Combining Texts

All the ideas for 'Theory of Knowledge (2nd edn)', 'The Analyst' and 'works'

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5 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
2945 Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer]
     Full Idea: Some philosophers (e.g Plato) begin with an account of reality, and then appended an account of how we can know it, ..but Descartes turned the tables, insisting that we must first decide what we can know.
     From: Keith Lehrer (Theory of Knowledge (2nd edn) [2000], I p.2)
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
2946 You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer]
     Full Idea: An analysis is always relative to some objective. It makes no sense to simply demand an analysis of goodness, knowledge, beauty or truth, without some indication of the purpose of the analysis.
     From: Keith Lehrer (Theory of Knowledge (2nd edn) [2000], I p.7)
     A reaction: Your dismantling of a car will go better if you know what a car is for, but you can still take it apart in ignorance.
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reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date.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.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
18091 Infinitesimals are ghosts of departed quantities [Berkeley]
     Full Idea: The infinitesimals are the ghosts of departed quantities.
     From: George Berkeley (The Analyst [1734]), quoted by David Bostock - Philosophy of Mathematics 4.3
     A reaction: [A famous phrase, but as yet no context for it]