Ideas from 'Ontology and Mathematical Truth' by Michael Jubien [1977], by Theme Structure
[found in 'Philosophy of Mathematics: anthology' (ed/tr Jacquette,Dale) [Blackwell 2002,063121870x]].
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
9967

'Impure' sets have a concrete member, while 'pure' (abstract) sets do not

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
9968

A model is 'fundamental' if it contains only concrete entities

6. Mathematics / A. Nature of Mathematics / 3. Numbers / d. Natural numbers
9965

There couldn't just be one number, such as 17

6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / a. Structuralism
9966

The subjectmatter of (pure) mathematics is abstract structure

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
9963

If we all intuited mathematical objects, platonism would be agreed

9962

How can pure abstract entities give models to serve as interpretations?

9964

Since mathematical objects are essentially relational, they can't be picked out on their own

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
9969

The empty set is the purest abstract object
