64 ideas
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] |
18767 | Free logics has terms that do not designate real things, and even empty domains [Anderson,CA] |
11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
14187 | If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [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] |
14188 | Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read] |
14182 | If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read] |
14183 | Maybe arguments are only valid when suppressed premises are all stated - but why? [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] |
14184 | In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read] |
14186 | Logical connectives contain no information, but just record combination relations between facts [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] |
18763 | Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA] |
18771 | Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA] |
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] |
18769 | Do mathematicians use 'existence' differently when they say some entity exists? [Anderson,CA] |
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] |
18770 | We can distinguish 'ontological' from 'existential' commitment, for different kinds of being [Anderson,CA] |
18766 | 's is non-existent' cannot be said if 's' does not designate [Anderson,CA] |
18768 | We cannot pick out a thing and deny its existence, but we can say a concept doesn't correspond [Anderson,CA] |
18765 | Individuation was a problem for medievals, then Leibniz, then Frege, then Wittgenstein (somewhat) [Anderson,CA] |
10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
18764 | The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles [Anderson,CA] |
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] |
14185 | Conditionals are just a shorthand for some proof, leaving out the details [Read] |
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] |
19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |
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] |