96 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| 14227 | We could refer to tables as 'xs that are arranged tablewise' [Inwagen] |
| 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] |
| 10662 | Mereology is 'nihilistic' (just atoms) or 'universal' (no restrictions on what is 'whole') [Inwagen, by Varzi] |
| 9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
| 17587 | The 'Law' of Excluded Middle needs all propositions to be definitely true or definitely false [Inwagen] |
| 17558 | Variables are just like pronouns; syntactic explanations get muddled over dummy letters [Inwagen] |
| 17583 | There are no heaps [Inwagen] |
| 17578 | I reject talk of 'stuff', and treat it in terms of particles [Inwagen] |
| 17582 | Singular terms can be vague, because they can contain predicates, which can be vague [Inwagen] |
| 17556 | Material objects are in space and time, move, have a surface and mass, and are made of some stuff [Inwagen] |
| 8264 | Maybe table-shaped particles exist, but not tables [Inwagen, by Lowe] |
| 17565 | Nihilism says composition between single things is impossible [Inwagen] |
| 14228 | If there are no tables, but tables are things arranged tablewise, the denial of tables is a contradiction [Liggins on Inwagen] |
| 14468 | Actions by artefacts and natural bodies are disguised cooperations, so we don't need them [Inwagen] |
| 17571 | Every physical thing is either a living organism or a simple [Inwagen] |
| 17562 | The statue and lump seem to share parts, but the statue is not part of the lump [Inwagen] |
| 17574 | If you knead clay you make an infinite series of objects, but they are rearrangements, not creations [Inwagen] |
| 17531 | I assume matter is particulate, made up of 'simples' [Inwagen] |
| 17560 | If contact causes composition, do two colliding balls briefly make one object? [Inwagen] |
| 17561 | If bricks compose a house, that is at least one thing, but it might be many things [Inwagen] |
| 17566 | I think parthood involves causation, and not just a reasonably stable spatial relationship [Inwagen] |
| 14230 | We can deny whole objects but accept parts, by referring to them as plurals within things [Inwagen, by Liggins] |
| 17557 | Special Composition Question: when is a thing part of something? [Inwagen] |
| 17564 | The essence of a star includes the released binding energy which keeps it from collapse [Inwagen] |
| 17575 | The persistence of artifacts always covertly involves intelligent beings [Inwagen] |
| 17577 | When an electron 'leaps' to another orbit, is the new one the same electron? [Inwagen] |
| 17589 | If you reject transitivity of vague identity, there is no Ship of Theseus problem [Inwagen] |
| 17588 | We should talk of the transitivity of 'identity', and of 'definite identity' [Inwagen] |
| 17572 | Actuality proves possibility, but that doesn't explain how it is possible [Inwagen] |
| 17579 | Counterparts reduce counterfactual identity to problems about similarity relations [Inwagen] |
| 17590 | A merely possible object clearly isn't there, so that is a defective notion [Inwagen] |
| 17591 | Merely possible objects must be consistent properties, or haecceities [Inwagen] |
| 17563 | The strong force pulls, but also pushes apart if nucleons get too close together [Inwagen] |
| 17559 | Is one atom a piece of gold, or is a sizable group of atoms required? [Inwagen] |
| 17586 | At the lower level, life trails off into mere molecular interaction [Inwagen] |
| 17568 | A tumour may spread a sort of life, but it is not a life, or an organism [Inwagen] |
| 17581 | Being part of an organism's life is a matter of degree, and vague [Inwagen] |
| 17584 | Some events are only borderline cases of lives [Inwagen] |
| 17569 | Unlike waves, lives are 'jealous'; it is almost impossible for them to overlap [Inwagen] |
| 17580 | One's mental and other life is centred on the brain, unlike any other part of the body [Inwagen] |
| 17570 | The chemical reactions in a human life involve about sixteen elements [Inwagen] |
| 17585 | Life is vague at both ends, but could it be totally vague? [Inwagen] |
| 17567 | A flame is like a life, but not nearly so well individuated [Inwagen] |
| 17576 | If God were to 'reassemble' my atoms of ten years ago, the result would certainly not be me [Inwagen] |
| 17573 | There is no reason to think that mere existence is a valuable thing [Inwagen] |