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Ideas from 'Mathematical Truth' by Paul Benacerraf [1973], by Theme Structure

[found in 'Philosophy of Mathematics: readings (2nd)' (ed/tr Benacerraf/Putnam) [CUP 1983,0-521-29648-x]].

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6. Mathematics / A. Nature of Mathematics / 1. Mathematics
9935 Mathematical truth is always compromising between ordinary language and sensible epistemology
                        Full Idea: Most accounts of the concept of mathematical truth can be identified with serving one or another of either semantic theory (matching it to ordinary language), or with epistemology (meshing with a reasonable view) - always at the expense of the other.
                        From: Paul Benacerraf (Mathematical Truth [1973], Intro)
                        A reaction: The gist is that language pulls you towards platonism, and epistemology pulls you towards empiricism. He argues that the semantics must give ground. He's right.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
17927 Realists have semantics without epistemology, anti-realists epistemology but bad semantics
                        Full Idea: Benacerraf argues that realists about mathematical objects have a nice normal semantic but no epistemology, and anti-realists have a good epistemology but an unorthodox semantics.
                        From: report of Paul Benacerraf (Mathematical Truth [1973]) by Mark Colyvan - Introduction to the Philosophy of Mathematics 1.2
9936 The platonist view of mathematics doesn't fit our epistemology very well
                        Full Idea: The principle defect of the standard (platonist) account of mathematical truth is that it appears to violate the requirement that our account be susceptible to integration into our over-all account of knowledge.
                        From: Paul Benacerraf (Mathematical Truth [1973], III)
                        A reaction: Unfortunately he goes on to defend a causal theory of justification (fashionable at that time, but implausible now). Nevertheless, his general point is well made. Your theory of what mathematics is had better make it knowable.