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All the ideas for 'Review of Bob Hale's 'Abstract Objects'', 'Elements of Geometry' and 'On Eternal and Immutable Morality'

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22 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
9184 We can't presume that all interesting concepts can be analysed [Williamson]
2. Reason / E. Argument / 6. Conclusive Proof
8623 Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / c. Derivations rules of PC
13907 If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
6297 Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9603 An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
9894 A unit is that according to which each existing thing is said to be one [Euclid]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
8738 Postulate 2 says a line can be extended continuously [Euclid, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
22278 Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid]
8673 Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend]
10250 Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid]
10302 Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]
14157 Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
1600 Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
9183 Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / c. Tabula rasa
6230 If the soul were a tabula rasa, with no innate ideas, there could be no moral goodness or justice [Cudworth]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
6228 Senses cannot judge one another, so what judges senses cannot be a sense, but must be superior [Cudworth]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
6229 Sense is fixed in the material form, and so can't grasp abstract universals [Cudworth]
22. Metaethics / B. Value / 1. Nature of Value / c. Objective value
6227 Keeping promises and contracts is an obligation of natural justice [Cudworth]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
6225 Obligation to obey all positive laws is older than all laws [Cudworth]
28. God / A. Divine Nature / 4. Divine Contradictions
6224 An omnipotent will cannot make two things equal or alike if they aren't [Cudworth]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
6223 If the will and pleasure of God controls justice, then anything wicked or unjust would become good if God commanded it [Cudworth]
6226 The requirement that God must be obeyed must precede any authority of God's commands [Cudworth]