On Monday, August 19, 2019 at 9:43:38 AM UTC-5, Bruno Marchal wrote: > > > On 19 Aug 2019, at 11:50, Philip Thrift <[email protected] <javascript:>> > 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]> 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/ >> >> 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 > > > Given all the novel, unpredicted stuff one reads every day in the science news feeds about some new material (materials science), molecules, phases (of matter), why is it so hard to think that matter is not some naive ("numerical-Turing-emulable") stuff that most theoretical physicists think it is and that it has no protopsychical properties.
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