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Ideas for 'works', 'System of Logic' and 'Axiomatic Thought'

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5 ideas

6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics

17967

To decide some questions, we must study the essence of mathematical proof itself [Hilbert]

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

17965

The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers

8742	The only axioms needed are for equality, addition, and successive numbers [Mill, by Shapiro]

17964

Number theory just needs calculation laws and rules for integers [Hilbert]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic

9800	Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal [Mill]