> On 11 Dec 2018, at 19:34, Philip Thrift <[email protected]> wrote: > > > > On Tuesday, December 11, 2018 at 12:13:14 PM UTC-6, Brent 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 <[email protected] <>> 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 <[email protected] <>> 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. > > Brent > > > > "truth=proof" is what (intuitionistic) type theory is about. Curry-Howard > correspondence makes "proof=program”.
OK. It is important, but it corresponds to the inner god ([]p & p), and of course, with Mechanism, we need some Outer-god too (p), or we become solipsistic. > > two axiom sets = two programming languages (like Python versions 1,0 and 2.0) Yes, but only when interpreting the axioms in that way. To be sure some people like Krivine have extend the curry Howard iso to classical logic, but that is not relevant here. Bruno > > - 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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > 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 [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.
