76 ideas
| 6887 | Linguistic philosophy approaches problems by attending to actual linguistic usage [Mautner] |
| 6881 | Analytic philosophy studies the unimportant, and sharpens tools instead of using them [Mautner] |
| 5439 | The 'hermeneutic circle' says parts and wholes are interdependent, and so cannot be interpreted [Mautner] |
| 9959 | 'Real' definitions give the essential properties of things under a concept [Mautner] |
| 9961 | 'Contextual definitions' replace whole statements, not just expressions [Mautner] |
| 9958 | Recursive definition defines each instance from a previous instance [Mautner] |
| 9960 | A stipulative definition lays down that an expression is to have a certain meaning [Mautner] |
| 9957 | Ostensive definitions point to an object which an expression denotes [Mautner] |
| 6219 | The fallacy of composition is the assumption that what is true of the parts is true of the whole [Mautner] |
| 13689 | 'Theorems' are formulas provable from no premises at all [Sider] |
| 13705 | Truth tables assume truth functionality, and are just pictures of truth functions [Sider] |
| 13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
| 13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
| 13711 | System B introduces iterated modalities [Sider] |
| 13708 | S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider] |
| 13712 | Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider] |
| 13714 | We can treat modal worlds as different times [Sider] |
| 13720 | Converse Barcan Formula: □∀αφ→∀α□φ [Sider] |
| 13718 | The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider] |
| 13723 | System B is needed to prove the Barcan Formula [Sider] |
| 13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
| 6888 | Fuzzy logic is based on the notion that there can be membership of a set to some degree [Mautner] |
| 13678 | The most popular account of logical consequence is the semantic or model-theoretic one [Sider] |
| 13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
| 13682 | Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider] |
| 13680 | Maybe logical consequence is a primitive notion [Sider] |
| 13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
| 6877 | Entailment is logical requirement; it may be not(p and not-q), but that has problems [Mautner] |
| 6880 | Strict implication says false propositions imply everything, and everything implies true propositions [Mautner] |
| 6879 | 'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q [Mautner] |
| 6878 | A person who 'infers' draws the conclusion, but a person who 'implies' leaves it to the audience [Mautner] |
| 6889 | Vagueness seems to be inconsistent with the view that every proposition is true or false [Mautner] |
| 13696 | When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider] |
| 13700 | A 'total' function must always produce an output for a given domain [Sider] |
| 13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |
| 6890 | Quantifiers turn an open sentence into one to which a truth-value can be assigned [Mautner] |
| 13688 | Good axioms should be indisputable logical truths [Sider] |
| 13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
| 13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider] |
| 13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
| 13685 | Natural deduction helpfully allows reasoning with assumptions [Sider] |
| 13686 | We can build proofs just from conclusions, rather than from plain formulae [Sider] |
| 13697 | Valuations in PC assign truth values to formulas relative to variable assignments [Sider] |
| 13684 | The semantical notion of a logical truth is validity, being true in all interpretations [Sider] |
| 13704 | It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider] |
| 13724 | In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider] |
| 13698 | In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider] |
| 13699 | Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider] |
| 13701 | A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider] |
| 13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
| 13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider] |
| 13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
| 13694 | We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider] |
| 13683 | A relation is a feature of multiple objects taken together [Sider] |
| 13702 | The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider] |
| 13721 | 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider] |
| 13707 | Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider] |
| 13709 | Logical truths must be necessary if anything is [Sider] |
| 13716 | 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider] |
| 6886 | Counterfactuals are not true, they are merely valid [Mautner] |
| 6885 | Counterfactuals are true if in every world close to actual where p is the case, q is also the case [Mautner] |
| 6884 | Counterfactuals say 'If it had been, or were, p, then it would be q' [Mautner] |
| 6883 | Maybe counterfactuals are only true if they contain valid inference from premisses [Mautner] |
| 6882 | Counterfactuals presuppose a belief (or a fact) that the condition is false [Mautner] |
| 5449 | Essentialism is often identified with belief in 'de re' necessary truths [Mautner] |
| 13717 | Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider] |
| 13719 | Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider] |
| 6898 | Fallibilism is the view that all knowledge-claims are provisional [Mautner] |
| 6452 | 'Sense-data' arrived in 1910, but it denotes ideas in Locke, Berkeley and Hume [Mautner] |
| 4783 | Observing lots of green x can confirm 'all x are green' or 'all x are grue', where 'grue' is arbitrary [Mautner, by PG] |
| 4782 | 'All x are y' is equivalent to 'all non-y are non-x', so observing paper is white confirms 'ravens are black' [Mautner, by PG] |
| 6899 | The references of indexicals ('there', 'now', 'I') depend on the circumstances of utterance [Mautner] |
| 6896 | Double effect is the distinction between what is foreseen and what is intended [Mautner] |
| 6897 | Double effect acts need goodness, unintended evil, good not caused by evil, and outweighing [Mautner] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 5452 | 'Essentialism' is opposed to existentialism, and claims there is a human nature [Mautner] |