Combining Texts

All the ideas for 'Foundations of Geometry', 'De Mundo (On the World)' and 'Syntagma'

expand these ideas     |    start again     |     specify just one area for these texts

9 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
13472 Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
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 / A. Nature of Existence / 3. Being / a. Nature of Being
16789 Only supernatural means could annihilate anything once it had being [Hobbes]
8. Modes of Existence / B. Properties / 8. Properties as Modes
16730 If matter is entirely atoms, anything else we notice in it can only be modes [Gassendi]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
16619 We observe qualities, and use 'induction' to refer to the substances lying under them [Gassendi]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
16593 Atoms are not points, but hard indivisible things, which no force in nature can divide [Gassendi]
16729 How do mere atoms produce qualities like colour, flavour and odour? [Gassendi]