Combining Texts

All the ideas for 'fragments/reports', 'Principles of Arithmetic, by a new method' and 'Natural Minds'

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13 ideas

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]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
The taste of chocolate is a 'finer-grained' sensation than the taste of sweetness [Polger]
16. Persons / B. Nature of the Self / 1. Self and Consciousness
The mind and the self are one, and the mind-self is a biological phenomenon [Polger]
17. Mind and Body / C. Functionalism / 5. Teleological Functionalism
Teleological functions explain why a trait exists; causal-role functions say what it does [Polger]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Identity theory says consciousness is an abstraction: a state, event, process or property [Polger]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
A mummified heart has the teleological function of circulating blood [Polger]
Teleological notions of function say what a thing is supposed to do [Polger]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]