> On 4 Dec 2018, at 09:06, Philip Thrift <[email protected]> wrote: > > > > On Monday, December 3, 2018 at 7:46:22 PM UTC-6, Brent wrote: > > > On 12/3/2018 9:59 AM, Philip Thrift wrote: >> But that is close to the solipsist move. The fact that we cannot define >> truth does not entail that some notion of truth does not make sense. In >> particular, Peano arithmetic can already define an infinity of approximation >> of truth, namely sigma_i and pi_i truth (the truth of the sentences will a >> finite and fixed number of quantifier, as opposed to finite sentences with >> an arbitrary finite number of quantifier). >> >> We can invoke truth, but we can develop meta-discourse relating truth to >> theories, like we cannot invoke our own consciousness does not prevent us to >> try theories about it. >> It is a bit like “I cannot study my own brain”, but I can still infer some >> theories of my brain by looking at the brain of others and then assuming >> that I am not different. > > So are do these theories produce true or false propositions? > >> >> Bruno >> >> >> >> >> A different perspective (!) of "truth" comes from - vs. PA (Peano >> arithmetic) - PLT (programming language theory - the legacy to a large >> extent of John C. Reynolds [ https://en.wikipedia.org/wiki/John_C._Reynolds >> <https://en.wikipedia.org/wiki/John_C._Reynolds> - who was originally a >> theoretical physicist ], and sort of in parallel the whole type-theory >> gang). Rather than an external "god-like" notion of truth, truth is in the >> programming. >> >> - pt >> >> > Can you give an example of "truth in the programming" and how it differs from > the mathematical idea of true and the correspondence theory of truth? > > Brent > > > > Truth in programming follows the Brouwerian concept of truth: > [ https://plato.stanford.edu/entries/brouwer/ ]
OK, that is the first person truth, captured by the []p & p variant of []p, allowed and imposed by incompleteness (we don’t have the provability of []p -> p, but of course (([]p & p) -> p). > > > > There is no determinant of mathematical truth outside the activity of > thinking; a proposition only becomes true when the subject has experienced > its truth (by having carried out an appropriate mental construction); > similarly, a proposition only becomes false when the subject has experienced > its falsehood (by realizing that an appropriate mental construction is not > possible). > > There is no determinant of mathematical truth outside the activity of > computing; a proposition only becomes true when the program has produced its > truth (by having carried out an appropriate computational construction); > similarly, a proposition only becomes false when the program has produced its > falsehood (by computing that an appropriate computational construction is not > possible). Yes, []p & p is a bit solipsistic, like we all are from the exclusive first person point of view. That is good psychology, but bad metaphysics. Brouwer said once to his enthusiastic students “how can you appreciate a course given by someone who does not believe in your existence?”. Good question! 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.
