A quantifier shift is a
logical fallacy In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (; Latin for " tdoes not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic syst ...
in which the
quantifiers of a statement are erroneously transposed during the
rewriting
In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a well-formed formula, formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewr ...
process. The change in the logical nature of the statement may not be obvious when it is stated in a
natural language
In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages ...
like
English
English usually refers to:
* English language
* English people
English may also refer to:
Peoples, culture, and language
* ''English'', an adjective for something of, from, or related to England
** English national ide ...
.
Definition
The
fallacious deduction is that:
''For every A, there is a B, such that C. Therefore, there is a B, such that for every A, C.''
:
However, an inverse switching:
:
is logically valid.
Examples
1. Every person has a woman that is their mother. Therefore, there is a woman that is the mother of every person.
:
It is fallacious to conclude that there is ''one woman'' who is the mother of ''all people''.
However, if the major premise ("every person has a woman that is their mother") is assumed to be true, then it is valid to conclude that there is ''some'' woman who is ''any given person's'' mother.
2. Everybody has something to believe in. Therefore, there is something that everybody believes in.
:
It is fallacious to conclude that there is ''some particular concept'' to which everyone subscribes.
It is valid to conclude that each person believes ''a given concept''. But it is entirely possible that each person believes in a unique concept.
3. Every
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''Cardinal n ...
has a successor
, the smallest of all natural numbers that are greater than
. Therefore, there is a natural number
that is a successor to all natural numbers.
:
It is fallacious to conclude that there is a single natural number that is the successor of every natural number.
References
*
Robert Audi
Robert N. Audi (born November 1941) is an American philosopher whose major work has focused on epistemology, ethics (especially on ethical intuitionism), rationality and the theory of action. He is O'Brien Professor of Philosophy at the Universi ...
(General Editor),
The Cambridge Dictionary of Philosophy
''The Cambridge Dictionary of Philosophy'' (1995; second edition 1999; third edition 2015) is a dictionary of philosophy published by Cambridge University Press and edited by the philosopher Robert Audi
Robert N. Audi (born November 1941) is an A ...
(Second Edition), 1999, pp. 272–3.
*A. R. Lacey, Dictionary of Philosophy (Third Revised Edition) (
Barnes & Noble
Barnes & Noble Booksellers is an American bookseller. It is a Fortune 1000 company and the bookseller with the largest number of retail outlets in the United States. As of July 7, 2020, the company operates 614 retail stores across all 50 U. ...
, 1996).
*Introduction to
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
, Harry J. Gensler, p. 220
*
Antony G. Flew, Dictionary of Philosophy: Revised Second Edition
*Harry J. Gensler, Historical Dictionary of Logic
{{Formal Fallacy
Quantificational fallacies