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 - 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/ ] *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). - 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.
