctive proposition composed of one affirmative part and one negative part.
With respect to the fourth point it should be noted that many tules are given for exceptive propositions. One is that if the nonexceptive counterpart of an exceptive proposition is true, then the exceptive is false. This is clear from what has been said.
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