Combining Texts

All the ideas for 'Foundations of Geometry', 'Structure and Ontology' and 'The Handbook [Encheiridion]'

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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]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
A structure is an abstraction, focussing on relationships, and ignoring other features [Shapiro]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
We see nature's will in the ways all people are the same [Epictetus]
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
Epictetus says we should console others for misfortune, but not be moved by pity [Epictetus, by Taylor,C]
If someone is weeping, you should sympathise and help, but not share his suffering [Epictetus]
25. Social Practice / D. Justice / 3. Punishment / a. Right to punish
Perhaps we should persuade culprits that their punishment is just? [Epictetus]