Combining Texts

All the ideas for 'Some Main Problems of Philosophy', 'Protocol Sentences' and 'Review of Chihara 'Struct. Accnt of Maths''

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9 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
17992 The main aim of philosophy is to describe the whole Universe. [Moore,GE]
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]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
10486 If we are rebuilding our ship at sea, we should jettison some cargo [Boolos on Neurath]
8485 We must always rebuild our ship on the open sea; we can't reconstruct it properly in dry-dock [Neurath]