> On 11 Dec 2018, at 20:09, Brent Meeker <[email protected]> wrote: > > > > On 12/11/2018 10:34 AM, Philip Thrift 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". > > That's Bruno's idea.
Actually not really. I would have liked to be able to exploit the CurrHoward correspondence, but for technical reason, this can only work for the “[]p & p” modes. > Arithmetic believes what is provable in arithmetic. Precisely: the machine believes A = the machine asserts/proves A. I limit myself to correct machine, as the goal is not applied human real life psychology, but the derivation of physics and theology. > But what is provable is only true conditional on the axioms and the rules of > inference. No. What is provable is only provable conditional on the axioms and rules of inference. Like what is believable is only believable conditional to a brain structure and the physical laws. Bruno > > Brent > >> >> 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] >> <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] > <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.
