On Monday, November 19, 2018 at 5:24:48 AM UTC-6, Bruno Marchal wrote: > > > On 17 Nov 2018, at 03:58, John Clark <[email protected] <javascript:>> > wrote: > > On Fri, Nov 16, 2018 at 12:42 PM Bruno Marchal <[email protected] > <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 [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.
