Combining Texts

All the ideas for 'Definitiones cogitationesque metaphysicae', 'Foundations of Geometry' and 'Tropes'

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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]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
We might treat both tropes and substances as fundamental, so we can't presume it is just tropes [Daly]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
More than one trope (even identical ones!) can occupy the same location [Daly]
If tropes are linked by the existence of concurrence, a special relation is needed to link them all [Daly]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Substance is that which can act [Leibniz]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
Nature can be fully explained by final causes alone, or by efficient causes alone [Leibniz]