52 ideas
16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
16878 | We must be clear about every premise and every law used in a proof [Frege] |
13252 | Some truths have true negations [Beall/Restall] |
18901 | Truthmakers are facts 'of' a domain, not something 'in' the domain [Sommers] |
13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
18904 | 'Predicable' terms come in charged pairs, with one the negation of the other [Sommers, by Engelbretsen] |
18895 | Logic which maps ordinary reasoning must be transparent, and free of variables [Sommers] |
13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
13254 | A doesn't imply A - that would be circular [Beall/Restall] |
13255 | Relevant logic may reject transitivity [Beall/Restall] |
13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
13253 | There are several different consequence relations [Beall/Restall] |
13240 | A sentence follows from others if they always model it [Beall/Restall] |
18897 | Predicate logic has to spell out that its identity relation '=' is an equivalent relation [Sommers] |
18893 | Translating into quantificational idiom offers no clues as to how ordinary thinkers reason [Sommers] |
18903 | Sommers promotes the old idea that negation basically refers to terms [Sommers, by Engelbretsen] |
18894 | Predicates form a hierarchy, from the most general, down to names at the bottom [Sommers] |
16865 | 'Theorems' are both proved, and used in proofs [Frege] |
13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
16871 | A truth can be an axiom in one system and not in another [Frege] |
16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
18900 | Unfortunately for realists, modern logic cannot say that some fact exists [Sommers] |
9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
16875 | We use signs to mark receptacles for complex senses [Frege] |
16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
18898 | In standard logic, names are the only way to refer [Sommers] |
13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
16874 | The parts of a thought map onto the parts of a sentence [Frege] |