123 ideas
9408 | Science studies phenomena, but only metaphysics tells us what exists [Mumford] |
9429 | Many forms of reasoning, such as extrapolation and analogy, are useful but deductively invalid [Mumford] |
9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon] |
9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
9513 | We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon] |
9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon] |
9508 | The sign |- may be read as 'therefore' [Lemmon] |
9516 | A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon] |
9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon] |
9519 | A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon] |
9529 | A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon] |
9531 | 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon] |
9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
9530 | A wff is 'contingent' if produces at least one T and at least one F [Lemmon] |
9532 | 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon] |
9533 | A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon] |
9528 | A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon] |
9518 | A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon] |
9398 | ∧I: Given A and B, we may derive A∧B [Lemmon] |
9397 | CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon] |
9394 | MPP: Given A and A→B, we may derive B [Lemmon] |
9402 | RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon] |
9395 | MTT: Given ¬B and A→B, we derive ¬A [Lemmon] |
9400 | ∨I: Given either A or B separately, we may derive A∨B [Lemmon] |
9401 | ∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon] |
9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
9393 | A: we may assume any proposition at any stage [Lemmon] |
9399 | ∧E: Given A∧B, we may derive either A or B separately [Lemmon] |
9521 | 'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- Q [Lemmon] |
9522 | 'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon] |
9525 | We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon] |
9524 | We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon] |
9523 | De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon] |
9527 | The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon] |
9526 | We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon] |
9537 | Truth-tables are good for showing invalidity [Lemmon] |
9538 | A truth-table test is entirely mechanical, but this won't work for more complex logic [Lemmon] |
9536 | If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology [Lemmon] |
9539 | Propositional logic is complete, since all of its tautologous sequents are derivable [Lemmon] |
13909 | Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....' [Lemmon] |
13902 | 'Gm' says m has property G, and 'Pmn' says m has relation P to n [Lemmon] |
13911 | The 'symbols' are bracket, connective, term, variable, predicate letter, reverse-E [Lemmon] |
13910 | Our notation uses 'predicate-letters' (for 'properties'), 'variables', 'proper names', 'connectives' and 'quantifiers' [Lemmon] |
13904 | Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon] |
13906 | With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [Lemmon] |
13908 | UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon] |
13901 | Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon] |
13903 | Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon] |
13905 | If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon] |
13900 | 'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional → [Lemmon] |
9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
9427 | For Humeans the world is a world primarily of events [Mumford] |
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] |
14333 | Dispositions and categorical properties are two modes of presentation of the same thing [Mumford] |
14336 | Categorical predicates are those unconnected to functions [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] |
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] |
9446 | Properties are just natural clusters of powers [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] |
14298 | Dispositions can be contrasted either with occurrences, or with categorical properties [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] |
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] |
14291 | Dispositions are not just possibilities - they are features of actual things [Mumford] |
14299 | There could be dispositions that are never manifested [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] |
9435 | A 'porridge' nominalist thinks we just divide reality in any way that suits us [Mumford] |
9447 | If properties are clusters of powers, this can explain why properties resemble in degrees [Mumford] |
18617 | Substances, unlike aggregates, can survive a change of parts [Mumford] |
12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
14295 | Many artefacts have dispositional essences, which make them what they are [Mumford] |
12248 | How can we show that a universally possessed property is an essential property? [Mumford] |
18618 | Maybe possibilities are recombinations of the existing elements of reality [Mumford] |
18619 | Combinatorial possibility has to allow all elements to be combinable, which seems unlikely [Mumford] |
18620 | Combinatorial possibility relies on what actually exists (even over time), but there could be more [Mumford] |
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] |
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] |
14343 | To avoid a regress in explanations, ungrounded dispositions will always have to be posited [Mumford] |
14320 | Subatomic particles may terminate explanation, if they lack structure [Mumford] |
14324 | Ontology is unrelated to explanation, which concerns modes of presentation and states of knowledge [Mumford] |
14344 | Natural kinds, such as electrons, all behave the same way because we divide them by dispositions [Mumford] |
19068 | Causation interests us because we want to explain change [Mumford] |
9430 | Singular causes, and identities, might be necessary without falling under a law [Mumford] |
9445 | We can give up the counterfactual account if we take causal language at face value [Mumford] |
9443 | It is only properties which are the source of necessity in the world [Mumford] |
14338 | In the 'laws' view events are basic, and properties are categorical, only existing when manifested [Mumford] |
9444 | There are four candidates for the logical form of law statements [Mumford] |
14339 | Without laws, how can a dispositionalist explain general behaviour within kinds? [Mumford] |
14341 | Dretske and Armstrong base laws on regularities between individual properties, not between events [Mumford] |
9431 | Pure regularities are rare, usually only found in idealized conditions [Mumford] |
9441 | Regularity laws don't explain, because they have no governing role [Mumford] |
14340 | It is a regularity that whenever a person sneezes, someone (somewhere) promptly coughs [Mumford] |
9415 | Would it count as a regularity if the only five As were also B? [Mumford] |
9416 | Regularities are more likely with few instances, and guaranteed with no instances! [Mumford] |
9422 | If the best system describes a nomological system, the laws are in nature, not in the description [Mumford] |
9421 | The best systems theory says regularities derive from laws, rather than constituting them [Mumford] |
9432 | Laws of nature are necessary relations between universal properties, rather than about particulars [Mumford] |
9433 | If laws can be uninstantiated, this favours the view of them as connecting universals [Mumford] |
14345 | The necessity of an electron being an electron is conceptual, and won't ground necessary laws [Mumford] |
9434 | Laws of nature are just the possession of essential properties by natural kinds [Mumford] |
14307 | Some dispositions are so far unknown, until we learn how to manifest them [Mumford] |
9437 | To distinguish accidental from essential properties, we must include possible members of kinds [Mumford] |
9439 | The Central Dilemma is how to explain an internal or external view of laws which govern [Mumford] |
9412 | You only need laws if you (erroneously) think the world is otherwise inert [Mumford] |
9411 | There are no laws of nature in Aristotle; they became standard with Descartes and Newton [Mumford] |