Combining Texts

All the ideas for 'Commentary on 'Posterior Analytics'', 'Two Problems of Epistemology' and 'What is Cantor's Continuum Problem?'

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

8 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
16629 By comparing qualities and features, reason can gradually infer the nature of substance [Grosseteste]
14. Science / A. Basis of Science / 6. Falsification
18284 Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper]