O. K. writes: "the above announcement is surely false. If I have dialed a
number, I must have imagined it first. If I can imagine it, then it is NOT
non-existent. A number which can be conceptualized but does not 'really' exist
seems to be an impossibility. In other words, once a number is conceptualized,
it exists necessarily. Or no? Perhaps the resident Fregeans will have some
comment on this."
Or the resident Griceists, or the resident Popperians. I would think Popper
would take
i. You have reached a non-existent number.
as paradox in a Goedelian way. Grice would take a different stance. Although
Grice was a friend of J. L. Austin, who translated Frege's "Number" into
English, he (Grice -- I'm less sure about Austin) never read that essay
("Boring").
It seems that we have a cross-linguistic issue at hand, figuratively. If that
is the exact wording, then indeed, Popper would be right and (i) would be
paradoxical, since 'you' HAVE reached (by dialing) a number that is connected
to someone (or "someone") who has the ability to inform you that you have
dialed a non-existent number.
Grice would say that there is a respect for informativeness here. The
implicature being:
ii. You have dialed a non-existent number; to wit, a customer number which I
expect is what you were trying to dial. For I doubt that your m-intention in
dialing this number, for which a connection to a customer does not exist, was
to hear me informing you that you have dialed a number, for which a connection
to a customer does not exist. Or not.
Oddly, Grice would spend hours on the telephone, with George Myro, playing what
they called 'phone chess'. They lived a bit far away: Grice had moved to the
Berkeley hills, and Myro lived in Oakland.
Austin's and Frege's point about the existence (or lack thereof) of numbers,
while EXPLICATED, since barely the issue under IMPLICATURE.
Cheers,
Speranza
