Combining Texts

All the ideas for 'fragments/reports', 'German Philosophy: a very short introduction' and 'Principles of Arithmetic, by a new method'

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10 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

13949

All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]

18113

PA concerns any entities which satisfy the axioms [Peano, by Bostock]

17634

Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

15653

We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

17635

Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]

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]

23. Ethics / A. Egoism / 1. Ethical Egoism

3031	The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius]