Combining Texts

All the ideas for 'Dthat', 'On Platonism in Mathematics' and 'Reply to Second Objections'

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5 ideas

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

10304	Very few things in set theory remain valid in intuitionist mathematics [Bernays]
	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 [Bernays]
	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 [Bernays]
	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.

11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito

3622	The Cogito is not a syllogism but a self-evident intuition [Descartes]
	Full Idea: When someone says 'I am thinking, therefore I am, or I exist', he does not deduce existence from thought by means of a syllogism, but recognises it as something self-evident by a simple intuition of the mind.
	From: René Descartes (Reply to Second Objections [1641], 140)

19. Language / B. Reference / 3. Direct Reference / b. Causal reference

14080	Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J]
	Full Idea: Kaplan notes that the causal theory of reference can be understood in two quite different ways, as part of the semantics (involving descriptions of causal processes), or as metasemantics, explaining why a term has the referent it does.
	From: report of David Kaplan (Dthat [1970]) by Jonathan Schaffer - Deflationary Metaontology of Thomasson 1
	A reaction: [Kaplan 'Afterthought' 1989] The theory tends to be labelled as 'direct' rather than as 'causal' these days, but causal chains are still at the heart of the story (even if more diffused socially). Nice question. Kaplan takes the meta- version as orthodox.