Re: Existence, Self-identity and Uniqueness.

Hi

Owen wrote:
The introduction of "the x:Fx" does not render FOL= inconsistent at
all, unles you foolishly assume that non-referring descriptions are
values of the indidvidual variable.

Or to bring it to the point. In FOL (with
or without =), individual variables have
always a value. That is why it is called first
order logic. The variables range in a first
order fashion over the domain.

Compare to second order logic, where we can
have variables ranging over subsets of the
domain.

There is no mechanism in FOL which looks
at some side conditions for the variables.
And if you introduce such side conditions,
you might run into troubles, as I showed.
Because FOL is not made for this.

So a side condition "non-referring descriptions"
cannot be handled in a satisfactory way
the way you did it in your definitions
of "the x:Fx". You might also consult:

"As observed in Section 1, one of the key motivations for Russell's theory of descriptions was the idea that it could ameliorate the problem of non-denoting expressions — expressions like ‘Pegasus’, ‘The Golden Mountain’, and ‘The Present King of France’. It is now widely believed that this solution is not altogether satisfactory in the case of fictions (like ‘Pegasus’), and that it is unhappy in all cases when we embed the descriptions in a certain class of intensional constructions."
http://plato.stanford.edu/entries/descriptions/

A lot of ink seems to have been spilled over
relatively simple perplexities. Especially
if one is not cautious about what is FOL,
and what is not FOL.

Bye
.