On Friday, November 16, 2018 at 11:05:51 AM UTC-6, Bruno Marchal wrote: > > > On 15 Nov 2018, at 18:13, Philip Thrift <[email protected] <javascript:>> > wrote: > > > > On Thursday, November 15, 2018 at 5:15:39 AM UTC-6, Bruno Marchal wrote: >> >> >> On 13 Nov 2018, at 11:06, Philip Thrift <[email protected]> wrote: >> >> >> >> On Monday, November 12, 2018 at 8:35:23 PM UTC-6, Bruno Marchal wrote: >>> >>> >>> A model is a model of a theory. The notion of model of a model can make >>> sense, by considering non axiomatisable theory, but that can lead to >>> confusion, so it is better to avoid this. When a model is seen as a theory, >>> if it contains arithmetic, the theory cannot be axiomatised, proofs cannot >>> be checked, the set of theorems is not recursively enumerable, etc. >>> >>> >>> Bruno >>> >>> >>> >> This is why some have mathematical theories (alternatives to ZF) that >> have finite (i.e. Only a finite number of numbers needed!) models (e.g. *Jan >> Mycielski,* "Locally Finite Theories" [ >> https://www.jstor.org/stable/2273942 ]). In this approach quantifiers >> are effectively replaced by typed quantifiers, where the type says "this >> quantifier ranges over some finite set". >> >> Another approach is to nominalize physical theories theories (*Hartry >> Field*, *Science Without Numbers,* summary [ >> http://www.nyu.edu/projects/dorr/teaching/objectivity/Handout.5.10.pdf >> ]). In this approach the model of the theory is a finite set of (references >> to) physical objects. >> >> This is the best point-of-view to have: *The set of natural numbers >> simply doesn't exist!* >> >> >> >> I agree. It is actually a consequence of mechanism. The set of natural >> numbers does not exist, nor any infinite set. But that does not make a >> physical universe into something existing. Analysis, physics, sets, … >> belongs to the numbers “dreams” (a highly structured set, which has no >> ontology, but a rich and complex phenomenological accounts). >> >> I gave my axioms (Arithmetic, or Kxy = x, Sxyz = xz(yz)). As you can see, >> there is no axiom of infinity. >> >> Bruno >> >> PS Sorry for the delay. >> >> > > > The "highest" programming may be higher-type (or higher-order) programming: > > > http://www.cs.bham.ac.uk/~mhe/papers/introduction-to-higher-order-computation-NLS-2017.pdf > examples @ http://www.cs.bham.ac.uk/~mhe/ > > > "Higher-order [programming involves] infinite objects, such as infinite > strings, real numbers, and even functions themselves, etc. [which > themselves] are computable. And, more importantly, how to compute them. In > practice, computation with infinite objects often takes place in languages > such as ML, Haskell, Agda etc. In theory, some canonical systems are > Godel’s system T, Platek-Scott-Plotkin PCF, Martin-Lof’s dependent type > theory, among many others. But how can we (or a computer) compute with > infinite objects, given that we have a finite amount of time and a finite > amount of memory and a finite amount of any resource? *Topology comes to > the rescue* [revolving] around the [finite vs. infinite dichotomy], > mediated by topology. *We can say that topology is precisely about the > relation between finiteness and infiniteness that is relevant to > computation.*" > > > > But there is a new biochemical programming language: > > *CRN++: Molecular Programming Language* > (Submitted on 19 Sep 2018) > https://arxiv.org/abs/1809.07430 > "We present its syntax and semantics, and build a compiler translating > CRN++ programs into chemical reactions...laying the foundation of a > comprehensive framework for molecular programming." > > A programming language whose purpose is to create bugs! > > So the question becomes: Is bioprogramming > programming? (if biomatter > has experiential qualities in addition to informational quantities) > > > Assuming some primary matter, and some non mechanist theory, why not. That > seems to quite speculative, though, and adding difficulties to a subject > which is already difficult when assuming the “simplifying” assumption of > Mechanism. With mechanism, the mind-body problem reduced into justifying > the existence of a canonical measure on all computations “seen from inside” > (which admits a number of modes, imposed by incompleteness). In case the > physics in the head of the universal machine/number departs from > observation, we get the mean to make sense of some non-mechanism, and this > might show you right. So let us continue the testing/comparison. > > What do you think your biomatter do which would be non Turing emulable, > nor “first person measurable(*) and in what sense would that be relevant > with respect of consciousness? > > I have no doubt chemical computation is a wonderful subject, but with > “Indexical Digital Mechanism”, the theology and the physics is independent > of the language and the basic theories as far as they are Turing > complete(*), the physical appearance, needs to be justified in term of a > relative measure state/computations "seen from inside” (Incompleteness > makes the usual standard definition getting sense in those “enough rich” > Turing complete(**) theories. > > Bruno > > > (*) This provides some “free oracle”, like the random oracle and the > halting oracle, due to the limiting behaviour of the first person > indeterminacy). > > (**) Turing complete means that for all p sigma_1 (shape ExA(x, y), A > decidable) we have, with “[]” Gödel’s arithmetical provability predicate, > > p -> []p > > is true. > > Löbian (sufficiently rich) means that for all such p,"p -> []p" is not > only true, but provable. Put it in another way, this means that > > [](p -> []p) > > is true. (This makes the machine obeying to G and G* and their intensional > variants). > > (See all definitions in the second part of sane04, I recall them in most > of my papers). > > > *What do you think your biomatter do which would be non Turing emulable, nor “first person measurable(*) and in what sense would that be relevant with respect of consciousness?*
One analogy I came up with (will see how this goes): Think of a Turing computing that doesn't manipulate (only) symbols (information, or numbers), but manipulates (also) emojis [ https://emojipedia.org/ ]! Now emojis themselves are symbols of course, but suppose that they "embody" real elements of *experience* that are ontologically separate from *information* (or numbers). (One could call this *e-Turing* computing non-Turing or not, depending on whether how one defines unconventional computing.) - pt -- 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 https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
