PS You do know you can delete posts from the EL, don't you?
On 17 August 2014 17:23, LizR <[email protected]> wrote: > 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. 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.
