Combining Texts

All the ideas for 'Necessary Existents', 'The Nature of Universals and Propositions' and 'Ontology and Mathematical Truth'

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10 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]
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
9962 How can pure abstract entities give models to serve as interpretations? [Jubien]
9963 If we all intuited mathematical objects, platonism would be agreed [Jubien]
9964 Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
8511 Stout first explicitly proposed that properties and relations are particulars [Stout,GF, by Campbell,K]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
9969 The empty set is the purest abstract object [Jubien]
19. Language / D. Propositions / 3. Concrete Propositions
19216 Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]