Square of Opposition - The Problem of Existential Import

The Problem of Existential Import

Subcontraries, which medieval logicians represented in the form 'quoddam A est B' (some particular A is B) and 'quoddam A non est B' (some particular A is not B) cannot both be false, since their universal contradictory statements (every A is B / no A is B) cannot both be true. This leads to a difficulty that was first identified by Peter Abelard. 'Some A is B' seems to imply 'something is A'. For example 'Some man is white' seems to imply that at least one thing is a man, namely the man who has to be white if 'some man is white' is true. But 'some man is not white' also seems to imply that something is a man, namely the man who is not white if 'some man is not white' is true. But Aristotelian logic requires that necessarily one of these statements is true. Both cannot be false. Therefore (since both imply that something is a man) it follows that necessarily something is a man, i.e. men exist. But (as Abelard points out, in the Dialectica) surely men might not exist?

For with absolutely no man existing, neither the proposition 'every man is a man' is true nor 'some man is not a man'.

Abelard also points out that subcontraries containing subject terms denoting nothing, such as 'a man who is a stone', are both false.

If 'every stone-man is a stone' is true, also its conversion per accidens is true ('some stone-men are stones'). But no stone is a stone-man, because neither this man nor that man etc. is a stone. But also this 'a certain stone-man is not a stone' is false by necessity, since it is impossible to suppose it is true.

Terence Parsons argues that ancient philosophers did not experience the problem of existential import as only the A and I forms had existential import.

Affirmatives have existential import, and negatives do not. The ancients thus did not see the incoherence of the square as formulated by Aristotle because there was no incoherence to see.

He goes on to cite medieval philosopher William of Ockham

In affirmative propositions a term is always asserted to supposit for something. Thus, if it supposits for nothing the proposition is false. However, in negative propositions the assertion is either that the term does not supposit for something or that it supposits for something of which the predicate is truly denied. Thus a negative proposition has two causes of truth.

And points to Boethius' translation of Aristotle's work as giving rise to the mistaken notion that the O form has existential import.

But when Boethius comments on this text he illustrates Aristotle's doctrine with the now-famous diagram, and he uses the wording 'Some man is not just'. So this must have seemed to him to be a natural equivalent in Latin. It looks odd to us in English, but he wasn't bothered by it.