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 ] >>>>> >>>> >>>> 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 ] >>>>> >>>>> >>>> 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/ ] >>> >>> 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 ]). >>> >>> >> 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 ] > > > *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". two axiom sets = two programming languages (like Python versions 1,0 and 2.0) - 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.
