On Feb 8, 6:08 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> you say that you are a formalist. I gave you the definition of realism
> which works for the understanding of the reasoning. It is the
> acceptation of (P v ~P) when P is intended on the domain of the
> natural numbers.
I can accept that as a *formal* rule that doens't mean anything
just like I can accept that some but not all Snarks are Boojums. You
to ontological conclusions just by writing down an axiom. Worse, the
to use the Law of the Exclude Middle or not (it can of course be
incurring a contradiction) is typically motivated by ontological
We think LEM applies to past events because we think they either
or they didn't. We doubt that it applies to future events.
> That's all.
> By standard use of numbers I mean the element (N, +, *) as
> taught by mathematicians. I show that comp makes *some* theology as
> part of the discourse of machine. This should not give any trouble,
> *especially* to a formalist.
The idea that a hypothetical machine would give certain hypothetical
responses wouldn't, but of course, you are saying more than that:
you are saying that *I* am an immaterial machine. And that's an
ontological claim which cannot be supported by a merely formal
> A mathematical anti-realist is an ambiguous expression. How could them
> believe in Church thesis which is equivalent with the assertion that a
> universal number exist in arithmetic.
In the way that I have explained to you a thousand times: the
that certain entities exist is just taken as part of the game.
> If it is formal game playing, just play the game.
If I just play the game I am never going to conclude that
I *am* a dreaming machine, any more than I am going to
conclude I am Supermario
>The theory is enough
> precise to allow that.
> Do you have a definition of formalism which does not rely on
> arithmetical realism.
Yes: formalism is the claim that no mathematical
entities actually exist, that mathematics is just
the exploration of the consequences of various rules
and axioms, and that mathematical truth is contextual
to the system employed and has no wider significance.
>AR is the weakest assumption on which all
> mathematician agree (except ulrafinitist).
Formalists think it is true as well,,,but it is not a truth
about anything outside the game.
>By works done by Glivenko,
> Gödel and Heyting we know that intuitionist arithmetic (typically anti-
> realist) and classical arithmetic are essentially identical, and
> process the same ontology.
You mean the same model. Ontology cannot be proven by
mathematical argument, it is meta-mathematical and metaphysical.
>Real math (and formal) differences appears
> only in analysis and set theory (on which I tend to be not realist,
> although the work is neutral on this).
Formalists do not differ on which parts of maths are
true and false, they differ on its epistemology and
> Could you define *formally* 'real existence'?
There is no reason I should, and at least one reason I shouldn't:
I have stated that real existence cannot be established by formal
Formalists do not think everything is merely formal
game playing, they think maths is *as opposed to* other
things which are not.
>Could you define
> formally 'primitively material', so that we can continue to agree or
> disagree on something. Or you might try to get my point, after all. It
> only shows the difficulty with such notions.
All philosophical problems are difficult, and that is no excuse
for pretending that there is nothing to a notion such a "real
>Obviously, as Chalmers
> rightly insists, no formal characterization of consciousness can be
> given. But comp makes it possible to retrieve formality as the meta-
> level. That's the S4Grz1 formalism. It makes its possible to work on a
> purely formal account of what machine cannot formalize, and it shows
> that machine can, like us, build meta-formal account of those things.
> Once and for all, keep it mind that when I utter that a number exist,
> I am just like PA proving a sentence of the form ExP(x), and
> everything will flow easily (well with some effort).
Nope. The claim that I am, ontologically, an immaterial dreaming
does not follow from PA.
> unnecessary metaphysics just add noise.
The conclusion is metaphysical, therefore the argument
must be or the conclusion is a non-sequitur. Therefore
metaphysics is a necessity for you.
>Study the proof, and criticize
> it. You might be adding an interpretative layer which exists only in
> your mind, I'm afraid.
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