Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Foundations of Geometry' and 'Questions on Aristotle's Physics'

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9 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 / c. Counting procedure
17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
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]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16678 Without magnitude a thing would retain its parts, but they would have no location [Buridan]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
16793 A thing is (less properly) the same over time if each part is succeeded by another [Buridan]
14. Science / A. Basis of Science / 2. Demonstration
16577 Induction is not demonstration, because not all of the instances can be observed [Buridan]
14. Science / C. Induction / 2. Aims of Induction
16576 Science is based on induction, for general truths about fire, rhubarb and magnets [Buridan]