Combining Texts

All the ideas for 'What is Cantor's Continuum Problem?st1=Kurt Gödel', 'Theory of Knowledge (2nd ed 1977)' and 'On the Notion of Cause'

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14 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
Philosophers usually learn science from each other, not from science [Russell]
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]
10. Modality / A. Necessity / 2. Nature of Necessity
'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument [Russell]
11. Knowledge Aims / A. Knowledge / 5. Aiming at Truth
We have a basic epistemic duty to believe truth and avoid error [Chisholm, by Kvanvig]
26. Natural Theory / C. Causation / 7. Eliminating causation
The law of causality is a source of confusion, and should be dropped from philosophy [Russell]
If causes are contiguous with events, only the last bit is relevant, or the event's timing is baffling [Russell]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
Striking a match causes its igniting, even if it sometimes doesn't work [Russell]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
In causal laws, 'events' must recur, so they have to be universals, not particulars [Russell]
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
The constancy of scientific laws rests on differential equations, not on cause and effect [Russell]