Psychology Dictionary of ArgumentsHome
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| Law of the Excluded Middle: an assertion is either true or false. "There is no third possibility."See also bivalence, anti-realism, multivalued logic._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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Peter Geach on Excluded Middle - Dictionary of Arguments
I 76ff Law of excluded middle/Geach: the law is valid without any exception. Even Aristotle 9 Chap. De Interpretatione: tomorrow's sea battle: no refutation. No multi-valued logic: if we get the same truth value, if we ascribe P and its negation, then if P u P and P v P. - The same as for simple predication. Geach: only exception: vagueness. >Vagueness, cf. >Multi-valued logic. I 74 (A) For any x, either x is F or x is not F (B) For any predicate P and any object x, either P or its negation is true of x. I 75 in most cases we can treat (A) and (B) as equivalent. At first glance, the two look less fundamental than: (C) Either p or not p (D) Every sentence is either true itself or has a true negation Negation/Predicate Negation/Geach: the negation used in (A) and mentioned in (B) is the predicate negation. Negation/Sentence negation/Geach: The negation used in (C) and mentioned in (D) is the sentence negation. Negation/Everyday language/Geach: Here it is usually a part of the sentence that is negated, but the effect is that the whole sentence is negated. >Negation. I 76 Excluded Third/Geach: Semantic formulations often use the term "true" or "false" while omitting negation: E.g. For each predicate P and each object x, P is either true of x or false of x. E.g. Each proposition is either true or false. GeachVs: I cannot see any advantage in this. Negation must be used explicitly anyway. We lose nothing if we say instead of "false" that the negation is "true of". Excluded Middle/Quantification/Geach: The reason for my quantification of the law in (A) is to make it clearer what can be considered as a substitution of "x", e.g., no empty names. >Quantification. Empty names: are a matter of how to make them right. Question: why can't we use "every man" for x? I 78 Excluded Middle/Geach: Seems more substantial than other laws because it seems to be a premise like "either so and so or not so and so". or: "If so...then so...and if not so...then not so..." GeachVs: this is not a good argument, because, whatever comes out of "Either p or not p" and "If p then q" and "If not p then r" follows would also follow from the last two premises alone! Wittgenstein: with such superfluous assumptions we have to look for a hidden deception. When one realizes that one is to be taken by surprise, one then looks for the mistake in the wrong place._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Gea I P.T. Geach Logic Matters Oxford 1972 |
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> Counter arguments against Geach
> Counter arguments in relation to Excluded Middle
