49 ideas
22140 | The greatest philosophers are methodical; it is what makes them great [Grice] |
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] |
15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
15427 | The Cut Rule expresses the classical idea that entailment is transitive [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] |
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] |
15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
15412 | Models leave out meaning, and just focus on truth values [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] |
13856 | Conditionals are truth-functional, but we must take care with misleading ones [Grice, by Edgington] |
8948 | The odd truth table for material conditionals is explained by conversational conventions [Grice, by Fisher] |
13767 | Conditionals might remain truth-functional, despite inappropriate conversational remarks [Edgington on Grice] |
14277 | A person can be justified in believing a proposition, though it is unreasonable to actually say it [Grice, by Edgington] |
10990 | Conditionals are truth-functional, but unassertable in tricky cases? [Grice, by Read] |
7752 | Only the utterer's primary intention is relevant to the meaning [Grice] |
7751 | Meaning needs an intention to induce a belief, and a recognition that this is the speaker's intention [Grice] |
7753 | We judge linguistic intentions rather as we judge non-linguistic intentions, so they are alike [Grice] |
22330 | Grice said patterns of use are often semantically irrelevant, because it is a pragmatic matter [Grice, by Glock] |
18045 | Grice's maxim of quality says do not assert what you believe to be false [Grice, by Magidor] |
10991 | Key conversational maxims are 'quality' (assert truth) and 'quantity' (leave nothing out) [Grice, by Read] |
18046 | Grice's maxim of quantity says be sufficiently informative [Grice, by Magidor] |
18044 | Grice's maxim of manner requires one to be as brief as possible [Grice, by Magidor] |
20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |