> On 13 Dec 2018, at 00:57, Brent Meeker <meeke...@verizon.net> wrote: > > > > On 12/12/2018 3:19 AM, Bruno Marchal wrote: >> >>> On 10 Dec 2018, at 20:26, Brent Meeker <meeke...@verizon.net >>> <mailto:meeke...@verizon.net>> wrote: >>> >>> >>> >>> On 12/9/2018 11:38 PM, Philip Thrift wrote: >>>> >>>> >>>> On Sunday, December 9, 2018 at 8:43:59 PM UTC-6, Jason wrote: >>>> >>>> >>>> On Sun, Dec 9, 2018 at 2:02 PM Philip Thrift <cloud...@gmail.com >>>> <javascript:>> wrote: >>>> >>>> >>>> On Sunday, December 9, 2018 at 9:36:39 AM UTC-6, Jason wrote: >>>> >>>> >>>> On Sun, Dec 9, 2018 at 2:53 AM Philip Thrift <cloud...@gmail.com <>> wrote: >>>> >>>> >>>> On Saturday, December 8, 2018 at 2:27:45 PM UTC-6, Jason wrote: >>>> >>>> I think truth is primitive. >>>> >>>> Jason >>>> >>>> >>>> As a matter of linguistics (and philosophy), truth and matter are linked: >>>> >>>> "As a matter of fact, ..." >>>> "The truth of the matter is ..." >>>> "It matters that ..." >>>> ... >>>> [ https://www.etymonline.com/word/matter >>>> <https://www.etymonline.com/word/matter> ] >>>> >>>> I agree they are linked. Though matter may be a few steps removed from >>>> truth. Perhaps one way to interpret the link more directly is thusly: >>>> >>>> There is an equation whose every solution (where the equation happens to >>>> be true, e.g. is satisfied when it has certain values assigned to its >>>> variables) maps its variables to states of the time evolution of the wave >>>> function of our universe. You might say that we (literally not >>>> figuratively) live within such an equation. That its truth reifies what >>>> we call matter. >>>> >>>> But I think truth plays an even more fundamental roll than this. e.g. >>>> because the following statement is true "two has a successor" then there >>>> exists a successor to 2 distinct from any previous number. Similarly, the >>>> truth of "9 is not prime" implies the existence of a factor of 9 besides 1 >>>> and 9. >>>> >>>> Jason >>>> >>>> >>>> >>>> >>>> Schopenhauer 's view: "A judgment has material truth if its concepts are >>>> based on intuitive perceptions that are generated from sensations. If a >>>> judgment has its reason (ground) in another judgment, its truth is called >>>> logical or formal. If a judgment, of, for example, pure mathematics or >>>> pure science, is based on the forms (space, time, causality) of intuitive, >>>> empirical knowledge, then the judgment has transcendental truth." >>>> [ https://en.wikipedia.org/wiki/Truth >>>> <https://en.wikipedia.org/wiki/Truth> ] >>>> >>>> >>>> I guess I am referring to transcend truth here. Truth concerning the >>>> integers is sufficient to yield the universe, matter, and all that we see >>>> around us. >>>> >>>> Jason >>>> >>>> >>>> >>>> In my view there is basically just material (from matter) truth and >>>> linguistic (from language) truth. >>>> >>>> [ https://codicalist.wordpress.com/2018/06/18/to-tell-the-truth/ >>>> <https://codicalist.wordpress.com/2018/06/18/to-tell-the-truth/> ] >>>> >>>> Relations and functions are linguistic: relational type theory (RTT) , >>>> functional type theory (FTT) languages. >>>> >>>> Numbers are also linguistic beings, the (fictional) semantic objects of >>>> Peano arithmetic (PA). >>>> >>>> Numbers can be "materialized" via nominalization (cf. Hartry Field, refs. >>>> in [ https://en.wikipedia.org/wiki/Hartry_Field >>>> <https://en.wikipedia.org/wiki/Hartry_Field> ]). >>>> >>>> >>>> Assuming the primacy of matter assumes more and explains less, than >>>> assuming the primacy of arithmetical truth. >>>> >>>> Jason >>>> >>>> >>>> >>>> In today's era of mathematics, Joel David Hamkins (@JDHamkins >>>> <https://twitter.com/JDHamkins>) has shown there is a "multiverse" of >>>> truths: >>>> >>>> The set-theoretic multiverse >>>> [ https://arxiv.org/abs/1108.4223 <https://arxiv.org/abs/1108.4223> ] >>>> >>>> The multiverse view in set theory, introduced and argued for in this >>>> article, is the view that there are many distinct concepts of set, each >>>> instantiated in a corresponding set-theoretic universe. The universe view, >>>> in contrast, asserts that there is an absolute background set concept, >>>> with a corresponding absolute set-theoretic universe in which every >>>> set-theoretic question has a definite answer. The multiverse position, I >>>> argue, explains our experience with the enormous diversity of >>>> set-theoretic possibilities, a phenomenon that challenges the universe >>>> view. In particular, I argue that the continuum hypothesis is settled on >>>> the multiverse view by our extensive knowledge about how it behaves in the >>>> multiverse, and as a result it can no longer be settled in the manner >>>> formerly hoped for. >>>> >>>> >>>> What this means is that for mathematics (a language category), truth >>>> depends on the language. >>> >>> I think Hamkins could say the same thing in French. His example of the >>> continuum hypothesis just says that by adding as axioms different >>> undecidable propositions we get different sets of theorems. He doesn't use >>> the word "truth" and I think with good reason. Theorems in mathematics >>> aren't "true" in any normal sense of the word. What is true is that the >>> axioms imply the theorem...given the rules of inference. >> >> By incompleteness truth is bigger than what *any* consistent can prove. Of >> course you can say that the meaning of >> >> [Exyz(x^3 + y^3 + z^3 = 33) v ~ (Exyz(x^3 + y^3 + z^3 = 33)) >> >> Is true because it is an substitution instance of the tautology A v ~A. > > Which is exactly what I'd say; and is the only way that you can know it is > true.
Believe. Not true. But with the numbers, unlike with sets, most people believe this. > >> But you can also reflect on this, and believe it is true, because either >> such numbers do exist, or they don’t. > > The phrase following "because" is just rephrasing A v ~A. In the frame of the numbers. We do intuit well the notion of standard natural numbers. There is no equivalent notion for sets, real numbers, etc. The intuition is equivalent with the idea that a machine stop or does not stop. > >> But "Exyz(x^3 + y^3 + z^3 = 33) “ is an open problem. Such open problem >> would not make sense if you define truth by proof. > > Many mathematicians would say you have discovered it. The problem or the numbers? We do discover problem, indeed. That is why it cannot be fictionalism. > But you could only discover it by finding a proof I don't define truth by > proof. You can prove what is false just by choice of axioms. So having a > proof doesn't prove the conclusion is true; OK. > it only shows that it is true that the conclusion follows from the premises. But that is not truth, that is belief. True is when the belief fits with (some intended) reality. > >> >> Recently I have proven that TOT (the set of Gödel numbers of the codes of >> the total computable function is not recursively enumerable. That proofs >> would have no meaning if truth = proof. Intuitionism is recovered in >> Mechanism as the particular first person solipsistic view ([]p & p, S4Grz1). > > Many mathematicians would say you have discovered it. But you could only > discover it by finding a proof. Not at all. Mathematicians “knows” (believes) in conjecture well before they find proof. Intuition always precedes the finding of the proofs. Mathematicians reason semantically. Proofs are a mean of sharing intuition, but the intuition comes from experience and life. Like reality precedes brain. > >> >> In mathematical logic, we study since long the difference between proof and >> truth (satisfied by a reality). > > Yes, you create a whole theology around not all truths are provable. But you > ignore that what is false is also provable. Provable is only relative to > axioms. I make my theory clear. (Kxy = x; Sxyz = xz(yz), elementary arithmetic). False is not provable in that theory. Of course, I can only hope that you believe that elementary arithmetic is consistent, and true with respect to the standard model. But that is always the case when we discuss with other people. We hope they don’t believe in 2+2=5. Bruno > > Brent > >> >> Bruno >> >> PS I will use the word “reality" instead of “model", as most physicisst >> continue to use “model” for theories. >> >> >> >> >>> >>> Brent > > > -- > 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 > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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.
