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Ideas of Paul Bernays, by Text

[Swiss, 1888 - 1977, Professor at Göttingen. Worked closely with Hilbert.]

1934 On Platonism in Mathematics
p.263 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])
p.261 p.261 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.
p.268 p.268 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.