Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 1 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Implication Paradox | Wessel | I 129 C.I.Lewis VsParadoxes of the implication: "strict implication": modal: instead of "from contradiction any statement": "from impossible ..." >Implication, strict, >Modalities, >Modal logic. WesselVsLewis, C.I.: circular: modal terms only from logical entailment relationship - 2.Vs: strict Implication cannot occur in provable formulas of propositional calculus as an operator. >Consequence, >Operators. I 140ff Paradoxes of implication: strategy: avoid contradiction as antecedent and tautology as consequent. >Tautologies, >Antecedent, >Consequent. I 215 Paradoxes of implication/quantifier logic: Additional paradoxes: for individual variables x and y may no longer be used as any singular terms - otherwise from "all Earth's moons move around the earth" follows "Russell moves around the earth". Solution: Limiting the range: all individuals of the same area, for each subject must be clear: P (x) v ~ P (x) - that is, each predicate can be meant as a propositional function - Wessel: but that is all illogical. >Logic, >Domain. |
Wessel I H. Wessel Logik Berlin 1999 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Russell, B. | Lewis, C.I. Vs Russell, B. | Hughes I 190 Strict implication/C.I.LewisVsRussell/LewisVsPrincipia Mathematica(1)/PM: (1912) a series of systems, VsParadoxes of (material implication). Paradoxes of implication/Hughes/Cresswell: usually from Principia Mathematica: a) a true statement is implied by any statement: (1) p > (q > p) b) a false statement implies any statement: (2) ~p > (p > q) Both together are called the paradox of (material) implication. Since either the antecedens of (1) or the antecedens of (2) must be true for each statement p, it is also easy to derive (3) from (1) and (2): (3) (p > q) v ( q > p). I 191 i.e. of two statements always the first implies the second or vice versa. I 191 Paradox of material implication: summarized: of two statements the first always implies the second or vice versa C.I.Lewis: did not intend to reject this thesis, on the contrary, (1) and (2) were "neither mysterious wisdom, nor great discoveries, nor great absurdities", but they reflect the truth-functional sense with which "implicate" is used in Principia Mathematica. Strict implication/C.I.Lewis: there is a stronger sense of "imply", according to which "p implies q" means that q follows from p. Here it is not the case that a true one is implied by every statement, or that out of a false one any follows. This stronger form leads to pairs of statements, none of which imply the other. Strict implication: necessary implication. Notation(s): "strimp". Strict disjunction/C.I.Lewis: analog to the strict implication: necessary disjunction. analog: Strict equivalence/C.I.Lewis: necessary equivalence. Hughes I 191 Strict implication/C.I.Lewis: p strimp q: "p follows from q" avoids paradox of (material) implication leads to pairs of statements, none of which implies the other. C.I.Lewis: introduces a whole series of systems, e.g. in the book "A Survey of Logic": the "Survey System". Basic operator here: logical impossibility, and conjunction/negation). strict implication: first comprehensively discussed in "Symbolic Logic" Lewis and Langford, (1932). (Systems S1 and S2). (Also the first comprehensive treatment of modal logical systems ever). Basic operator here: Possibility. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Hughes I G.E. Hughes Maxwell J. Cresswell Einführung in die Modallogik Berlin New York 1978 |
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