126 ideas
| 6123 | Empirical investigation can't discover if holes exist, or if two things share a colour [Merricks] |
| 19215 | Arguers often turn the opponent's modus ponens into their own modus tollens [Merricks] |
| 14415 | A ground must be about its truth, and not just necessitate it [Merricks] |
| 14408 | Truthmaker needs truths to be 'about' something, and that is often unclear [Merricks] |
| 14395 | If a ball changes from red to white, Truthmaker says some thing must make the change true [Merricks] |
| 14398 | Truthmaker says if an entity is removed, some nonexistence truthmaker must replace it [Merricks] |
| 14403 | If Truthmaker says each truth is made by the existence of something, the theory had de re modality at is core [Merricks] |
| 14397 | Truthmaker demands not just a predication, but an existing state of affairs with essential ingredients [Merricks] |
| 14396 | If 'truth supervenes on being', worlds with the same entities, properties and relations have the same truths [Merricks] |
| 14400 | If truth supervenes on being, that won't explain why truth depends on being [Merricks] |
| 14394 | It is implausible that claims about non-existence are about existing things [Merricks] |
| 14390 | Truthmaker isn't the correspondence theory, because it offers no analysis of truth [Merricks] |
| 14412 | Speculations about non-existent things are not about existent things, so Truthmaker is false [Merricks] |
| 14414 | I am a truthmaker for 'that a human exists', but is it about me? [Merricks] |
| 14418 | Being true is not a relation, it is a primitive monadic property [Merricks] |
| 14391 | If the correspondence theory is right, then necessary truths must correspond to something [Merricks] |
| 19205 | 'Snow is white' only contingently expresses the proposition that snow is white [Merricks] |
| 14419 | Deflationism just says there is no property of being truth [Merricks] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 9399 | ∧E: Given A∧B, we may derive either A or B separately [Lemmon] |
| 9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
| 9393 | A: we may assume any proposition at any stage [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] |
| 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] |
| 19209 | Simple Quantified Modal Logc doesn't work, because the Converse Barcan is a theorem [Merricks] |
| 19208 | The Converse Barcan implies 'everything exists necessarily' is a consequence of 'necessarily, everything exists' [Merricks] |
| 9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
| 19207 | Sentence logic maps truth values; predicate logic maps objects and sets [Merricks] |
| 14393 | The totality state is the most plausible truthmaker for negative existential truths [Merricks] |
| 6143 | Prolonged events don't seem to endure or exist at any particular time [Merricks] |
| 6135 | A crumbling statue can't become vague, because vagueness is incoherent [Merricks] |
| 14413 | Some properties seem to be primitive, but others can be analysed [Merricks] |
| 6145 | Intrinsic properties are those an object still has even if only that object exists [Merricks] |
| 14416 | An object can have a disposition when the revelant conditional is false [Merricks] |
| 6124 | I say that most of the objects of folk ontology do not exist [Merricks] |
| 6134 | Is swimming pool water an object, composed of its mass or parts? [Merricks] |
| 14392 | Fregeans say 'hobbits do not exist' is just 'being a hobbit' is not exemplified [Merricks] |
| 6125 | We can eliminate objects without a commitment to simples [Merricks] |
| 14229 | Merricks agrees that there are no composite objects, but offers a different semantics [Merricks, by Liggins] |
| 6142 | The 'folk' way of carving up the world is not intrinsically better than quite arbitrary ways [Merricks] |
| 14472 | If atoms 'arranged baseballwise' break a window, that analytically entails that a baseball did it [Merricks, by Thomasson] |
| 14469 | Overdetermination: the atoms do all the causing, so the baseball causes no breakage [Merricks] |
| 6137 | Clay does not 'constitute' a statue, as they have different persistence conditions (flaking, squashing) [Merricks] |
| 6127 | 'Unrestricted composition' says any two things can make up a third thing [Merricks] |
| 6131 | Composition as identity is false, as identity is never between a single thing and many things [Merricks] |
| 6132 | Composition as identity is false, as it implies that things never change their parts [Merricks] |
| 6141 | There is no visible difference between statues, and atoms arranged statuewise [Merricks] |
| 6130 | 'Composition' says things are their parts; 'constitution' says a whole substance is an object [Merricks] |
| 6138 | It seems wrong that constitution entails that two objects are wholly co-located [Merricks] |
| 6128 | Objects decompose (it seems) into non-overlapping parts that fill its whole region [Merricks] |
| 14410 | You believe you existed last year, but your segment doesn't, so they have different beliefs [Merricks] |
| 19214 | In twinning, one person has the same origin as another person [Merricks] |
| 6136 | Eliminativism about objects gives the best understanding of the Sorites paradox [Merricks] |
| 14417 | Counterfactuals aren't about actuality, so they lack truthmakers or a supervenience base [Merricks] |
| 6133 | If my counterpart is happy, that is irrelevant to whether I 'could' have been happy [Merricks] |
| 14402 | If 'Fido is possibly black' depends on Fido's counterparts, then it has no actual truthmaker [Merricks] |
| 6150 | The 'warrant' for a belief is what turns a true belief into knowledge [Merricks] |
| 6144 | You hold a child in your arms, so it is not mental substance, or mental state, or software [Merricks] |
| 6140 | Maybe the word 'I' can only refer to persons [Merricks] |
| 6149 | Free will and determinism are incompatible, since determinism destroys human choice [Merricks] |
| 6148 | Human organisms can exercise downward causation [Merricks] |
| 6146 | Before Creation it is assumed that God still had many many mental properties [Merricks] |
| 6147 | The hypothesis of solipsism doesn't seem to be made incoherent by the nature of mental properties [Merricks] |
| 19217 | I don't accept that if a proposition is directly about an entity, it has a relation to the entity [Merricks] |
| 19203 | A sentence's truth conditions depend on context [Merricks] |
| 19200 | Propositions are standardly treated as possible worlds, or as structured [Merricks] |
| 19206 | 'Cicero is an orator' represents the same situation as 'Tully is an orator', so they are one proposition [Merricks] |
| 19202 | Propositions are necessary existents which essentially (but inexplicably) represent things [Merricks] |
| 19204 | True propositions existed prior to their being thought, and might never be thought [Merricks] |
| 19210 | The standard view of propositions says they never change their truth-value [Merricks] |
| 19201 | Propositions can be 'about' an entity, but that doesn't make the entity a constituent of it [Merricks] |
| 19211 | Early Russell says a proposition is identical with its truthmaking state of affairs [Merricks] |
| 19212 | Unity of the proposition questions: what unites them? can the same constituents make different ones? [Merricks] |
| 19213 | We want to explain not just what unites the constituents, but what unites them into a proposition [Merricks] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 17960 | Eternalism says all times are equally real, and future and past objects and properties are real [Merricks] |
| 17961 | Growing block has a subjective present and a growing edge - but these could come apart [Merricks, by PG] |
| 14411 | Maybe only presentism allows change, by now having a property, and then lacking it [Merricks] |
| 14407 | Presentist should deny there is a present time, and just say that things 'exist' [Merricks] |
| 14406 | Presentists say that things have existed and will exist, not that they are instantaneous [Merricks] |
| 14405 | How can a presentist explain an object's having existed? [Merricks] |