Combining Texts

All the ideas for 'German Philosophy: a very short introduction', 'What is Cantor's Continuum Problem?' and 'Set Theory and related topics (2nd ed)'

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11 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes

8920	Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]

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]

11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism

22049

Transcendental idealism aims to explain objectivity through subjectivity [Bowie]

11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism

22055

The Idealists saw the same unexplained spontaneity in Kant's judgements and choices [Bowie]

22054

German Idealism tried to stop oppositions of appearances/things and receptivity/spontaneity [Bowie]

22056

Crucial to Idealism is the idea of continuity between receptivity and spontaneous judgement [Bowie]