John, List: Curious response! We concur on the need to capture the essential meanings of linguistic sentences in set-theoretic representations of the sentence. Simply imposing formal rules on a sentence may not be sufficient to capture the intended meaning of the logic of the sentence. Despite this challenge, set theoretic expressions, within the context of its formal symbolic rules, can be extendable indefinitely and preserve valid conclusions - computer's work very well.
In the context of electronic computers, Hilbert's criteria for mathematics are satisfied: Consistency. Completeness. Decidability. Despite the flaw found by Godel for infinite numbers, Hilbert's criteria function very nicely for finite calculations. And, BTW, Hilbert's criteria work very nicely for chemistry, even though the symbolic logic for chemistry is very remote from the symbolic logic of set theory and Venn diagrams. Mathematics is something beyond set theory! What Ben's conclusions bring to fore, and of course, CSP's numerous logic texts, is deeper than mere "pragmatics" ( I think the use of the term of pragmatics in this context merely obscures the reality of the Trojan horse at the gate. A wooden horse outside the gate remains a wooden horse inside the gate.) Allow a simplistic example. We have formal symbolic logical systems for: set theory mathematics (at least finite arithmetic) music dance (yes! dance!) chemistry Can you suggest a philosophical and scientifically valid (validity here means empirically reproducible) approach (beyond the slightly flawed first pair - set theory and mathematics) to transliterate among these modes of representations of human perceptions? An overwhelming number of scientific and philosophical issues ride on finding a valid transliteration between these formal logics and related informal logics (such as the logic of inheritance.) Viewed from a different angle, the question can be simplified to the undergraduate level by asking: Is set theory extendable to the unity of the natural sciences? Cheers Jerry On Feb 28, 2015, at 5:04 AM, John Collier wrote: > Jerry, List, > > Just a brief point to clarify what I meant. I agree that informal rhetoric > requires interpretation, but I believe that to be true of formal language as > well. In fact I have argued in several places now, including my PhD thesis, > that interpretation always requires consideration of pragmatics first, and > semantics can only follow that. In what I said I had assumed that the first > part had been done. > > This has consequences for the issue at hand. If there are problems, then the > problems lie in pragmatics. I believe that in artificial examples it is quite > possible for the relevant pragmatics to be underdetermined, since the context > is (at least in part) missing. Some of the discussion has involved unusual > contexts to produce counterexamples, which I think supports my point. > > In any case, I don’t think we really disagree here. We were just working to > somewhat different ends (different pragmatics). > > Best, > John > > From: Jerry LR Chandler [mailto:jerry_lr_chand...@me.com] > Sent: February 28, 2015 12:49 AM > To: Peirce Discussion Forum (PEIRCE-L@list.iupui.edu) > Cc: Jon Awbrey; John Collier; Benjamin Udell > Subject: Re: [PEIRCE-L] Re: Contradictories, contraries, etc > > John, List: > > Thanks for your response. > > I phrased my concerns as questions in order to stimulate a through evaluation > of conclusions that Ben had drawn. > > Your response is at least partially true in that the interpretation of any > rhetoric statement as a set theoretic symbolization requires that at some > parts of the meaning of the rhetoric statement ought to represented in the > symbolizations of the translations from one form to another form. > > However, the simple fact of the matter is that most rhetorical statements do > not translate well from the rhetorical form to the strict formal logical form > of set theory. The reason for this broad assertion is simple. Most human > rhetoric is informal and is not intended, expected nor interpreted as formal > statements. Judgments are necessary.
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