Combining Texts

All the ideas for 'works (fragments)', 'works' and 'Foundations of Geometry'

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11 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason

1815	Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius]

1812	All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius]

1811	Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius]

1813	All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius]

5. Theory of Logic / G. Quantification / 2. Domain of Quantification

17743

De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki]

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]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma

8850	Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M]

13. Knowledge Criteria / E. Relativism / 1. Relativism

1814	Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius]