On Wednesday, October 3, 2018 at 2:54:46 AM UTC-5, Bruno Marchal wrote: > > > On 2 Oct 2018, at 17:11, Philip Thrift <[email protected] <javascript:>> > wrote: > > > > On Tuesday, October 2, 2018 at 9:25:17 AM UTC-5, Bruno Marchal wrote: >> >> >> On 2 Oct 2018, at 09:53, Philip Thrift <[email protected]> wrote: >> >> >> >> On Tuesday, October 2, 2018 at 2:20:10 AM UTC-5, Bruno Marchal wrote: >>> >>> >>> On 1 Oct 2018, at 14:20, [email protected] wrote: >>> >>> >>> >>> On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote: >>>> >>>> >>>> On 30 Sep 2018, at 16:30, Philip Thrift <[email protected]> wrote: >>>> >>>> >>>> >>>> On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote: >>>>> >>>>> [Re:] forcing theory in set theories with classes. >>>>> >>>>> >>>>> Bruno >>>>> >>>>> >>>>> >>>> Do you follow the work of Joel David Hamkins (forcing applied to >>>> set-theoretic "multiverse", etc.) >>>> >>>> (I have a basic idea of a type-theoretic parallel to this.) >>>> >>>> *The set-theoretic multiverse* >>>> https://arxiv.org/abs/1108.4223 >>>> >>>> Joel David Hamkins >>>> @JDHamkins >>>> Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow >>>> in Philosophy, University College Oxford. Formerly of New York. >>>> http://jdh.hamkins.org >>>> >>>> >>>> The math is interesting, and could be of some use, but it is a priori >>>> far too much Aristotelian to be coherent with the mechanist hypothesis. >>>> That should follow “easily” from the result described in most of my papers >>>> on this subject. The author does not seem aware of the mind-body problem, >>>> which put extreme constraints on what the physical reality can come from. >>>> Even Peano arithmetic, although integral part of the notion of observer, >>>> is >>>> too much rich for the ontology, where not only the axiom of infinity is >>>> too >>>> strong, >>>> >>> >>> *Since you want to banish the concept of infinity from mathematics, how >>> would you define, say, the limit of an "infinite" series? How would you >>> even discuss this series in the context of finite mathematics? AG* >>> >>> >>> >>> Good question. >>> >>> The answer is not simple technically. The point is that using only the >>> theory Q (Robinson Arithmetic) or SK (the combinators), I can define the >>> universal (Turing, Church) machine, and the concept of infinity will be a >>> tool used by them in their mathematics. >>> >>> I do not ban anything from mathematics, nor from physics. I ban only >>> infinity from the ontological terms. I ban only infinity in the >>> metaphysics/theology. (Even God is not ontological, like in Proclus or >>> Plotinus theology). >>> >>> Have you understand the post on Church’s thesis. You might tell me as >>> this will help me to see how to proceed to make you grasp all this. >>> >>> Bruno >>> >>> >>> >> >> What do you think of bounded arithmetic and other "finitist" approaches? >> >> https://en.wikipedia.org/wiki/Bounded_arithmetic >> see bibliography: >> http://jeanpaulvanbendegem.be/home/papers/strict-finitism/ >> >> >> I wrote a paper on this, in a book in honour to Jean-paul Vanbendegem. >> But its approach is more than finitist, and a bit less than ultra-finitism. >> It does not fit the study of the “theology” of the machine, and is thus >> useless for deriving physics. That does not mean it is not interesting >> pragmatically, on the contrary, it is well fitted with the goal to make >> usable programs. I do think that mathematically, it is also a restriction >> of Post creativity (Turing universality in set theoretical terms) to sub >> creativity. There is no possible universal machine there. >> >> >> >> >> >> Computable real analysis (one can teach computable calculus instead of >> "conventional" calculus) is essentially finitist: >> https://en.wikipedia.org/wiki/Computable_analysis >> >> One can formulate the *Axiom of Infinity* [ >> https://en.wikipedia.org/wiki/Axiom_of_infinity ] in a type of bounded >> set theory (Jan Mycielski [ https://en.wikipedia.org/wiki/Jan_Mycielski >> ], described in >> https://books.google.com/books/about/Understanding_the_Infinite.html?id=GvGqRYifGpMC >> >> ]. What results is an "ontology" of bigger and bigger finite sets of >> numbers with gaps in them. >> >> >> >> Yes, and