Re: Existence, Self-identity and Uniqueness.

On Thu, 28 Dec 2006 12:28:03 +0100, Jan Burse <janburse@xxxxxxxxxxx>
said:
Hi

Owen wrote:
Jan Burse wrote:
Wrong again.
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.
I don't do that, why do you persist in doing that??

I was on purpose using some foolishly substitutions.
Someone has to do sometimes foolishly things to
show inconsistency, even in the precence of initially
innocent concepts.

I did this to show you that you are not strictly
working in FOL=. Because FOL= does not distinguish
between foolishly and non foolishly substitutions.

How do you bar foolishly substitutions from FOL=?
How do you control the following reasoning step,
which works in FOL= (even in FOL without =):

forall x A(x)
-------------
A(t)

Note again A is a formula. So we could also rewrite
the step as follows:

forall x A
----------
A[x/t]

Here A[x/t] denotes the result of substituting t for
x in the formula A. How do you control this, and still
claim you have FOL= at hand?

In his original post, Owen appears simply to be introducing definite
descriptions (i.e., expressions of the form "(the x:Fx)") á la Russell
as "incomplete symbols" -- they are not genuine singular terms in the
language, but only occur as parts of convenient definitions for more
complex expressions. Hence, they not available for substitution in
inference patterns like universal instantiation. So construed, his
introduction of definite descriptions does not take him beyond the
bounds of FOL=.


.

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