Volume 65, Issue 4, October 1982
Metaphysics and Logic
Presuppositions for Logic
Positivists identify science and certainty and in the name of the utter rationality of science deny that it rests on speculative presuppositions. The Logical Positivists took a step further and tried to show such presuppositions really no presuppositions at all but rather poorly worded sentences. Rules of sentence formation, however, rest on the presuppositions about the nature of language. This makes us unable to determine the status of mathematics, which is these days particularly irksome since this question is now-since Abraham Robinson-one that mathematicians cannot ignore. Since mathematics is the paradigm of a logical discourse, logic must offer a system adequate enough to serve mathematics. This fact makes it difficult to avoid making question-begging moves in both mathematics and logic. We must therefore view the rationality of logic as partial and hope it is stepwise improvable. The theory of rationality thus turns to be the major presupposition of logic, and one which has ample metaphysical background to it. The very supposition, basic to all logic, that language is divisible into form and
content is under suspicion-mathematics perhaps belongs to neither.