On Tuesday, October 2, 2018 at 2:20:10 AM UTC-5, Bruno Marchal wrote: > > > On 1 Oct 2018, at 14:20, agrays...@gmail.com <javascript:> wrote: > > > > On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote: >> >> >> On 30 Sep 2018, at 16:30, Philip Thrift <cloud...@gmail.com> 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/ 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. - 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. 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.
