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Single Idea 10306

[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique ]

Full Idea

Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction.

Gist of Idea

Mathematical abstraction just goes in a different direction from logic

Source

Paul Bernays (On Platonism in Mathematics [1934], p.268)

Book Ref

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.268

A Reaction

His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic.

The 3 ideas from Paul Bernays

10304 Very few things in set theory remain valid in intuitionist mathematics [Bernays]
10303 Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
10306 Mathematical abstraction just goes in a different direction from logic [Bernays]