73 ideas
16512 | Semantic facts are preferable to transcendental philosophical fiction [Wiggins] |
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] |
10973 | A theory is logically closed, which means infinite premisses [Read] |
11007 | Quantifiers are second-order predicates [Read] |
10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
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] |
17529 | Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins] |
17530 | The sortal needed for identities may not always be sufficient to support counting [Wiggins] |
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] |
16523 | Realist Conceptualists accept that our interests affect our concepts [Wiggins] |
16524 | Conceptualism says we must use our individuating concepts to grasp reality [Wiggins] |
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] |
16526 | Animal classifications: the Emperor's, fabulous, innumerable, like flies, stray dogs, embalmed…. [Wiggins] |
16492 | Individuation needs accounts of identity, of change, and of singling out [Wiggins] |
16493 | Individuation can only be understood by the relation between things and thinkers [Wiggins] |
16496 | Singling out extends back and forward in time [Wiggins] |
10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
16495 | The only singling out is singling out 'as' something [Wiggins] |
16501 | In Aristotle's sense, saying x falls under f is to say what x is [Wiggins] |
16506 | Every determinate thing falls under a sortal, which fixes its persistence [Wiggins] |
16509 | Natural kinds are well suited to be the sortals which fix substances [Wiggins] |
16514 | Artefacts are individuated by some matter having a certain function [Wiggins] |
16510 | Nominal essences don't fix membership, ignore evolution, and aren't contextual [Wiggins] |
16503 | 'What is it?' gives the kind, nature, persistence conditions and identity over time of a thing [Wiggins] |
16499 | A restored church is the same 'church', but not the same 'building' or 'brickwork' [Wiggins] |
16515 | A thing begins only once; for a clock, it is when its making is first completed [Wiggins] |
16517 | Priests prefer the working ship; antiquarians prefer the reconstruction [Wiggins] |
16497 | Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity [Wiggins] |
16502 | Identity is primitive [Wiggins] |
16498 | Identity cannot be defined, because definitions are identities [Wiggins] |
16521 | A is necessarily A, so if B is A, then B is also necessarily A [Wiggins] |
16505 | By the principle of Indiscernibility, a symmetrical object could only be half of itself! [Wiggins] |
16494 | We want to explain sameness as coincidence of substance, not as anything qualitative [Wiggins] |
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] |
16522 | It is hard or impossible to think of Caesar as not human [Wiggins] |
10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
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] |
16525 | Our sortal concepts fix what we find in experience [Wiggins] |
10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
16518 | We conceptualise objects, but they impinge on us [Wiggins] |
16511 | A 'conception' of a horse is a full theory of what it is (and not just the 'concept') [Wiggins] |
11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |