Combining Texts

All the ideas for 'A Specimen of Discoveries', 'Continuity and Irrational Numbers' and 'Philosophical Implications of Mathematical logic'

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

9 ideas

2. Reason / A. Nature of Reason / 4. Aims of Reason
5035 The two basics of reasoning are contradiction and sufficient reason [Leibniz]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
22329 Logic is highly general truths abstracted from reality [Russell, by Glock]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
17611 We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
10572 A cut between rational numbers creates and defines an irrational number [Dedekind]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
17612 Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18087 If x changes by less and less, it must approach a limit [Dedekind]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
21569 It is good to generalise truths as much as possible [Russell]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
5038 Assume that mind and body follow their own laws, but God has harmonised them [Leibniz]
29. Religion / D. Religious Issues / 3. Problem of Evil / b. Human Evil
5037 God doesn't decide that Adam will sin, but that sinful Adam's existence is to be preferred [Leibniz]