> On 15 Nov 2018, at 18:13, Philip Thrift <cloudver...@gmail.com> 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 <cloud...@gmail.com <javascript:>> >> 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 >> <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 >> <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). > > - 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.