# [FOM] Denotation version of Gupta's puzzle

Sandy Hodges SandyHodges at attbi.com
Fri Mar 14 03:48:35 EST 2003

```On a certain day five brothers each make a single utterance:

Albert says "Seven."

Bertrand says "The sum of the numbers designated by David and Ethelred."

Charles says "Ten minus the sum of the numbers designated by David and
Ethelred."

David says "Ninety-nine."

Ethelred says "The sum of the numbers designated by Albert, Bertrand,
and Charles."

SH: I think that the five brothers utterances designate 7, 116, -106,
99, and 17 respectively.
-----------------------
DB:
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, ...

-----------------
SH: I am unclear as to which of my opinions Dean thinks is based on the
confusion he mentions, and also what alternative view he holds.   Does
he think the five brothers' utterances do not denote 7, 116, -106, 99,
and 17 respectively?

If Bertrand's utterance does not denote anything, what about an
utterance by a sixth brother, Fred, who says

"The sum of the numbers denoted by Albert and David."

Does Fred's utterance denote 106?

A seventh brother, George, says:
"The sum of the numbers denoted by Albert and Bertrand"

If Bertrand's utterance does not denote anything, does George's
utterance denote 7?
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Sandy Hodges / Alameda,  California,   USA
mail to SandyHodges at attbi.com will reach me.

```