more from Kurt Gdel

Single Idea 10043

[catalogued under 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism]

Full Idea

Classes and concepts may be conceived of as real objects, ..and are as necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions, with neither case being about 'data'.

Gist of Idea

Mathematical objects are as essential as physical objects are for perception


Kurt Gdel (Russell's Mathematical Logic [1944], p.456)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.456

A Reaction

Note that while he thinks real objects are essential for mathematics, be may not be claiming the same thing for our knowledge of logic. If logic contains no objects, then how could mathematics be reduced to it, as in logicism?