Combining Texts

All the ideas for '09: Galatians', 'Why Medieval Philosophy Matters' and 'Principles of Arithmetic, by a new method'

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14 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Science rests on scholastic metaphysics, not on Hume, Kant or Carnap [Boulter]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
PA concerns any entities which satisfy the axioms [Peano, by Bostock]
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
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
Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
8. Modes of Existence / D. Universals / 2. Need for Universals
Thoughts are general, but the world isn't, so how can we think accurately? [Boulter]
10. Modality / A. Necessity / 6. Logical Necessity
Logical possibility needs the concepts of the proposition to be adequate [Boulter]
14. Science / A. Basis of Science / 3. Experiment
Experiments don't just observe; they look to see what interventions change the natural order [Boulter]
14. Science / B. Scientific Theories / 1. Scientific Theory
Science begins with sufficient reason, de-animation, and the importance of nature [Boulter]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Our concepts can never fully capture reality, but simplification does not falsify [Boulter]
19. Language / E. Analyticity / 3. Analytic and Synthetic
Aristotelians accept the analytic-synthetic distinction [Boulter]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
The facts about human health are the measure of the values in our lives [Boulter]
25. Social Practice / B. Equalities / 1. Grounds of equality
Jew and Greeks, bond and free, male and female, are all one in Christ [Paul]