On Feb 8, 6:08 pm, Bruno Marchal <marc...@ulb.ac.be> wrote: Peter, > > 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 ontologically, just like I can accept that some but not all Snarks are Boojums. You cannot come to ontological conclusions just by writing down an axiom. Worse, the decision to use the Law of the Exclude Middle or not (it can of course be dropped without incurring a contradiction) is typically motivated by ontological considerations. We think LEM applies to past events because we think they either happened 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 premise. > 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 assertion 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 ontology. > 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 arguments. 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 existence" >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 machine does not follow from PA. >Adding > 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. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to email@example.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.