quantifier shift fallacy
A fallacy of reversing the order of two quantifiers . The common form is that of moving from a statement of the form ‘every x has a related y ’ to one of the form ‘there is some y related to every x ’. An easily detected instance would be inferring from ‘everyone has a mother’ to ‘there is someone who is everyone's mother’. More subtle instances would be trading on the two different meanings that can be given to statements like ‘there is some proposition presupposed in every investigation’. Does this mean that for all investigations there is some possibly different presupposition, or that there is some unique common presupposition? Similarly ‘there is something that is the meaning of all our activities’, which smooths the fallacious transition from ‘each activity has a meaning’ which is probably true to ‘there is a Purpose common to all of them’ which is probably false. The fallacy is obvious in quantification theory, where it is represented as moving from (∀x )(∃y )(Rxy ) to (∃y )(∀x )(Rxy ).

Philosophy dictionary. . 2011.

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