Combining Texts

All the ideas for 'Two Problems of Epistemology', 'works' and 'Martin Heidegger in conversation'

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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reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date.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.

7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)

15584	I say the manifestation of Being needs humans, and humans only exist as reflected in Being [Heidegger]
	Full Idea: The fundamental thought of my thinking is precisely that Being, or the manifestation of Being, needs human beings and that, vice versa, human beings are only human beings if they are standing in the manifestation of Being.
	From: Martin Heidegger (Martin Heidegger in conversation [1969], p.82), quoted by Richard Polt - Heidegger: an introduction 5 'Signs'
	A reaction: I don't think I understand the second half of this, but I sense some sort of intuition that the consciousness of humans 'enlarges' Being, or bestows an identity on it, or some such thing.

14. Science / A. Basis of Science / 6. Falsification

18284	Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper]
	Full Idea: Whereas particular reality statements are in principle completely verifiable or falsifiable, things are different for general reality statements: they can indeed be conclusively falsified, they can acquire a negative truth value, but not a positive one.
	From: Karl Popper (Two Problems of Epistemology [1932], p.256), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 18 'Laws'
	A reaction: This sounds like a logician's approach to science, but I prefer to look at coherence, where very little is actually conclusive, and one tinkers with the theory instead.