85 ideas
| 15801 | Many philosophers aim to understand metaphysics by studying ourselves [Chisholm] |
| 15802 | I use variables to show that each item remains the same entity throughout [Chisholm] |
| 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] |
| 15832 | Events are states of affairs that occur at certain places and times [Chisholm] |
| 15829 | The mark of a state of affairs is that it is capable of being accepted [Chisholm] |
| 15809 | A state of affairs pertains to a thing if it implies that it has some property [Chisholm] |
| 15828 | I propose that events and propositions are two types of states of affairs [Chisholm] |
| 15830 | Some properties can never be had, like being a round square [Chisholm] |
| 15827 | Some properties, such as 'being a widow', can be seen as 'rooted outside the time they are had' [Chisholm] |
| 15804 | If some dogs are brown, that entails the properties of 'being brown' and 'being canine' [Chisholm] |
| 15810 | Maybe we can only individuate things by relating them to ourselves [Chisholm] |
| 15805 | Being the tallest man is an 'individual concept', but not a haecceity [Chisholm] |
| 15807 | A haecceity is a property had necessarily, and strictly confined to one entity [Chisholm] |
| 15814 | A peach is sweet and fuzzy, but it doesn't 'have' those qualities [Chisholm] |
| 12852 | If x is ever part of y, then y is necessarily such that x is part of y at any time that y exists [Chisholm, by Simons] |
| 15808 | A traditional individual essence includes all of a thing's necessary characteristics [Chisholm] |
| 12851 | Intermittence is seen in a toy fort, which is dismantled then rebuilt with the same bricks [Chisholm, by Simons] |
| 15806 | The property of being identical with me is an individual concept [Chisholm] |
| 15826 | There is 'loose' identity between things if their properties, or truths about them, might differ [Chisholm] |
| 3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
| 15819 | Do sense-data have structure, location, weight, and constituting matter? [Chisholm] |
| 15816 | 'I feel depressed' is more like 'he runs slowly' than like 'he has a red book' [Chisholm] |
| 15817 | If we can say a man senses 'redly', why not also 'rectangularly'? [Chisholm] |
| 15818 | So called 'sense-data' are best seen as 'modifications' of the person experiencing them [Chisholm] |
| 15831 | Explanations have states of affairs as their objects [Chisholm] |
| 15811 | I am picked out uniquely by my individual essence, which is 'being identical with myself' [Chisholm] |
| 15815 | Sartre says the ego is 'opaque'; I prefer to say that it is 'transparent' [Chisholm] |
| 15813 | People use 'I' to refer to themselves, with the meaning of their own individual essence [Chisholm] |
| 15803 | Bad theories of the self see it as abstract, or as a bundle, or as a process [Chisholm] |
| 15821 | Determinism claims that every event has a sufficient causal pre-condition [Chisholm] |
| 15824 | There are mere omissions (through ignorance, perhaps), and people can 'commit an omission' [Chisholm] |
| 15822 | The concept of physical necessity is basic to both causation, and to the concept of nature [Chisholm] |
| 15823 | Some propose a distinct 'agent causation', as well as 'event causation' [Chisholm] |
| 15820 | A 'law of nature' is just something which is physically necessary [Chisholm] |