Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'Hilbert's Programme' and 'On Minerals'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17809 Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel]
     Full Idea: Usually Gödel's incompleteness theorems are taken as showing a limitation on the syntactic approach to an understanding of the concept of infinity.
     From: Georg Kreisel (Hilbert's Programme [1958], 05)
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17810 The study of mathematical foundations needs new non-mathematical concepts [Kreisel]
     Full Idea: It is necessary to use non-mathematical concepts, i.e. concepts lacking the precision which permit mathematical manipulation, for a significant approach to foundations. We currently have no concepts of this kind which we can take seriously.
     From: Georg Kreisel (Hilbert's Programme [1958], 06)
     A reaction: Music to the ears of any philosopher of mathematics, because it means they are not yet out of a job.
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
19347 Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
     Full Idea: For individuation, substance needs three properties: independence, to separate it from other things; unity, to call it one thing, rather than an aggregate; and permanence or stability over time. Its other role is as subject for predicates.
     From: Franklin Perkins (Leibniz: Guide for the Perplexed [2007], 3.1)
     A reaction: Perkins is describing the Aristotelian view, which is taken up by Leibniz. 'Substance' is not a controversial idea, if we see that it only means that the world is full of 'things'. It is an unusual philosopher wholly totally denies that.
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
16756 Substantial forms must exist, to explain the stability of metals like silver and tin [Albertus Magnus]
     Full Idea: There is no reason why the matter in any natural thing should be stable in its nature, if it is not completed by a substantial form. But we see that silver is stable, and tin and other metals. Therefore they will seem to be perfected by substantial forms.
     From: Albertus Magnus (On Minerals [1260], III.1.7), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.2
     A reaction: Illuminating. This may be the best reason for proposing substantial forms. Once materialism arrives, the so-called 'laws' of nature have to be imposed on the material to do the job - but what the hell is a law supposed to be?
27. Natural Reality / C. Space / 3. Points in Space
17811 The natural conception of points ducks the problem of naming or constructing each point [Kreisel]
     Full Idea: In analysis, the most natural conception of a point ignores the matter of naming the point, i.e. how the real number is represented or by what constructions the point is reached from given points.
     From: Georg Kreisel (Hilbert's Programme [1958], 13)
     A reaction: This problem has bothered me. There are formal ways of constructing real numbers, but they don't seem to result in a name for each one.