Combining Texts

Ideas for 'The Problem of Empty Names', 'Replies on 'Limits of Abstraction'' and 'New Essays on Human Understanding'

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8 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

13008

Geometry, unlike sensation, lets us glimpse eternal truths and their necessity [Leibniz]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

10573

Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts

10575

Why should a Dedekind cut correspond to a number? [Fine,K]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero

10574

Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units

12956

Only whole numbers are multitudes of units [Leibniz]

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

12937

We shouldn't just accept Euclid's axioms, but try to demonstrate them [Leibniz]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory

10560

Set-theoretic imperialists think sets can represent every mathematical object [Fine,K]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

10568

Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K]