40 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
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] |
13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
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] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
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] |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
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] |
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] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [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] |
17503 | Theories can never represent accurately, because their components are abstract [Cartwright,N, by Portides] |