On Monday, November 19, 2018 at 5:24:48 AM UTC-6, Bruno Marchal wrote: > > > On 17 Nov 2018, at 03:58, John Clark <johnk...@gmail.com <javascript:>> > wrote: > > On Fri, Nov 16, 2018 at 12:42 PM Bruno Marchal <mar...@ulb.ac.be > <javascript:>> wrote: > > >> *> A practical difficulty here is that logicians used the term model like >> painters: the model is the reality* >> > > Mathematician can use one part of mathematics to model another part, for > example Descartes found a way for geometry to model algebra, and those 2 > things can have equal complexity; > > > > Those are representations, which is related notion, but it is different > from the notion of model in logic. The notion of model “modelises” the > notion of reality. A “concrete group” is a model of the finite syntactical > theory of group. The structure (N, 0, +, *) is a model, among infinitely > many others or the Peano Syntactical theory of numbers. > > > > > > but that like using English to talk about the English word "cat". Whenever > mathematics tries to model something that is not itself, like something > physical, > > > Which might be part of mathematics. Unless you assume a physical reality > out of mathematics, or out of the mind of the Turing machine, which “live” > in the standard model of arithmetic, in fact in all models of arithmetic. > > > > > it always comes off looking second best because mathematics is just a > language, a very very good language for describing physical law but a > language nevertheless. > > > That is not correct. We do use a language, but the reality (model(s)) are > not a language. In logic, we have to distinguish the language (which decide > which sentences are grammatically correct formula) from a theory, which is > a finite (or recursively enumerable) set of formula (called axioms), and a > model, or reality, which is a mathematical structure, or something else, > which satisfies the axioms, and such that the inference rule preserves that > satisfaction relation. > > > > > > But, I hear you say, the numbers 11 and 13 are prime and that fact is > unchanging and eternal! Well yes, but the English words "cat" and "bat" > rhyme and that fact is also unchanging and eternal. > > > Not in the same sense, and if you make things precise, for mechanism, a > theory with bat and cat rhyming can be Turing universal, and then it is > just a change of basic ontology. The idea here is to use a theory where > everyone agree on the simple operational meaning. See the combinator theory > thread for a different example than arithmetic. > > > > > >> > *I alluded to the fact that you can identify (by clear definable >> bijection) a model with the set of (Gödel number) of all true sentences in >> (the standard model of) arithmetic.* >> > > Mathematics can't even identify all true sentences about arithmetic much > less become the master of physical reality. We know the sentence "the 4th > Busy Beaver number is 107" belongs in the set of true sentences, but what > about "the 5th Busy Beaver number is 47,176,870"? It's either true or its > not but will you or I anybody or anything ever know which one? Nobody > knows and nobody knows if we'll ever know, but we do know that nothing will > ever know what the 8000th Busy Beaver number is even though its well > defined and finite. > > > > You make my point. The value of the busy beaver function is arithmetical > well defined, but not computable, which illustrates that the arithmetical > reality kicks back, and is indeed very huge. After Gödel we know that we > can only scratch that kind of reality. Yet, its conceptually clarity make > us accepting realism, which is basically the idea that the excluded > principle is valid there. > > > > > *>You already need 2+2=4 to make sense of matter,* >> > > Recent studies see to indicate that without a working brain a person's IQ > tends to drop rather dramatically, so you've got it precisely backwards yet > again, you need matter to make sense of 2+2=4 or to male sense of anything > at all. > > > > Assuming Aristotle theology (materialism), but there is no evidence, and > it is refuted by Mechanism. > > The IQ test can only observe the 3-1 person, not the 1-1 person. The 1p > can only associate its own consciousness to an infinity of representation > of its body in arithmetic, and the notion of “having no brain” is relative > to the computations, so your argument needs your ontological commitment in > some primary matter, for which there is no evidence found yet. > > > > > > > *But you don’t need silicon,* >> > > True, carbon and carbon compounds will also work. > > >> > or “being made-of” to define the numbers. >> > > You need a brain made of some sort of matter to define numbers > > > > Sure. But the numbers does not need me to exist. 2+2=4 even if I was not > born. > > You seem to confuse “I can define number” and “the number itself”. Indeed > a brain to grasp 2+2=4, but I need a brain to observe a far away galaxy. > Yet we agree that the galaxies do not need Hubble to exist, and it is the > same with the numbers, given that we will explain the brain by the notion > of digital machine, and I have to assume the numbers at the start to make > sense of the terms like machine, brain, etc. > > You are only keeping Mouloud your personal materialist credo, but that is > not how to proceed when doing science. > > > > or to define anything at all, not that there is anything special or even > very interesting in the act of definition, you need a brain made of matter > to do anything. > > >> *> If 2+2=4 depends on matter, tell me how a magnetic field, or a >> electromagnetic field, or a gravitational field, or any physical field >> could pertubate 2+2=4.* >> > > 2+2=4 is a description in the language of mathematics about how some > physical properties behave. For example, the mass of 2 protons and the mass > 2 more protons equals the mass of 4 protons. But 2+2=4 doesn't work for > everything, the temperature of 2 hot water bottles and 2 hot water bottles > does not equal the temperature of 4 hot water bottles. Temperature doesn't > add up in the same way that mass does, a different description is needed to > describe what's going on. > > > > No problem. 2+2=4 should not be applied in all context, of course. > > > > > >> *>computations, can be defined in* [blah blah] >> > > Who cares?? Definitions are just a human convention, a definition of a > computation can't compute and a definition of a airliner can fly you to > London. > > > A definition of a computation is not a computation. But can be used to > show that all computation are done in the models of arithmetic. > > > > > > > You confuse the [blah blah] >> > > No, you confuse the difference between a cat and the word "cat" . The > difference is one can have kittens but a word can’t. > > > Yes, that is what I insist. So please stop confusing the language “2+2=4” > with the fact that 2+2=4. Same for the computations. Arithmetic contains > all description of computations should not be confused with the fact that > all computations are also realised, done, executed, through the truth of > the number relations. “Cat” is not a cat, “one” is not the number 1 either. > > > > > > >> > the models/realities intended will be usually much more complex, as >> you said above. >> > > Mathematical models are ALWAYS simpler and less rich than the physical > reality they try to represent. > > > > With “model” used in the sense of the physicist. That is true for > arithmetic too, as you allude above. The arithmetical reality (model) is > far more complex than any theories of arithmetic. > > > > So why in the world would you say the physics is modeling the mathematics > when its obvious that the mathematics is trying, with limited success, to > model the physics? > > > > No one says that physics model mathematics. With mechanism, physics is > reducible to the theology of numbers, which is not reducible to any other > theory, and is of course not an axiomatisable theory, except, miraculously > for its propositional parts, as we know since Solovay 1976. > > Bruno > > John K Clark > >

There are two types of people: Those who say "There are mathematical objects." Those who say "There are no mathematical objects." I was just thinking about a certain irony about Hartry Field*: His last name has meanings in both physics and mathematics, and he is the founder o*f nominalized semantics* for theories of physics — where a 'field' may be nominalized away! * https://en.wikipedia.org/wiki/Hartry_Field https://books.google.com/books/about/Science_Without_Numbers.html?id=Exc1DQAAQBAJ - 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.