86 ideas
| 21757 | Philosophy is the conceptual essence of the shape of history [Hegel] |
| 8187 | Frege was strongly in favour of taking truth to attach to propositions [Frege, by Dummett] |
| 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] |
| 18772 | We can treat designation by a few words as a proper name [Frege] |
| 14075 | Proper name in modal contexts refer obliquely, to their usual sense [Frege, by Gibbard] |
| 10424 | A Fregean proper name has a sense determining an object, instead of a concept [Frege, by Sainsbury] |
| 18773 | People may have different senses for 'Aristotle', like 'pupil of Plato' or 'teacher of Alexander' [Frege] |
| 4978 | The meaning of a proper name is the designated object [Frege] |
| 10510 | Frege ascribes reference to incomplete expressions, as well as to singular terms [Frege, by Hale] |
| 18937 | If sentences have a 'sense', empty name sentences can be understood that way [Frege, by Sawyer] |
| 18940 | It is a weakness of natural languages to contain non-denoting names [Frege] |
| 18939 | In a logically perfect language every well-formed proper name designates an object [Frege] |
| 9462 | Frege is intensionalist about reference, as it is determined by sense; identity of objects comes first [Frege, by Jacquette] |
| 18936 | Frege moved from extensional to intensional semantics when he added the idea of 'sense' [Frege, by Sawyer] |
| 10533 | We can't get a semantics from nouns and predicates referring to the same thing [Frege, by Dummett] |
| 4893 | Frege was asking how identities could be informative [Frege, by Perry] |
| 18752 | 'The concept "horse"' denotes a concept, yet seems also to denote an object [Frege, by McGee] |
| 22318 | Frege failed to show when two sets of truth-conditions are equivalent [Frege, by Potter] |
| 4980 | The meaning (reference) of a sentence is its truth value - the circumstance of it being true or false [Frege] |
| 9180 | Holism says all language use is also a change in the rules of language [Frege, by Dummett] |
| 4981 | The reference of a word should be understood as part of the reference of the sentence [Frege] |
| 15597 | Frege's Puzzle: from different semantics we infer different reference for two names with the same reference [Frege, by Fine,K] |
| 17002 | Frege's 'sense' is ambiguous, between the meaning of a designator, and how it fixes reference [Kripke on Frege] |
| 18778 | Every descriptive name has a sense, but may not have a reference [Frege] |
| 7805 | Frege started as anti-realist, but the sense/reference distinction led him to realism [Frege, by Benardete,JA] |
| 4976 | The meaning (reference) of 'evening star' is the same as that of 'morning star', but not the sense [Frege] |
| 4977 | In maths, there are phrases with a clear sense, but no actual reference [Frege] |
| 4979 | We are driven from sense to reference by our desire for truth [Frege] |
| 15155 | Expressions always give ways of thinking of referents, rather than the referents themselves [Frege, by Soames] |
| 11126 | 'Sense' gives meaning to non-referring names, and to two expressions for one referent [Frege, by Margolis/Laurence] |
| 8164 | Frege was the first to construct a plausible theory of meaning [Frege, by Dummett] |
| 9817 | Earlier Frege focuses on content itself; later he became interested in understanding content [Frege, by Dummett] |
| 8171 | Frege divided the meaning of a sentence into sense, force and tone [Frege, by Dummett] |
| 4954 | Frege uses 'sense' to mean both a designator's meaning, and the way its reference is determined [Kripke on Frege] |
| 7304 | Frege explained meaning as sense, semantic value, reference, force and tone [Frege, by Miller,A] |