Abstract

And so the matter might be allowed to rest. But unfortunately, despite the prevailing consensus that there really isn't any issue any longer between the two types of logic, we should like in this paper to reopen the whole issue. Our justification for so doing is that, so far as we know, in most of the discussions of the nature of the difference between Aristotelian logic and mathematical logic there has not been too much attention paid to the metaphysical question as to what precisely so-called logical "forms" may be said to be. Thus everyone --both Aristotelians and mathematical logicians--quite glibly use the term "formal logic." But we wonder if either the one party or the other has ever stopped long enough seriously to consider the fact that the actual ontological status that is ascribed to such forms is very different for the one tradition from what it is for the other. Indeed, we cannot help feeling that as soon as such metaphysical differences are clearly recognized, philosophers may well come to see that Aristotelian logic and mathematical logic are not "both 'logic' in the strictest sense of the word," nor do they "both have, vaguely speaking, the same subject matter."