Combining Texts

All the ideas for 'Epistemic Justification', 'Ontology and Mathematical Truth' and 'Abstract Entities'

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14 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
'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
A model is 'fundamental' if it contains only concrete entities [Jubien]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
There couldn't just be one number, such as 17 [Jubien]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
The subject-matter of (pure) mathematics is abstract structure [Jubien]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
If we all intuited mathematical objects, platonism would be agreed [Jubien]
How can pure abstract entities give models to serve as interpretations? [Jubien]
Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien]
7. Existence / A. Nature of Existence / 4. Abstract Existence
Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer]
7. Existence / D. Theories of Reality / 1. Ontologies
Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Can properties exemplify other properties? [Swoyer]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
The empty set is the purest abstract object [Jubien]
9. Objects / A. Existence of Objects / 5. Simples
Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
'Access' internalism says responsibility needs access; weaker 'mentalism' needs mental justification [Kvanvig]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Strong foundationalism needs strict inferences; weak version has induction, explanation, probability [Kvanvig]