66 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] |
21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
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] |
17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
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] |
9175 | We may fix the reference of 'Cicero' by a description, but thereafter the name is rigid [Kripke] |
9171 | The function of names is simply to refer [Kripke] |
6067 | Existential quantifiers just express the quantity of things, leaving existence to the predicate 'exists' [McGinn] |
6042 | The quantifier is overrated as an analytical tool [McGinn] |
6069 | 'Partial quantifier' would be a better name than 'existential quantifier', as no existence would be implied [McGinn] |
6068 | We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn] |
17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
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] |
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] |
9174 | It is necessary that this table is not made of ice, but we don't know it a priori [Kripke] |
6079 | If 'possible' is explained as quantification across worlds, there must be possible worlds [McGinn] |
9172 | A 'rigid designator' designates the same object in all possible worlds [Kripke] |
9173 | We cannot say that Nixon might have been a different man from the one he actually was [Kripke] |
9176 | Modal statements about this table never refer to counterparts; that confuses epistemology and metaphysics [Kripke] |
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] |
9177 | Identity theorists must deny that pains can be imagined without brain states [Kripke] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
9178 | Pain, unlike heat, is picked out by an essential property [Kripke] |
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] |
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] |