🚀 go-pugleaf

We better be careful or we're going to end up agreeing on more than
just the inadequacy of ZF.

In article  <1992Nov6.193134.17283@guinness.idbsu.edu> Randall Holmes writes:
]Re Gudeman:
]
]Your criterion for an acceptable property is wrong.
]
]...  Some perfectly well-defined open sentences which
]have truth values no matter what is substituted into them cannot have
]extensions or intensions.

OK, you have a point.  The open sentence "__ is not true of
itself" does not form a proposition if you replace the blanks with
something that stands for the sentence's (non-existent) proposition,
but then you can't expect _any_ open sentence to form a proposition if
you fill its blanks with non-existent things.  I'll have to rethink my
criterion, but that really does not affect my main point about
recursion.

]Once again, there is no problem with
]self-membership or non-self-membership holding of particular objects;
]there simply is no "object" which is the extension of
]"self-membership" or "non-self-membership".  And this does not mean
]that the objects in the universe are not unambiguously divided between
]the self-members and the non-self-members; there is no ambiguity, no
]gray area between them.  But there cannot be a set of the
]non-self-members.

I think we agree that there is no property (read "nonspatio-temporal
mathematical object") associated with the set of open sentences of the
form "__ is an element of __".  Our difference is that you think there
is a metaphysical explanation for this fact, and I think it can be
explained entirely in terms of incorrect use of language.
-- 
					David Gudeman
gudeman@cs.arizona.edu