Combining Texts

All the ideas for 'The Logic of Boundaryless Concepts', '74: Reply to Colotes' and 'Principles of Arithmetic, by a new method'

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13 ideas

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic guides thinking, but it isn't a substitute for it [Rumfitt]
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]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt]
16. Persons / B. Nature of the Self / 7. Self and Body / c. Self as brain controller
Rather than being the whole soul, maybe I am its chief part? [Plutarch]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
If atoms have no qualities, they cannot possibly produce a mind [Plutarch]
20. Action / B. Preliminaries of Action / 1. Intention to Act / c. Reducing intentions
Action needs an affinity for a presentation, and an impulse toward the affinity [Plutarch]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The good life involves social participation, loyalty, temperance and honesty [Plutarch]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
If only atoms exist, how do qualities arise when the atoms come together? [Plutarch]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
No one will ever find a city that lacks religious practices [Plutarch]