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All the ideas for 'Dthat', 'The Problem of Natural Laws' and 'works'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics

12427	All of mathematics is properties of the whole numbers [Kronecker]
	Full Idea: All the results of significant mathematical research must ultimately be expressible in the simple forms of properties of whole numbers.
	From: Leopold Kronecker (works [1885], Vol 3/274), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 09.5
	A reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date. Natural numbers have a special status, but not sufficient to support this claim.

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers

10091	God made the integers, all the rest is the work of man [Kronecker]
	Full Idea: God made the integers, all the rest is the work of man.
	From: Leopold Kronecker (works [1885]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Intro
	A reaction: This famous remark was first quoted in Kronecker's obituary. A response to Dedekind, it seems. See Idea 10090. Did he really mean that negative numbers were the work of God? We took a long time to spot them.

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.

26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities

4800	Natural laws result from eliminative induction, where enumerative induction gives generalisations [Cohen,LJ, by Psillos]
	Full Idea: Cohen contends that statements that express laws of nature are the products of eliminative induction, where accidentally true generalisations are the products of enumerative induction.
	From: report of L. Jonathan Cohen (The Problem of Natural Laws [1980], p.222) by Stathis Psillos - Causation and Explanation §7.1
	A reaction: The idea is that enumerative induction only offers the support of positive instances, where eliminative induction involves attempts to falsify a range of hypotheses. This still bases laws on observed regularities, rather than essences or mechanisms.