> On 17 Dec 2018, at 01:02, Brent Meeker <meeke...@verizon.net> wrote: > > > > On 12/16/2018 2:04 PM, Jason Resch wrote: >> >> >> On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett <bhkellet...@gmail.com >> <mailto:bhkellet...@gmail.com>> wrote: >> On Mon, Dec 17, 2018 at 8:56 AM Jason Resch <jasonre...@gmail.com >> <mailto:jasonre...@gmail.com>> wrote: >> On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker <meeke...@verizon.net >> <mailto:meeke...@verizon.net>> wrote: >> >> But a system that is consistent can also prove a statement that is false: >> >> axiom 1: Trump is a genius. >> axiom 2: Trump is stable. >> >> theorem: Trump is a stable genius. >> >> So how is this different from flawed physical theories? >> >> Physical theories do not claim to prove theorems - they are not systems of >> axioms and theorems. Attempts to recast physics in this form have always >> failed. >> >> >> Physical theories claim to describe models of reality. You can have a fully >> consistent physical theory that nevertheless fails to accurately >> describe the physical world, or is an incomplete description of the physical >> world. Likewise, you can have an axiomatic system that is consistent, but >> fails to accurately describe the integers, or is less complete than we would >> like. > > But it still has theorems. And no matter what the theory is, even if it > describes the integers (another mathematical abstraction), it will fail to > describe other things. > > ISTM that the usefulness of mathematics is that it's identical with its > theories...it's not intended to describe something else.
You confuse mathematics and metamathematics (classical logic). You confuse truth and theorem. Before Gödel the mathematicians thought they could secure the use of the infinities through the finite manipulation of their names. After Gödel there is a complete reversal of the situation. We just cannot secure the finite realm itself, except to reassure us in invoking the infinite. The number theorist love that surprising aspect of number theory, but it is come from very tiny fragment of it being essentially undecidable, and that is when it is rich enough to prove the existence of the universal number. Above our substitution level we are confronted with a finite number of universal number. Below our substitution level we are confronted with an infinity of universal number, actually a continuum (of some sort). It is not a matter of choice: invoking some ontological engagement does not solve the problem, and with mechanism, it makes it worst. There is nothing wrong in physics. What is wrong, with mechanism, is the metaphysical decision to not pursue the research of the origin of the physical laws in arithmetic, or any sigma_1 complete set for reference. The ontology needs only one sigma_1 complete set. The phenomenology is unbounded in mathematical complexity. Bruno > > Brentent > > -- > 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.
