Combining Texts

All the ideas for 'fragments/reports', 'Principles of Arithmetic, by a new method' and 'Could There Be Unicorns?'

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18 ideas

1. Philosophy / D. Nature of Philosophy / 4. Divisions of Philosophy
Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
It was realised that possible worlds covered all modal logics, if they had a structure [Dummett]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett]
Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
In S4 the actual world has a special place [Dummett]
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]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
To explain generosity in a person, you must understand a generous action [Dummett]
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman]