Ideas from 'On Platonism in Mathematics' by Paul Bernays [1934], by Theme Structure

[found in 'Philosophy of Mathematics: readings (2nd)' (ed/tr Benacerraf/Putnam) [CUP 1983,0-521-29648-x]].

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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

10304

Very few things in set theory remain valid in intuitionist mathematics

			Full Idea: Very few things in set theory remain valid in intuitionist mathematics.
			From: Paul Bernays (On Platonism in Mathematics [1934])

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

10303

Restricted Platonism is just an ideal projection of a domain of thought

			Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought.
			From: Paul Bernays (On Platonism in Mathematics [1934], p.261)
			A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

10306

Mathematical abstraction just goes in a different direction from logic

			Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction.
			From: Paul Bernays (On Platonism in Mathematics [1934], 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.