List: In her book, Charles Peirces’s Pragmatic Pluralism, Rosenthal states: … the literature on Peirce contains “no fewer than thirteen distinct interpretations of Peirce’s views on the nature of truth”, attributing the account to Robert Almeder.
She apparently intends contrast CSP’s concept with the notions of correspondence and coherence. (My source of this information is Google Books.) Can anyone provide the putative listing of Almeter with the original text citations? Cheers Jerry > On Mar 9, 2017, at 8:09 AM, John F Sowa <[email protected]> wrote: > > Jerry, Clark, list, > > In my response to Jeff B.D., I was defending the claim that board > games are versions of mathematics. But I definitely do *not* restrict > math to board games or to set-theoretic models. > > Jerry >> Many mathematicians reject set theory as a foundation for mathematics > > Yes. Peirce did and so do I. The four board games I cited illustrate > diagrammatic reasoning. But those diagrams use only discrete set > theory. Peirce also considered continuous diagrams, and so do I. > I would also allow diagrams for any mathematical structures anyone > might propose or discover -- including quantum-mechanical diagrams. > >>>> JFS >>>> Thanks for the reference. On page 134, Béziau makes the >>>> following point, and Peirce would agree: >>> JYB >>> Universal logic is not a logic but a general theory of different >>> logics. >> Jerry >> Analyze this quote. Is [JYB] saying anything more beyond >> a contradiction of terms? > > Peirce's semiotic is a general theory of all kinds of sign systems. > Those systems include, as special cases, all natural languages and > all versions of formal logic. I agree with Montague that the > underlying semantics of NLs and formal logics are essentially the > same, but I would add that formal logics are weaker than NLs. > > I interpreted JYB as saying that universal logic is a theory about > logics in the same sense that CSP's semiotic is a theory about logics. > But JYB's notion of universal logic is weaker than CSP's semiotic. > >>> JYB >>> This general theory is no more a logic itself than is >>> meteorology a cloud. >> Jerry >> What the hell is this supposed to mean? Merely an ill-chosen metaphor? > > My interpretation of JYB: Universal logic is to any particular logic > as meteorology is to clouds. > > Jerry >> Chemical isomers are not mathematical homomorphisms because of the >> intrinsic nature of chemical identities. Thus, this reasoning is >> not relevant to the composition of Boscovichian points. > > I would not impose any restrictions on the kinds of diagrams or the > mappings that define similarity. If you can define a Boscovichian > diagram for chemistry, I believe that Peirce's notion of diagrammatic > reasoning could accommodate that diagram. > > Implication: Instead of defining a special kind of logic for every > kind of subject matter, I would just change the kinds of diagrams > -- quantum mechanical diagrams, Boscovichian diagrams, or whatever > mathematical structures anyone might discover or imagine. > > JLRC >> Semiotics is not, in my view, a foundation for logic which is >> grounded on antecedent and consequences. > > That is a Fregean view of logic, not a Peircean view. For his > Begriffsschrift, Frege chose implication, negation, and the > universal quantifier as his primitives. > > For his algebraic logic, Peirce started with Boolean algebra and > added quantifiers. But he later switched to existential graphs. > The early version distinguished Alpha (Boolean) from Beta (which > added the line of identity). But he later started with relational > graphs (existence and conjunction) and added ovals for negation. > > For beginning students, Boolean algebra is too abstract. It just > represents an NL sentence with a single letter like 'p'. Peirce's > relational graphs are a better starting point because they can be > translated to and from actual NL sentences. As a pedagogically > sounder approach, I follow Peirce's later tutorials (circa 1909). > See the first 25 slides of http://www.jfsowa.com/talks/egintro.pdf > > Note slides 3 and 4 which come from Peirce's own intro in MS 145. > In slide 8, I discuss one of CSP's examples that has a direct > mapping to and from RDF -- the basic notation for the Semantic Web. > > Many people believe RDF is a good starting point for logic. I hate > the RDF notation, but I use the comparison to show semantic webbers > how a real logic can be defined on top of something like RDF. > > Also note CSP's rules of inference (slide 25). They are grounded > in the need to preserve truth (as determined by endoporeutic). And > they apply equally well to Kamp's Discourse Representation Structures, > which Kamp designed for NL semantics. > > Note slide 31, which presents two *derived rules of inference* > that are implied by the rules in slide 25. These derived rules > emphasize generalization and specialization. I believe that it is > more appropriate to say that logic is a theory of generalization > and specialization. That includes implication as a special case > (p implies q iff p is more specialized than q). > > There is much more to say, some of which I say in the slides > http://www.jfsowa.com/talks/ppe.pdf . See slides 39 to 60. > In particular, note slide 59 about Turing oracles. > > Clark >> The problem with the game theoretical view of mathematics is >> the question of realism. > > I'm not sure what you mean by "game theoretical view". > There are three options, with some similarities among them: > > 1. The idea that games like chess are mathematical systems. > > 2. The point that Peirce's endoporeutic may be characterized > as an example of Hintikka's game theoretical semantics. > > 3. Wittgenstein's debate with Turing. (I prefer LW's side.) > > Clark >> there’s a difference between how we use the language of >> mathematics and what the objects of mathematics are. That >> is what are the relationship between the game and reality. > > The issues of nominalism vs. realism are orthogonal to all three > of these kinds of games. > > Clark >> I think we have to think through carefully what sort of game we >> are playing if we’re going to use that as our metaphor. > > Yes. But I believe that both nominalists and realists could adapt > any of the three "game theoretical views" to metaphors that are > compatible with their ways of thinking and talking. > > Summary: What I'm trying to emphasize is the fundamental > importance of diagrammatic reasoning for logic, mathematics, > language, science, and everyday life. The model-theoretic > semantics used to define truth in formal logics is a special > case of diagrammatic reasoning. > > John > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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