Never mind, you stated your position nice and clearly, perhaps more clearly than you normally do on the EL.
(...or is that why you're saying "OOPS!" ? :-) On 17 August 2014 16:54, meekerdb <[email protected]> wrote: > OOPS! I didn't intend to post this to the everything-list; although it > may serve as an introduction for James Lindsay if he decides to join the > list. I wrote to him after reading his book "dot dot do" which is about > infinity in mathematics and philosophy. > > Brent > > > On 8/16/2014 9:28 PM, meekerdb wrote: > > On 8/16/2014 4:57 PM, James Lindsay wrote: > > Hi Brent, > > Thanks for the note. I like the thought about mathematics as a refinement > of language. I also think of it as a specialization of philosophy, or even > a highly distilled variant upon it with limited scope. Indeed, I frequently > conceive of mathematics as a branch of philosophy where we (mostly) agree > upon the axioms and (mostly) know we're talking about abstract ideas, to be > distinguished from what I feel like I get from many philosophers. > > I am not familiar with Bruno Marchal, > > > Here's his paper that describes his TOE. It rests on two points for which > he gives arguments: (1) If consciousness is instantiated by certain > computational processes which could be realized in different media (so > there's nothing "magici" about them being done in brains) then they can > exist the way arithmetic exist (i.e. in "platonia"). And in platonia there > is a universal dovetailer, UD, that computes everything computable (and > more), so it instantiates all possible conscious thoughts including those > that cause us to infer the existence of an external physical world. The > problem with his theory, which he recognizes, is that this apparently > instantiates too much. But as physicist like Max Tegmark, Vilenkin, and > Krause talk about eternal inflation and infinitely many universes in which > all possible physics is realized, maybe the UD doesn't produce too much. > He thinks he can show that what it produces is like quantum mechanics > except for a measure zero. But I'm not convinced his measure is more than > wishful thinking. > > He's a nice fellow though and not a crank. So if you'd like to engage him > on any of this you can join the discussion list > [email protected]. > > and I am not expert in theories of anything, much less everything, > based upon computation or even computation theories. I remain a bit > skeptical of them, and overall, I would suggest that such things are likely > to be *theories* of everything, which is to say still on the map side of > the map/terrain divide. > > > I agree. But some people assume that there must be some ultimate ontology > of ur-stuff that exists necessarily - and mathematical objects are their > favorite candidates (if they're not religious). I don't think this is a > compelling argument since I regard numbers as inventions (not necessarily > human - likely evolution invented them). I think of ontologies as the > stuff that is in our theories. Since theories are invented to explain > things they may ultimately be circular, sort of like: mathematics-> > physics-> chemistry->biology-> intelligence-> mathematics. So you can > start with whatever you think you understand. If this circle of > explanation is big enough to include everything, then I claim it's > "virtuously" circular. > > Brent > "What is there? Everything! So what isn't there? Nothing!" > --- Norm Levitt, after Quine > > > Regarding your note about my Chapter 2, that's an interesting point that > he raises, and interestingly, I don't wholly disagree with him that it is > an integral feature of arithmetic that it is axiomatically incomplete > (though maybe I thought differently when I wrote the book). Particularly, I > don't think of it as a "bug," but I don't necessarily think of it as a > "feature" either. I'm pretty neutral to it, and I feel like I was trying to > express the idea in my book that it reveals mostly how theoretical, as > opposed to real, mathematics is. I'm not sure about this "more than a map" > thing yet, as by "map" I just mean abstract way to work with reality > instead of reality itself and hadn't read more into my own statement than > that. > > I would disagree with him, however, that it is related to the hard > problem of consciousness, I think, or perhaps it's better to say that I'm > very skeptical of such a claim. Brains are, however "immensely" complex, > finite things, and as such, I do not think that the lack of a complete > axiomatization of arithmetic is likely to be integrally related to the hard > problem of consciousness. Maybe I just don't understand what he's getting > at, though. Who knows? > > I also tend to agree with you--in some senses--about the ultrafinitists > probably being right. My distinction is that I'm fine with infinity as a > kind of fiction that we play with or use to make calculus/analysis more > accessible. I certainly agree with you that infinity probably shouldn't be > taken too seriously, particularly once they start getting weird and > (relatively) huge. > > There's something interesting to think about, though, when it comes to the > ideas of some infinities being larger than others. I was thinking a bit > about it the other day, in fact. That seems to be a necessary consequence > of little more than certain definitions on certain kinds of sets (with > "infinite" perhaps not even necessary here, using the finitists' > "indefinite" instead) and one-to-one correspondences. > > Anyway, thanks again for the note. > > Kindly, > James > > > On Sat, Aug 16, 2014 at 1:14 AM, meekerdb <[email protected]> wrote: > >> After seeing your posts on Vic's avoid-L list, I ordered your book. >> I'm generally inclined to see mathematics as a refinement of language - or >> in your terms a "map", not to be confused with the thing mapped. However I >> often argue with Bruno Marchal, a logician and neo-platonist, who has a TOE >> based on computation (Church-Turing) or number theory. I thought you book >> might help me. But I think Bruno would rightly object to your Chapter 2. >> He considers it an important feature of arithmetic that it is axiomatically >> incomplete, i.e. per Godel's theorem it is bigger than what can be proven >> from the axioms. He takes this as a feature, not a bug, to explain that if >> conscious thought is a computation this is why it cannot fully explain >> itself; and that is why "the hard problem" of consciousness is hard. I >> think there are simpler, evolutionary explanations for why consciousness >> does not include perception of brain functions, but I think Bruno has a >> point that arithmetic is bigger than what follows from Peano's axioms and >> so it is more than a map. >> >> I'm inclined to say Peano's axioms already "prove too much" and the >> ultrafinitists are right. Infinity is just a convenience to avoid saying >> how big, and shouldn't be taken too seriously. >> >> Brent Meeker >> > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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