In Defense Of The Square of Opposition

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The square of opposition in traditional logic is thought by many contemporary logicians to suffer from an inherent formal defect. Many of these logicians think that universal propositions in both affirmative and negative modes (traditionally called A and E propositions) do not have “existential import” for at times they can refer to a “null class”. Particular propositions (i.e. “Some S is P”) are held to clearly refer to actual existence and so the very notion of subalternation, where from, “All S is P” it is inferred that at least “Some S is P”, is erroneous.

But the reasons behind this charge are dubious at best, and in this essay I will examine a typical instance of this criticism and then offer what amounts to a traditional logician’s response from a scholastic perspective. It seems to me that with the scholastic understanding of supposition, there is nothing new in these charges that was not already explicitly or at least implicitly addressed by scholastic logicians.

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