Combining Texts

All the ideas for 'Towards a Critique of Hegel's Philosophy', 'Review of Chihara 'Struct. Accnt of Maths'' and 'On boundary numbers and domains of sets'

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16 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
19441 All philosophies presuppose their historical moment, and arise from it [Feuerbach]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
19442 I don't study Plato for his own sake; the primary aim is always understanding [Feuerbach]
2. Reason / C. Styles of Reason / 1. Dialectic
19444 Each proposition has an antithesis, and truth exists as its refutation [Feuerbach]
19445 A dialectician has to be his own opponent [Feuerbach]
3. Truth / A. Truth Problems / 3. Value of Truth
19443 Truth forges an impersonal unity between people [Feuerbach]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17832 Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13028 Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy]
5. Theory of Logic / L. Paradox / 3. Antinomies
17626 The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10185 Set theory is the standard background for modern mathematics [Burgess]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10184 Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess]
10189 There is no one relation for the real number 2, as relations differ in different models [Burgess]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10186 If set theory is used to define 'structure', we can't define set theory structurally [Burgess]
10187 Abstract algebra concerns relations between models, not common features of all the models [Burgess]
10188 How can mathematical relations be either internal, or external, or intrinsic? [Burgess]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
19446 To our consciousness it is language which looks unreal [Feuerbach]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
19447 The Absolute is the 'and' which unites 'spirit and nature' [Feuerbach]