Combining Texts

All the ideas for 'Philosophy of Mathematics', 'Causal and Metaphysical Necessity' and 'Modal and Anti-Luck Epistemology'

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16 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Restrict 'logical truth' to formal logic, rather than including analytic and metaphysical truths [Shoemaker]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
8. Modes of Existence / B. Properties / 1. Nature of Properties
A property's causal features are essential, and only they fix its identity [Shoemaker]
I claim that a property has its causal features in all possible worlds [Shoemaker]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
I now deny that properties are cluster of powers, and take causal properties as basic [Shoemaker]
10. Modality / A. Necessity / 5. Metaphysical Necessity
If something is possible, but not nomologically possible, we need metaphysical possibility [Shoemaker]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
Once you give up necessity as a priori, causal necessity becomes the main type of necessity [Shoemaker]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Empirical evidence shows that imagining a phenomenon can show it is possible [Shoemaker]
Imagination reveals conceptual possibility, where descriptions avoid contradiction or incoherence [Shoemaker]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
'Modal epistemology' demands a connection between the belief and facts in possible worlds [Black,T]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
Gettier and lottery cases seem to involve luck, meaning bad connection of beliefs to facts [Black,T]
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
'Grue' only has causal features because of its relation to green [Shoemaker]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
We might say laws are necessary by combining causal properties with Armstrong-Dretske-Tooley laws [Shoemaker]