Re: Gödel's sentence is not self-referential

On Nov 24, 12:26 pm, G. Frege <nomail@invalid> wrote:
On Sat, 24 Nov 2007 01:59:40 -0800 (PST), LauLuna

<laureanol...@xxxxxxxx> wrote:

3. A proposition can safely refer to the sentence that expresses it,
without any peril of circularity or paradox; consider

'this sentence has five words'

I get your point, LauLuna. Frege for example talked about the "thought"
a sentence expresses (which is its "sense"). One might equate Frege's
/thought/ with your /proposition/ (at least for the sake of the
argument).

Clearly

It rains.
and
Es regnet.

are zwo different sentences, but they express the same thought, namely
that it rains.

Now...



I believe that no proposition can be about itself [...]

Well... But why not? Consider:

(1) The thought sentence (1) expresses is clear!

:-)

Or maybe you will rather accept the following claim:

(2) The thought sentence (2) expresses is in no way clear!

:-)

Now it might seem that sentence (2) is _clearly_ true, since the thought
sentence (2) expresses is in now way clear! (But that does not prevent
the sentence from being true!)

F.

--

E-mail: info<at>simple-line<dot>de

I'd say (1) and (2) express no thought, hence no proposition, because
they fail referring to any thought.

If (1) and (2) were in fact able to accomplish self-reference, by
direct denotation, much easier would it be for:

(3) each proposition refers to something

to do it via subsumption under the concept of proposition.

But if (3) were efffectively self-referential, so would be:

(4) all non self-referential propositions are true

Now, if (4) could be self-referential it would be so iff it wouldn't.

I confess that my ultimate reason is of phenomenological origin; I
think no thought is about itself because no intentional act can be its
own intentional object. Suppose a function PSI(x) that takes
intentional objects and yields intentional acts. I dare say PSI(x) has
no fixed point. Assume there exists an x such that:

PSI(x) = x

We would have that

PSI(x) = PSI(PSI(x)) = PSI(PSI(PSI(x))), etc.

We would have an act and an object of infinite complexity, which seems
humanly impossible.

Regards

.