Combining Texts

All the ideas for 'Chomsky on himself', 'The Principles of Chemistry' and 'What is Cantor's Continuum Problem?'

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11 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]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
6649 Chomsky now says concepts are basically innate, as well as syntax [Chomsky, by Lowe]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
17402 Mendeleev saw three principles in nature: matter, force and spirit (where the latter seems to be essence) [Mendeleev, by Scerri]
27. Natural Reality / F. Chemistry / 2. Modern Elements
17399 Elements don't survive in compounds, but the 'substance' of the element does [Mendeleev]
27. Natural Reality / F. Chemistry / 3. Periodic Table
17400 Mendeleev focused on abstract elements, not simple substances, so he got to their essence [Mendeleev, by Scerri]
17401 Mendeleev had a view of elements which allowed him to overlook some conflicting observations [Mendeleev]