On Tuesday, October 2, 2018 at 2:20:10 AM UTC-5, Bruno Marchal wrote: > > > On 1 Oct 2018, at 14:20, [email protected] <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 <[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/ 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 [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.
