[FOM] Denotation version of Gupta's puzzle

Dean Buckner Dean.Buckner at btopenworld.com
Wed Mar 5 14:29:20 EST 2003

Looking at Hodges example, I think he is confusing the use of schematic
letters such as 'x' or 'y' in

 (a) Some x is such that x = 9 + x
 (b) Some y is such that y = 2y - 4

which don't ever have a reference, with proper names which (if they really
are names) always have a reference.  Clearly (a) is false and (b)is true,
but neither "x" nor "y" refers in either case, the reasons for which I refer
Hodges to any elementary textbook on logic and language.  This is not to be
confused with

 (c) A = 9 + A

which, *whatever* A refers to, is false.  Note that if 'A' does not have a
reference, then the whole sentence is meaningless since, if 'A' designates
nothing, then the sum of the numbers designated by '9' and 'A'" also
designates nothing.

Anticipating any reply that relies on a confusion between "designates
nothing" and "designates zero" I'll just say it is a very bad confusion
indeed.  (Contrast what happens when you put a 'not a number' expression in
a spreadsheet, and all the derived cells turn to 'not a number', with what
happens when you enter the number 0).

Dean Buckner

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