display all the ideas for this combination of texts
3 ideas
8943 | Three-valued logic says excluded middle and non-contradition are not tautologies [Fisher] |
Full Idea: In three-valued logic (L3), neither the law of excluded middle (p or not-p), nor the law of non-contradiction (not(p and not-p)) will be tautologies. If p has the value 'indeterminate' then so will not-p. | |
From: Jennifer Fisher (On the Philosophy of Logic [2008], 07.I) | |
A reaction: I quite accept that the world is full of indeterminate propositions, and that excluded middle and non-contradiction can sometimes be uncertain, but I am reluctant to accept that what is being offered here should be called 'logic'. |
8945 | Fuzzy logic has many truth values, ranging in fractions from 0 to 1 [Fisher] |
Full Idea: In fuzzy logic objects have properties to a greater or lesser degree, and truth values are given as fractions or decimals, ranging from 0 to 1. Not-p is defined as 1-p, and other formula are defined in terms of maxima and minima for sets. | |
From: Jennifer Fisher (On the Philosophy of Logic [2008], 07.II) | |
A reaction: The question seems to be whether this is actually logic, or a recasting of probability theory. Susan Haack attacks it. If logic is the study of how truth is preserved as we move between propositions, then 0 and 1 need a special status. |
8720 | A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Priest,G, by Friend] |
Full Idea: Priest and Routley have developed paraconsistent relevant logic. 'Relevant' logics insist on there being some sort of connection between the premises and the conclusion of an argument. 'Paraconsistent' logics allow contradictions. | |
From: report of Graham Priest (works [1998]) by Michèle Friend - Introducing the Philosophy of Mathematics 6.8 | |
A reaction: Relevance blocks the move of saying that a falsehood implies everything, which sounds good. The offer of paraconsistency is very wicked indeed, and they are very naughty boys for even suggesting it. |