Combining Texts

All the ideas for 'Foundations of Geometry', 'Against the Ethicists (one book)' and 'Transworld Heir Lines'

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14 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
Reasoning is impossible without a preconception [Sext.Empiricus]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Logicians like their entities to exhibit a maximum degree of purity [Kaplan]
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]
9. Objects / C. Structure of Objects / 7. Substratum
Models nicely separate particulars from their clothing, and logicians often accept that metaphysically [Kaplan]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
The simplest solution to transworld identification is to adopt bare particulars [Kaplan]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Unusual people may have no counterparts, or several [Kaplan]
Essence is a transworld heir line, rather than a collection of properties [Kaplan]
19. Language / A. Nature of Meaning / 8. Synonymy
Sentences might have the same sense when logically equivalent - or never have the same sense [Kaplan]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
Saying the good is useful or choiceworth or happiness-creating is not the good, but a feature of it [Sext.Empiricus]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
Like a warming fire, what is good by nature should be good for everyone [Sext.Empiricus]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
If a desire is itself desirable, then we shouldn't desire it, as achieving it destroys it [Sext.Empiricus]