30 ideas
| 4036 | What matters is not how many entities we postulate, but how many kinds of entities [Armstrong, by Mellor/Oliver] |
| 17962 | The truth-maker principle is that every truth has a sufficient truth-maker [Forrest] |
| 10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
| 10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
| 10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
| 10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
| 10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
| 10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
| 10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
| 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
| 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
| 10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
| 10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
| 10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
| 15754 | Without properties we would be unable to express the laws of nature [Armstrong] |
| 4034 | Whether we apply 'cold' or 'hot' to an object is quite separate from its change of temperature [Armstrong] |
| 8535 | To the claim that every predicate has a property, start by eliminating failure of application of predicate [Armstrong] |
| 8537 | Tropes fall into classes, because exact similarity is symmetrical and transitive [Armstrong] |
| 8538 | Trope theory needs extra commitments, to symmetry and non-transitivity, unless resemblance is exact [Armstrong] |
| 8539 | Universals are required to give a satisfactory account of the laws of nature [Armstrong] |
| 8529 | Deniers of properties and relations rely on either predicates or on classes [Armstrong] |
| 8532 | Resemblances must be in certain 'respects', and they seem awfully like properties [Armstrong] |
| 8530 | Change of temperature in objects is quite independent of the predicates 'hot' and 'cold' [Armstrong] |
| 8536 | We want to know what constituents of objects are grounds for the application of predicates [Armstrong] |
| 8531 | In most sets there is no property common to all the members [Armstrong] |
| 15753 | Essences might support Resemblance Nominalism, but they are too coarse and ill-defined [Armstrong] |
| 8533 | Predicates need ontological correlates to ensure that they apply [Armstrong] |
| 4035 | There must be some explanation of why certain predicates are applicable to certain objects [Armstrong] |
| 8541 | Regularities theories are poor on causal connections, counterfactuals and probability [Armstrong] |
| 8540 | The introduction of sparse properties avoids the regularity theory's problem with 'grue' [Armstrong] |