Combining Texts

All the ideas for 'Foundations of Geometry', 'Commentary on Euclid's 'Elements'' and 'The Thesis that Mathematics is Logic'

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7 ideas

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism

10066

Putnam coined the term 'if-thenism' [Putnam, by Musgrave]

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

13472

Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]

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

9546	Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]

18742

Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]

18217

Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]

14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations

13165

Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus]

18. Thought / E. Abstraction / 1. Abstract Thought

9569	The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus]