Combining Texts

All the ideas for 'fragments/reports', 'Essentials of Pragmatism' and 'Foundations of Geometry'

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9 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
Instead of seeking Truth, we should seek belief that is beyond doubt [Peirce]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
A 'conception', the rational implication of a word, lies in its bearing upon the conduct of life [Peirce]
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
The definition of a concept is just its experimental implications [Peirce]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]