Combining Philosophers

All the ideas for Herodotus, Georg Kreisel and Anaximenes

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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.

26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances

1497	For Anaximenes nature is air, which takes different forms by rarefaction and condensation [Anaximenes, by Simplicius]
	Full Idea: Unlike Anaximander, Anaximenes' underlying nature is not boundless, but specific, since he says that it is air, and claims that it is thanks to rarefaction and condensation that it manifests in different forms in different things.
	From: report of Anaximenes (fragments/reports [c.546 BCE], A5) by Simplicius - On Aristotle's 'Physics' 9.24.26-

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.

29. Religion / D. Religious Issues / 2. Immortality / a. Immortality

1513	The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]
	Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born.
	From: Herodotus (The Histories [c.435 BCE], 2.123.2)