83 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] |
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] |
10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
11011 | Same say there are positive, negative and neuter free logics [Read] |
11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
10986 | Not all validity is captured in first-order logic [Read] |
10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
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] |
10973 | A theory is logically closed, which means infinite premisses [Read] |
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] |
11007 | Quantifiers are second-order predicates [Read] |
6069 | 'Partial quantifier' would be a better name than 'existential quantifier', as no existence would be implied [McGinn] |
10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
6068 | We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn] |
10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
10988 | Any first-order theory of sets is inadequate [Read] |
10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
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] |
11016 | Would a language without vagueness be usable at all? [Read] |
11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
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] |
11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
10989 | The standard view of conditionals is that they are truth-functional [Read] |
11017 | Some people even claim that conditionals do not express propositions [Read] |
6080 | Modality is not objects or properties, but the type of binding of objects to properties [McGinn] |
10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
6079 | If 'possible' is explained as quantification across worlds, there must be possible worlds [McGinn] |
10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
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] |
10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
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] |
10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
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] |