Combining Texts

All the ideas for 'Philosophy of Mathematics', 'A World of Dispositions' and 'Law and Causality'

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13 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
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]
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]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read]
10. Modality / B. Possibility / 8. Conditionals / e. Supposition conditionals
Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge [Ramsey]
14. Science / B. Scientific Theories / 8. Ramsey Sentences
Mental terms can be replaced in a sentence by a variable and an existential quantifier [Ramsey]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
Kinds are arrangements of dispositions [Fetzer]
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]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
Causal laws result from the simplest axioms of a complete deductive system [Ramsey]
All knowledge needs systematizing, and the axioms would be the laws of nature [Ramsey]