Combining Texts

All the ideas for 'Foundations of Geometry', 'Truth-maker Realism: response to Gregory' and 'Kant and the Critique of Pure Reason'

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11 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
21463 Hamann, Herder and Jacobi were key opponents of the Enlightenment [Gardner]
21459 Kant halted rationalism, and forced empiricists to worry about foundations [Gardner]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
21460 Only Kant and Hegel have united nature, morals, politics, aesthetics and religion [Gardner]
2. Reason / E. Argument / 2. Transcendental Argument
21443 Transcendental proofs derive necessities from possibilities (e.g. possibility of experiencing objects) [Gardner]
3. Truth / B. Truthmakers / 2. Truthmaker Relation
18470 Maybe truth-making is an unanalysable primitive, but we can specify principles for it [Smith,B]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
13472 Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
21444 Modern geoemtry is either 'pure' (and formal), or 'applied' (and a posteriori) [Gardner]
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]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
21453 Leibnizian monads qualify as Kantian noumena [Gardner]