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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]) |
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. |
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. |