Combining Texts

All the ideas for 'Aquinas, Thomas', 'Commentary on Euclid's 'Elements'' and 'On the Foundations of Logic and Arithmetic'

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

5 ideas

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17697 The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
17698 Logic already contains some arithmetic, so the two must be developed together [Hilbert]
14. Science / A. Basis of Science / 2. Demonstration
22110 Demonstration provides depth of understanding and explanation (rather than foundations) [Kretzmann/Stump]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
13165 Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus]
18. Thought / E. Abstraction / 1. Abstract Thought
9569 The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus]