96 ideas
| 19023 | Slippery slope arguments are challenges to show where a non-arbitrary boundary lies [Vetter] |
| 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] |
| 19033 | Deontic modalities are 'ought-to-be', for sentences, and 'ought-to-do' for predicates [Vetter] |
| 19032 | S5 is undesirable, as it prevents necessities from having contingent grounds [Vetter] |
| 19036 | The Barcan formula endorses either merely possible things, or makes the unactualised impossible [Vetter] |
| 9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
| 19034 | The world is either a whole made of its parts, or a container which contains its parts [Vetter] |
| 19015 | Grounding can be between objects ('relational'), or between sentences ('operational') [Vetter] |
| 19012 | The Humean supervenience base entirely excludes modality [Vetter] |
| 19024 | A determinate property must be a unique instance of the determinable class [Vetter] |
| 17954 | Essence is a thing's necessities, but what about its possibilities (which may not be realised)? [Vetter] |
| 19021 | I have an 'iterated ability' to learn the violin - that is, the ability to acquire that ability [Vetter] |
| 19016 | We should think of dispositions as 'to do' something, not as 'to do something, if ....' [Vetter] |
| 19017 | Nomological dispositions (unlike ordinary ones) have to be continually realised [Vetter] |
| 19014 | How can spatiotemporal relations be understood in dispositional terms? [Vetter] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| 17953 | Real definition fits abstracta, but not individual concrete objects like Socrates [Vetter] |
| 17952 | Modal accounts make essence less mysterious, by basing them on the clearer necessity [Vetter] |
| 19030 | Why does origin matter more than development; why are some features of origin more important? [Vetter] |
| 19040 | We take origin to be necessary because we see possibilities as branches from actuality [Vetter] |
| 19008 | The modern revival of necessity and possibility treated them as special cases of quantification [Vetter] |
| 19029 | It is necessary that p means that nothing has the potentiality for not-p [Vetter] |
| 17959 | Metaphysical necessity is even more deeply empirical than Kripke has argued [Vetter] |
| 17957 | Maybe possibility is constituted by potentiality [Vetter] |
| 17955 | Possible worlds allow us to talk about degrees of possibility [Vetter] |
| 19028 | Possibilities are potentialities of actual things, but abstracted from their location [Vetter] |
| 19010 | All possibility is anchored in the potentiality of individual objects [Vetter] |
| 19013 | Possibility is a generalised abstraction from the potentiality of its bearer [Vetter] |
| 19019 | Potentiality is the common genus of dispositions, abilities, and similar properties [Vetter] |
| 19022 | Water has a potentiality to acquire a potentiality to break (by freezing) [Vetter] |
| 23705 | A potentiality may not be a disposition, but dispositions are strong potentialities [Vetter, by Friend/Kimpton-Nye] |
| 19009 | Potentiality does the explaining in metaphysics; we don't explain it away or reduce it [Vetter] |
| 19027 | Potentiality logic is modal system T. Stronger systems collapse iterations, and necessitate potentials [Vetter] |
| 19025 | Potentialities may be too weak to count as 'dispositions' [Vetter] |
| 19031 | There are potentialities 'to ...', but possibilities are 'that ....'. [Vetter] |
| 17958 | The apparently metaphysically possible may only be epistemically possible [Vetter] |
| 17956 | Closeness of worlds should be determined by the intrinsic nature of relevant objects [Vetter] |
| 19011 | If worlds are sets of propositions, how do we know which propositions are genuinely possible? [Vetter] |
| 19037 | Are there possible objects which nothing has ever had the potentiality to produce? [Vetter] |
| 19018 | Explanations by disposition are more stable and reliable than those be external circumstances [Vetter] |
| 19020 | Grounding is a kind of explanation, suited to metaphysics [Vetter] |
| 19039 | The view that laws are grounded in substance plus external necessity doesn't suit dispositionalism [Vetter] |
| 19038 | Dispositional essentialism allows laws to be different, but only if the supporting properties differ [Vetter] |
| 17993 | Laws are relations of kinds, quantities and qualities, supervening on the essences of a domain [Vetter] |
| 19026 | If time is symmetrical between past and future, why do they look so different? [Vetter] |
| 19041 | Presentists explain cross-temporal relations using surrogate descriptions [Vetter] |