Combining Texts

All the ideas for 'Grounding, Transitivity and Contrastivity', 'Ontology and Mathematical Truth' and 'Non-foundationalist epistemology'

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16 ideas

2. Reason / A. Nature of Reason / 6. Coherence
How can multiple statements, none of which is tenable, conjoin to yield a tenable conclusion? [Elgin]
Statements that are consistent, cotenable and supportive are roughly true [Elgin]
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
How can pure abstract entities give models to serve as interpretations? [Jubien]
If we all intuited mathematical objects, platonism would be agreed [Jubien]
Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
If ground is transitive and irreflexive, it has a strict partial ordering, giving structure [Schaffer,J]
As causation links across time, grounding links the world across levels [Schaffer,J]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
The empty set is the purest abstract object [Jubien]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Coherence is a justification if truth is its best explanation (not skill in creating fiction) [Elgin]
14. Science / D. Explanation / 2. Types of Explanation / b. Contrastive explanations
Explaining 'Adam ate the apple' depends on emphasis, and thus implies a contrast [Schaffer,J]
26. Natural Theory / A. Speculations on Nature / 1. Nature
I take what is fundamental to be the whole spatiotemporal manifold and its fields [Schaffer,J]
26. Natural Theory / C. Causation / 1. Causation
Nowadays causation is usually understood in terms of equations and variable ranges [Schaffer,J]