Combining Texts

All the ideas for 'The Courtier and the Heretic', 'Principles of Arithmetic, by a new method' and 'New system of communication of substances'

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11 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]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
13168 My formal unifying atoms are substantial forms, which are forces like appetites [Leibniz]
13169 I call Aristotle's entelechies 'primitive forces', which originate activity [Leibniz]
9. Objects / A. Existence of Objects / 5. Simples
13170 The analysis of things leads to atoms of substance, which found both composition and action [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
13171 Substance must necessarily involve progress and change [Leibniz]
24. Political Theory / D. Ideologies / 10. Theocracy
7825 The politics of Leibniz was the reunification of Christianity [Stewart,M]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
13167 We need the metaphysical notion of force to explain mechanics, and not just extended mass [Leibniz]