49 ideas
9376 | A sentence may simultaneously define a term, and also assert a fact [Boghossian] |
6345 | Minimalism is incoherent, as it implies that truth both is and is not a property [Boghossian, by Horwich] |
15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
15409 | All occurrences of variables in atomic formulas are free [Burgess] |
15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
9375 | Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian] |
15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
15412 | Models leave out meaning, and just focus on truth values [Burgess] |
15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
10185 | Set theory is the standard background for modern mathematics [Burgess] |
10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
9369 | 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian] |
9367 | The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian] |
9373 | That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian] |
9380 | We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian] |
9384 | We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian] |
9374 | If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian] |
9378 | If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian] |
9377 | 'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian] |
9372 | Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian] |
17721 | There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins] |
9368 | Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |