Combining Texts

All the ideas for 'Ontology and Mathematical Truth', 'A World of Dispositions' and 'Mathematics: Form and Function'

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13 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
9967 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
18189 ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
9968 A model is 'fundamental' if it contains only concrete entities [Jubien]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
9965 There couldn't just be one number, such as 17 [Jubien]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
9966 The subject-matter of (pure) mathematics is abstract structure [Jubien]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
9963 If we all intuited mathematical objects, platonism would be agreed [Jubien]
9962 How can pure abstract entities give models to serve as interpretations? [Jubien]
9964 Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / e. Dispositions as potential
15797 All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
9969 The empty set is the purest abstract object [Jubien]
9. Objects / C. Structure of Objects / 1. Structure of an Object
15800 All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
15798 Kinds are arrangements of dispositions [Fetzer]
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
15799 Lawlike sentences are general attributions of disposition to all members of some class [Fetzer]