> On 19 Aug 2019, at 11:50, Philip Thrift <[email protected]> wrote: > > > > On Monday, August 19, 2019 at 4:08:58 AM UTC-5, Bruno Marchal wrote: > >> On 18 Aug 2019, at 13:57, Philip Thrift <[email protected] <javascript:>> >> wrote: >> >> >> >> On Sunday, August 18, 2019 at 4:53:28 AM UTC-5, Bruno Marchal wrote: >> >> Model theory illustrate that pure mathematics has meaning. >> >> >> A model is a so-called 'structure': >> https://plato.stanford.edu/entries/model-theory/ >> <https://plato.stanford.edu/entries/model-theory/> >> >> But allowable structures, typically mathematical entities in the model >> theories of many, are only material (physical) entities in the model theory >> of Hartry Field. > > That is a bit of nonsense. Or Hartree Field notion of model has nothing to do > with what logicians called a model (a mathematical structure with a notion of > satisfaction). > > >> >> For example, a model of arithmetic could be an actual semiconductor logic >> gate chip with RAM. > > > I don’t understand this. A model of arithmetic is a set of object which > provides an interpretation of the terms (0, S(0), …), and an interpretation > of + and * (in terms of infinite set of couples). > > Bruno > > > > > > Conventional mathematical logicians only speak, write, and think in terms of > a fictional world.
With mechanism, all worlds are fictional. The only real things are 0, 1, 2, …, or K, S, KK, … Intuitively I doubt less that 4*n is even for all n, or that K is an eliminator, than F = GmM/r^2, which is an infinite extrapolation made from a finite number of fact. Also, when doing metaphysics, it is better to not decide in advance what is real and what is fiction. Now, if you have a doubt that a number, when multiplied by 4, gives an even number, I am not sure I can help. > > And that includes their models/structures/interpretations. Mechanism is OK with this. It simplifies the life to admit, even if temporarily, that a bit more exist, but at some point, that existence can be put in the phenomenology. > > The Field type of semantics of logic and mathematics only has actual material > entities (like computers at Best Buy, supercomputers at Los Alamos National > Lab, natural objects found in nature) in its domains. That is the Aristotelian axiom where “real” is defined by “physically real”, or “observable”, but the dream argument rise a doubt on this, especially when we understand that all computations can be proved to exist in arithmetic (even before translating this by “all models. > > Conventional mathematical logicians may not like it, but that is their own > psychological problem. If they believe in Digital Mechanism. they become inconsistent. That’s the whole point of the Universal Dovetailer argument. Unless your “matter” has a role for consciousness which is not Turing emulable, it will be realised arithmetically. Bruno > > @philipthrift > > -- > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/caff8b79-62e7-4ba5-b875-9114bc9605ae%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/caff8b79-62e7-4ba5-b875-9114bc9605ae%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/7E082BC4-081E-49D8-9420-598C444EF2CB%40ulb.ac.be.
