ABSTRACT. An analysis of traditional mathematical proof is undertaken, with an implicit contrast to formal derivations. The semantic interpretation of mathematical terms plays a role in the former that doesn't appear in the latter. This semantic interpretation, with an accompanying role for intuition, is explained in terms of inference packages, which are psychologically-bundled ways of phenomenologically exploring the effect of several assumptions at once without explicit recognition of what those assumptions are. Although its correspondence with a derivation is the (ultimate) justification for the success of a traditional proof, the certainty that mathematicians experience when they study successful traditional proofs is not due to that correspondence, but rather, for the most part, to the role of inference packages in their reasoning.



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