Re: Gödel's sentence is not self-referential

On Nov 25, 10:34 pm, G. Frege <nomail@invalid> wrote:
On Sun, 25 Nov 2007 12:49:37 -0800 (PST), LauLuna





<laureanol...@xxxxxxxx> wrote:

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!)

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

Huh?! How can they fail to refer to any thought?

Consider the following sentence:

(0) It rains.

Now consider the following sentence:

(1a) The thought sentence (0) expresses is clear!

Clearly (1a) expresses a thought, namely that the thought sentence (0)
expresses is clear.

Or slightly more vague: (1b) expresses the thought that the thought that
a certain sentence expresses is clear.

That's clear!

Now consider the sentence:

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

(1b) too (like 1a) expresses the thought that the thought that a certain
sentence -actually 1b- expresses is clear.

Not at all. I can touch fingertip A with fingertip B, but I can't
touch fingertip A with fingertip A.


But it's certainly reasonable to claim that the thought (1b) expresses
is NOT clear (due to self-reference). Hence one might be tempted to
claim

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

This exemplifies how no thought is about itself: if (1b) expresses an
unclear thought (which is not the case), it doesn't imply that (2)
does the same; why should both express the same thought? You were
still thinking of (1b) when you wrote (2). The function 'thought of'
has no fixpoint, much in the same way the function 'set of' has none.

And I don't doubt that (2) DOES express a thought: namely that the
thought sentence (2) expresses is in no way clear! Don't you think so?

(But it might be hard to assign a reasonable truth value to (2). :-)



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.

Huh? Fregean /thoughts/ (like /propositions/, I guess) have nothing to
do with "intentional acts" and/or "intentional objects" (whatever that
may be). (They are no "psychological" entities!)

Oh, Fregean thoughts are not phenomenological entities, you're right.

What I'm implicitly claiming here is that the way in which toughts, as
real temporal entities, occur in consciousness is of significance for
some logical problems. There is one essential law that holds for all
real temporal processes: the impossibility of circularity; this holds
also for thoughts: the intentional object of a thought must be there
previously, it cannot be created with the thought itself, hence it
cannot be the thought itself. One caveat: 'previously' doesn't refer
to a chronological order but to some order of determination.

What I'm doing in logic is trying to show that all the hierarchies
induced by paradoxes stem from the fact that no thought is about
itself. This is the mustard seed that blooms into the luxuriant world
of types, language levels, set theoretic cumulative hierarchy...

Deriving a quasi-logical fact from a quasi-psychological one seems to
imply deriving a necesssary fact from a contingent fact. This is in
fact not so. That no thought is about itself is no contingent fact,
it's an eidetic feature, an essential feature of intentional acts and,
as such, it's in no way contingent.

Please ignore this line!

Let me paraphrase:

'Please ignore the current (i.e. 'please ignore the current
(i.e.'please ignore...))...) request'.

Beautiful. How could I possibly ignore it?

How could I possibly ignore such a beautiful gadget


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