Combining Texts

All the ideas for 'Philosophy of Mathematics', 'Causal and Metaphysical Necessity' and 'The Structure of Paradoxes of Self-Reference'

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22 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10882 Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
15091 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
10884 A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
5. Theory of Logic / L. Paradox / 1. Paradox
13373 Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / b. König's paradox
13368 The 'least indefinable ordinal' is defined by that very phrase [Priest,G]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
13370 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / d. Richard's paradox
13369 By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
13366 The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox
13367 The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
13371 If you know that a sentence is not one of the known sentences, you know its truth [Priest,G]
13372 There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10885 Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10881 The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
8. Modes of Existence / B. Properties / 1. Nature of Properties
15095 A property's causal features are essential, and only they fix its identity [Shoemaker]
15097 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
15094 I now deny that properties are cluster of powers, and take causal properties as basic [Shoemaker]
10. Modality / A. Necessity / 5. Metaphysical Necessity
15099 If something is possible, but not nomologically possible, we need metaphysical possibility [Shoemaker]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
15101 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
15098 Empirical evidence shows that imagining a phenomenon can show it is possible [Shoemaker]
15100 Imagination reveals conceptual possibility, where descriptions avoid contradiction or incoherence [Shoemaker]
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
15096 'Grue' only has causal features because of its relation to green [Shoemaker]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
15093 We might say laws are necessary by combining causal properties with Armstrong-Dretske-Tooley laws [Shoemaker]