Combining Texts

All the ideas for 'Philosophical Essay on Probability', 'First Things First' and 'What is Cantor's Continuum Problem?'

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12 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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
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
Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
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
Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
Evidentialism is not axiomatic; the evidence itself inclines us towards evidentialism [Conee]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
If pure guesses were reliable, reliabilists would have to endorse them [Conee]
More than actual reliability is needed, since I may mistakenly doubt what is reliable [Conee]
Reliabilism is poor on reflective judgements about hypothetical cases [Conee]
13. Knowledge Criteria / C. External Justification / 7. Testimony
The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace]