Combining Texts

All the ideas for 'A World of Dispositions', 'Properties and Predicates' and 'Principles of Arithmetic, by a new method'

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14 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]
8. Modes of Existence / B. Properties / 2. Need for Properties
A property is merely a constituent of laws of nature; temperature is just part of thermodynamics [Mellor]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
There is obviously a possible predicate for every property [Mellor]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / e. Dispositions as potential
All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer]
8. Modes of Existence / D. Universals / 2. Need for Universals
We need universals for causation and laws of nature; the latter give them their identity [Mellor]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
If properties were just the meanings of predicates, they couldn't give predicates their meaning [Mellor]
9. Objects / C. Structure of Objects / 1. Structure of an Object
All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
Kinds are arrangements of dispositions [Fetzer]
26. Natural Theory / C. Causation / 8. Particular Causation / e. Probabilistic causation
Singular causation requires causes to raise the physical probability of their effects [Mellor]
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
Lawlike sentences are general attributions of disposition to all members of some class [Fetzer]