Combining Texts

All the ideas for 'Through the Looking Glass', 'A New Kind of Science' and 'Foundations of Geometry'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
13472 Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
20660 At one level maths and nature are very similar, suggesting some deeper origin [Wolfram]
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 / e. Being and nothing
21982 I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
27. Natural Reality / C. Space / 4. Substantival Space
20659 Space and its contents seem to be one stuff - so space is the only existing thing [Wolfram]