Combining Texts

All the ideas for 'Theory of Knowledge (2nd edn)', 'Foundations of Geometry' and 'Philosophical Explanations'

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8 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]

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]

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]

11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs

3570	Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M]

13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts

2748	A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]