Quantifier shift
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A quantifier shift is a logical fallacy in which the quantifiers of a statement are erroneously transposed during the rewriting process. The change in the logical nature of the statement may not be obvious when it is stated in a natural language like English.
A quantifier shift is a logical fallacy in which the quantifiers of a statement are erroneously transposed during the rewriting process. The change in the logical nature of the statement may not be obvious when it is stated in a natural language like English. 3. Every natural number n has a successor m = n + 1 , the smallest of all natural numbers that are greater than n . Therefore, there is a natural number {m} that is a successor to all natural numbers. \forall n \,\exists m \,Snm \vdash \exists m \,\forall n \,Snm It is fallacious to conclude that there is a single natural number that is the successor of every natural number. ==References== Robert Audi (General Editor), The Cambridge Dictionary of Philosophy (Second Edition), 1999, pp. 272–3. A. R. Lacey, Dictionary of Philosophy (Third Revised Edition) (Barnes & Noble, 1996). Introduction to Logic, Harry J. Gensler, p. 220 Antony G. Flew, Dictionary of Philosophy: Revised Second Edition Harry J. Gensler, Historical Dictionary of Logic
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