Combining Texts

All the ideas for 'Realism in Mathematics', 'Making Mind Matter More' and 'Ontology and Mathematical Truth'

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15 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
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 / 6. Mathematics as Set Theory / a. Mathematics is set theory
A natural number is a property of sets [Maddy, by Oliver]
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]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
The empty set is the purest abstract object [Jubien]
17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism
Either intentionality causes things, or epiphenomenalism is true [Fodor]
17. Mind and Body / D. Property Dualism / 2. Anomalous Monism
Contrary to the 'anomalous monist' view, there may well be intentional causal laws [Fodor]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
Lots of physical properties are multiply realisable, so why shouldn't beliefs be? [Fodor]