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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