87 ideas
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] |
13678 | The most popular account of logical consequence is the semantic or model-theoretic one [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] |
13679 | Maybe logical consequence is more a matter of provability than of truth-preservation [Sider] |
13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
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] |
13688 | Good axioms should be indisputable logical truths [Sider] |
13687 | No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider] |
13691 | Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider] |
13690 | Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [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] |
14334 | Modest realism says there is a reality; the presumptuous view says we can accurately describe it [Mumford] |
14306 | Anti-realists deny truth-values to all statements, and say evidence and ontology are inseparable [Mumford] |
13692 | A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider] |
13693 | A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider] |
13695 | Supervaluational logic is classical, except when it adds the 'Definitely' operator [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] |
14333 | Dispositions and categorical properties are two modes of presentation of the same thing [Mumford] |
14315 | Categorical properties and dispositions appear to explain one another [Mumford] |
14332 | There are four reasons for seeing categorical properties as the most fundamental [Mumford] |
14336 | Categorical predicates are those unconnected to functions [Mumford] |
14302 | A lead molecule is not leaden, and macroscopic properties need not be microscopically present [Mumford] |
14294 | Dispositions are attacked as mere regularities of events, or place-holders for unknown properties [Mumford] |
14316 | If dispositions have several categorical realisations, that makes the two separate [Mumford] |
14310 | Dispositions are classifications of properties by functional role [Mumford] |
14317 | I say the categorical base causes the disposition manifestation [Mumford] |
14313 | All properties must be causal powers (since they wouldn't exist otherwise) [Mumford] |
14318 | Intrinsic properties are just causal powers, and identifying a property as causal is then analytic [Mumford] |
14293 | Dispositions are ascribed to at least objects, substances and persons [Mumford] |
14326 | Unlike categorical bases, dispositions necessarily occupy a particular causal role [Mumford] |
14298 | Dispositions can be contrasted either with occurrences, or with categorical properties [Mumford] |
14314 | If dispositions are powers, background conditions makes it hard to say what they do [Mumford] |
14325 | Maybe dispositions can replace powers in metaphysics, as what induces property change [Mumford] |
14312 | Orthodoxy says dispositions entail conditionals (rather than being equivalent to them) [Mumford] |
14299 | There could be dispositions that are never manifested [Mumford] |
14291 | Dispositions are not just possibilities - they are features of actual things [Mumford] |
14323 | If every event has a cause, it is easy to invent a power to explain each case [Mumford] |
14328 | Traditional powers initiate change, but are mysterious between those changes [Mumford] |
14331 | Categorical eliminativists say there are no dispositions, just categorical states or mechanisms [Mumford] |
14295 | Many artefacts have dispositional essences, which make them what they are [Mumford] |
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] |
14309 | Truth-functional conditionals can't distinguish whether they are causal or accidental [Mumford] |
14311 | Dispositions are not equivalent to stronger-than-material conditionals [Mumford] |
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] |
14319 | Nomothetic explanations cite laws, and structural explanations cite mechanisms [Mumford] |
14342 | General laws depend upon the capacities of particulars, not the other way around [Mumford] |
14322 | If fragile just means 'breaks when dropped', it won't explain a breakage [Mumford] |
14337 | Maybe dispositions can replace the 'laws of nature' as the basis of explanation [Mumford] |
14320 | Subatomic particles may terminate explanation, if they lack structure [Mumford] |
14343 | To avoid a regress in explanations, ungrounded dispositions will always have to be posited [Mumford] |
14324 | Ontology is unrelated to explanation, which concerns modes of presentation and states of knowledge [Mumford] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
14344 | Natural kinds, such as electrons, all behave the same way because we divide them by dispositions [Mumford] |
14338 | In the 'laws' view events are basic, and properties are categorical, only existing when manifested [Mumford] |
14339 | Without laws, how can a dispositionalist explain general behaviour within kinds? [Mumford] |
14340 | It is a regularity that whenever a person sneezes, someone (somewhere) promptly coughs [Mumford] |
14341 | Dretske and Armstrong base laws on regularities between individual properties, not between events [Mumford] |
14345 | The necessity of an electron being an electron is conceptual, and won't ground necessary laws [Mumford] |
14307 | Some dispositions are so far unknown, until we learn how to manifest them [Mumford] |