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Posted by Harvey on October 4, 2001 02:19:23 UTC

Just a important clarification. Alex, when you asked about the composition of physical/material things as being reduced to [mathematical] concepts I think this is properly called a form of idealism (as contrasted with materialism). However, when referring to the view that mathematical reality exists as a priori to the physical world, then this view can be called mathematical realism (or platonism if you prefer). The difference, I think, is a merging of concepts in study of ontology (i.e., what all exists) and the study of categories - specifically substances. If a mathematical characterization is treated as an ontology to the world (e.g., truth values, possibility), the correct reference (I think) should be mathematical realism (or platonism). If treated as a substance (e.g., strings are purely mathematical objects), then I think arguably it should be called a form of mathematical idealism (or something like that).

The opposite correspondence is usually:

1. Universals: platonism nominalism

2. Substances: idealism materialism

3. Statements: realism antirealism

4. Phil of Math:
structuralism constructivism, etc

Anyway, this is all just my opinion. I'm sure this is a tad more philosophy than most people are interested in.

Warm regards, Harv

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