[FOM] Grim paradox

laureano luna laureanoluna at yahoo.es
Fri Oct 6 15:26:19 EDT 2006

Reading Patrick Grim (e. g.‘The Incomplete Universe’,
MIT Press, 1991) I have come to consider propositions
of the kind of the following: 

(p)  ‘all propositions that are not about themselves
are about something else’

(p) seems to express an evident truth about all
propositions that are not about themselves. But we
have that (p) is about (p) iff (p) is not about (p).

This is an instance of the general law asserting that
for any relation R there is no object x such that for
any object y, xRy iff –yRy, for otherwise we would
have that xRx iff –xRx.
Since this seems akin to Russell paradox and others, I
am afraid there is no easy solution. Does anyone know
of a particular proposal? 

I would thank any indication or suggestion.


Laureano Luna Cabañero

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