that is interesting. But not so much for the mind-body problem, >> where we cannot bound anything, except by omega. >> >> The weaker theory known from which my approach can work, is the >> delta_0-induction based on Q + the axioms for the exponential, known as >> Delta_0Exp. That is Q: >> >> 1) 0 ≠ s(x) >> 2) x ≠ y -> s(x) ≠ s(y) >> 3) x ≠ 0 -> Ey(x = s(y)) >> 4) x+0 = x >> 5) x+s(y) = s(x+y) >> 6) x*0=0 >> 7) x*s(y)=(x*y)+x >> >> + >> >> 8) x^0 = 1 >> 9) x^s(y) = x * (x^y) >> >> + the scheme of induction axioms: >> >> P(0) & [For all n (P(n) -> P(s(n)))] ->. For all n P(n), >> >> with P restricted to the delta_0 (= sigma_0 = pi_0 = recursive, >> decidable, …) formula. >> >> >> >> That is the weaker Löbian machine known today. >> >> In between Q and Delta_0Exp, you have all the bounded arithmetics. >> >> An excellent book on this is (without the many accent for the names): >> >> Hajek, P. & Pudlak P., 1993, Metamathematics of First-Order Arithmetic, >> Springer-Verlag. >> >> But no need of this for the mind body problem, which needs at least >> Delta_0Exp (Löbianity), for the observer. Of course I use the fact that Q >> can mimic Delta_0Exp. But Q does not believe what Delta_0Exp is saying, and >> the theology is for Delta_0Exp and all its consistent extensions, like PA, >> ZF, and you, and me … >> >> I need the sigma_1 completeness. It is not for practical computational >> application, but only for guessing what is fundamental to assume, to >> understand where the appearances come from. It might have application in >> the foundations of physics, though, and is the best way to figure out the >> structure of the afterlife or parallel life, etc. >> >> Bruno >> >> >> >> > When if comes to just physics, what is there in the application of any > theory of physics (QM, GR, The Standard Model, ...) to experiments can't be > done in replacing the theory with a Python program, of a Go program or > whatever. > > > Reality, even just the arithmetical reality is beyond what can accomplish > a program. > > The partial computable is the tiny sigma_1 reality (the true proposition > having the shape ExP(x) with P decidable). The arithmetical reality is the > union of all sigma_i reality (i = 0, 1, 2, …). It contains the truth of > proposition like (x)(Ey)(z)(Eu)P(x,y,z,u), which might be decidable or not. > > To apply a theory for a prediction in the physical reality, you need also > an identity brain/mind, which cannot been afforded in the arithmetical > reality, a priori. > > > > > > Physicists take a theory T and replace it with a program P that then is > used to match with data D. > > > How? You first person state of mind is realised by an infinity of > computations in the arithmetical reality, so the identity used by the > physicalist does not work. A vague consciousness of this is reflected in > the Boltzman brain problem, which is a very particular case in the > universal dovetailing that is isomorphic (for computability) with the > sigma_1 arithmetical reality. > > > > *The theory T is completely dispensable. *Only P matters, because it is > only P that us used to say whether a theory T matches D *in the results > sections of papers*. > > > The theory will corresponds to the observer. To say that the theory is > dispensable, is like to say that both a brain and a telescope is > dispensable for the existence of the far away galaxy. But brain, telescope > are also natural process that we have to explain. Proving, knowing, > observing, … are different from computing, even if they are definable in > term of computations and their relation with truth. Eventually, the > physical reality is a non computable things emerging from all computation. > > I assume Digital Mechanism all along, to be sure. > > Bruno > > > Suppose one starts with the PLTOS template:
PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ that is transformed via a compiler/assembler τ into an output object ο that executes in a computing substrate Σ. Suppose Σ = *UniversalNumbers* That is, the computing substrate is the actual Universal Numbers (arithmetic reality). What would be the programs and languages (π,λ) that could be defined? - 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.
