Combining Philosophers

Ideas for Paul Audi, Charles Sanders Peirce and Bob Hale

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6 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

10632

The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

14775

Numbers are just names devised for counting [Peirce]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

14776

That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

14788

Mathematics is close to logic, but is even more abstract [Peirce]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism

19295

Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale]

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism

19226

We now know that mathematics only studies hypotheses, not facts [Peirce]