> On Apr 20, 2016, at 9:17 AM, Jerry LR Chandler <[email protected]> > wrote: > > Of course, things are always more complex than they first appear. > I would argue for a completely connected world if my purpose were > metaphysical in nature. > But, language itself separates the world from its totality into manageable > parts. > And culture has found it convenient to separate academic disciplines. >
Not just language but the combination of signs and scholastic reals. That said if we go into more controversial territory and talk Peirce’s fundamental ontology then all there is at an ontological level is firstness, secondness and thirdness. Of course one can use most of Peirce’s thought without buying into his ontology. > I am simply saying that habits of PURE mathematicians do not allow > non-mathematical terms in mathematical reasoning, although they co-op many, > many terms from other disciplines and use them in a different sense. However while mathematical foundationalism is of less concern than it was in the early 20th century it does show that what counts as mathematical terms/operations are far from agreed upon. Which I think was part of Putnam’s point. > Applied mathematics, as a derogatory term to pure mathematicians, permits > sloppy usage. Perhaps, such is the case with Mochizuki case, which remains > open as to what it is. I think that ship has sailed. The issue in more Peircean terms are whether there is still inquiry into what pure mathematics is. > The issue of concern to me is the interpretation given to the meta-languages > that use mathematical symbols. > > Tarski’s insistence of the role of meta-languages in logical and mathematical > communication seems to be one of the roots of the “purification” of > mathematical proofs - and in logic itself. (See 13 Questions Universal Logic > paper) I think the more interesting question is whether there is a master meta-language or whether there’s a certain endless semiosis of translation (or dis-quotation). > The challenge such a question offers is that the difference that makes a > difference is the distinction between percept and precept. > From what perspective are you asking the question? Or, an other way of putting the interesting question is can one have a precept that is not perceptable. > BTW, you-all may interested in the paper by Carl Hempel, > > The theoretician's dilemma: A study in the logic of theory construction > > as a comparison to CSP’s perspectives. I’ll check it out. It’s been ages since I’ve read any Hempel.
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