[FRIAM] Truth: “Hunh! What is it good for? Absolutely Nothing!”

[gⅼеɳ ☣]

Whew!  Fantastic thread!  I'm grateful to be able to witness it.

I'd like to point out that Peirce (and as Dave points out, many of us) are what I'd call "Grand Unified Modelers" (GUMmers): those who think there is, in R. Rosen's terms a "largest model" ... a penultimate language that if we could only learn and speak *that* language, what Nick's describing as Peirce's defn of "truth" would be accurate.

Solomon Feferman has worked on this problem and his (now old) initial submission is described here:

  Gödel, Nagel, minds and machines
  https://math.stanford.edu/~feferman/papers/godelnagel.pdf

It's probably important to read the whole thing.  But you could just jump to section "5. One way to straddle the mechanist and anti-mechanist positions."

It's also useful to note that Lee Rudolph submitted a relevant piece awhile back: "Logic in Modeling", wherein he cites Soare's definition of a "computation", which requires it be *definite* ... i.e. that all variables be bound, which would outlaw Feferman's "schematic axioms".  (... if I understand correctly ... I am not a logician, mathematician, or meta-mathematician... so your results may vary.)

Peirce's (and Nick's) insistence on the definiteness/fixedness of the universe's "formal system S", is what lies at the heart of the disagreement between Nick and Dave.  I think it's also important to point out that BOTH Nick and Dave COULD BE wrong.  Dave's idea that "mathematical logic" is impoverished may not be right if something like Feferman's solution could work.  And Nick's idea that convergence within the universe's formal system, S, implies truth may be wrong if something like the problem Feferman (and Dave) are trying to solve actually is the case.

-- 
☣ gⅼеɳ