61 ideas
| 6052 | Definitions identify two concepts, so they presuppose identity [McGinn] |
| 6064 | Regresses are only vicious in the context of an explanation [McGinn] |
| 6088 | Truth is a method of deducing facts from propositions [McGinn] |
| 6084 | 'Snow does not fall' corresponds to snow does fall [McGinn] |
| 6085 | The idea of truth is built into the idea of correspondence [McGinn] |
| 6083 | The coherence theory of truth implies idealism, because facts are just coherent beliefs [McGinn] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 6086 | Truth is the property of propositions that makes it possible to deduce facts [McGinn] |
| 6087 | Without the disquotation device for truth, you could never form beliefs from others' testimony [McGinn] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 6051 | In 'x is F and x is G' we must assume the identity of x in the two statements [McGinn] |
| 6055 | Both non-contradiction and excluded middle need identity in their formulation [McGinn] |
| 6059 | Identity is unitary, indefinable, fundamental and a genuine relation [McGinn] |
| 6042 | The quantifier is overrated as an analytical tool [McGinn] |
| 6067 | Existential quantifiers just express the quantity of things, leaving existence to the predicate 'exists' [McGinn] |
| 6069 | 'Partial quantifier' would be a better name than 'existential quantifier', as no existence would be implied [McGinn] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 6068 | We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 6070 | Existence is a primary quality, non-existence a secondary quality [McGinn] |
| 6062 | Existence can't be analysed as instantiating a property, as instantiation requires existence [McGinn] |
| 6065 | We can't analyse the sentence 'something exists' in terms of instantiated properties [McGinn] |
| 6082 | If causal power is the test for reality, that will exclude necessities and possibilities [McGinn] |
| 6075 | Facts are object-plus-extension, or property-plus-set-of-properties, or object-plus-property [McGinn] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 6058 | Identity propositions are not always tautological, and have a key epistemic role [McGinn] |
| 6053 | Identity is as basic as any concept could ever be [McGinn] |
| 6043 | Type-identity is close similarity in qualities [McGinn] |
| 6044 | Qualitative identity is really numerical identity of properties [McGinn] |
| 6046 | Qualitative identity can be analysed into numerical identity of the type involved [McGinn] |
| 6045 | It is best to drop types of identity, and speak of 'identity' or 'resemblance' [McGinn] |
| 6066 | Existence is a property of all objects, but less universal than self-identity, which covers even conceivable objects [McGinn] |
| 6054 | Sherlock Holmes does not exist, but he is self-identical [McGinn] |
| 6047 | All identity is necessary, though identity statements can be contingently true [McGinn] |
| 6049 | Leibniz's Law says 'x = y iff for all P, Px iff Py' [McGinn] |
| 6048 | Leibniz's Law is so fundamental that it almost defines the concept of identity [McGinn] |
| 6050 | Leibniz's Law presupposes the notion of property identity [McGinn] |
| 6080 | Modality is not objects or properties, but the type of binding of objects to properties [McGinn] |
| 6079 | If 'possible' is explained as quantification across worlds, there must be possible worlds [McGinn] |
| 6081 | Necessity and possibility are big threats to the empiricist view of knowledge [McGinn] |
| 6071 | Scepticism about reality is possible because existence isn't part of appearances [McGinn] |
| 22371 | Determinism threatens free will if actions can be causally traced to external factors [Foot] |
| 6077 | Semantics should not be based on set-membership, but on instantiation of properties in objects [McGinn] |
| 6074 | Clearly predicates have extensions (applicable objects), but are the extensions part of their meaning? [McGinn] |
| 22372 | Not all actions need motives, but it is irrational to perform troublesome actions with no motive [Foot] |
| 22373 | People can act out of vanity without being vain, or even vain about this kind of thing [Foot] |
| 6072 | If Satan is the most imperfect conceivable being, he must have non-existence [McGinn] |
| 6073 | I think the fault of the Ontological Argument is taking the original idea to be well-defined [McGinn] |