Combining Texts

All the ideas for 'Ethical Studies', 'The Limits of Contingency' and 'The Foundations of Mathematics'

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20 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
18851 Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13430 Infinity: there is an infinity of distinguishable individuals [Ramsey]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
13428 Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
13427 Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
5. Theory of Logic / L. Paradox / 1. Paradox
13334 Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
13426 Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
13425 Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]
9. Objects / A. Existence of Objects / 4. Impossible objects
18852 A Meinongian principle might say that there is an object for any modest class of properties [Rosen]
10. Modality / A. Necessity / 5. Metaphysical Necessity
18849 Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant [Rosen]
18850 'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting [Rosen]
18858 Sets, universals and aggregates may be metaphysically necessary in one sense, but not another [Rosen]
18857 Standard Metaphysical Necessity: P holds wherever the actual form of the world holds [Rosen]
18856 Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things [Rosen]
10. Modality / A. Necessity / 6. Logical Necessity
18848 Something may be necessary because of logic, but is that therefore a special sort of necessity? [Rosen]
10. Modality / B. Possibility / 3. Combinatorial possibility
18855 Combinatorial theories of possibility assume the principles of combination don't change across worlds [Rosen]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
18853 A proposition is 'correctly' conceivable if an ominiscient being could conceive it [Rosen]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
22328 I just confront the evidence, and let it act on me [Ramsey]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
22325 A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
5655 Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
18854 The MRL view says laws are the theorems of the simplest and strongest account of the world [Rosen]