Ideas from 'Mathematical Truth' by Paul Benacerraf [1973], by Theme Structure
[found in 'Philosophy of Mathematics: readings (2nd)' (ed/tr Benacerraf/Putnam) [CUP 1983,052129648x]].
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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, antirealists epistemology but bad semantics




Full Idea:
Benacerraf argues that realists about mathematical objects have a nice normal semantic but no epistemology, and antirealists 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 overall 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.
