Gary f, John, list: Gary, so I take by your post that you're the skeptic and John is the proposer?
Best, J On Thu, Nov 2, 2017 at 7:15 PM, <g...@gnusystems.ca> wrote: > John, Jon A, list, > > > > John, you wrote, “Peirce's motivation [for his dialogic approach to EGs] > was the similarity to his theory of inquiry: a dialog between two parties, > one who proposes a theory and one who is skeptical. The proposer is trying > to find evidence for it, and the skeptic is trying to find evidence against > it.” But this is *very* different from Peirce’s own account of the dialog > between graphist and interpreter in the Lowell lectures, in CP 4.431, in > the Lowell Lectures, in the Syllabus and in every later text on EGs that > I’ve seen. In CP 4.395, for instance, we find: “*Convention No. I*. These > Conventions are supposed to be mutual understandings between two persons: a > *Graphist*, who expresses propositions according to the system of > expression called that of *Existential Graphs*, and an *Interpreter*, who > interprets those propositions and accepts them without dispute.” > > > > If the player you designate as the “skeptic” is essential to game theory, > then I am skeptical of your claim that EGs can be understood in > game-theoretical terms, unless you can show some textual evidence. As with > the other discrepancies I’ve already pointed out between your account of > EGs and Peirce’s account in the Lowells, I think this can only sow > confusion for those of us trying to understand exactly what Peirce was > doing in the Lowell Lectures. I don’t think it’s helpful to gloss over the > differences by claiming that your version is “isomorphic” to Peirce’s 1903 > version, and then blame the resulting confusion on Peirce. > > > > Gary f. > > > > -----Original Message----- > From: John F Sowa [mailto:s...@bestweb.net] > Sent: 2-Nov-17 16:08 > To: peirce-l@list.iupui.edu > Cc: Dau, Frithjof <frithjof....@sap.com> > Subject: Re: Fw: [PEIRCE-L] Lowell Lecture 2.6 > > > > Gary F, Jeff BD, Kirsti, Jon A, > > > > I didn't respond to your previous notes because I was tied up with other > work. Among other things, I presented some slides for a telecon sponsored > by Ontolog Forum. Slide 23 (cspsci.gif attached) includes my diagram of > Peirce's classification of the sciences and discusses the implications. > (For all slides: http://jfsowa.com/talks/contexts.pdf ) > > > > Among the implications: The sharp distinction between "formal logic", > which is part of mathematics, from logic as a normative science and the > many studies of reasoning in linguistics, psychology, and education. > > > > Peirce was very clear about the infinity of mathematical theories. > > As pure mathematics, the only point to criticize would be the clarity and > precision of the definitions and reasoning. But applications may be > criticized as irrelevant, inadequate, or totally wrong. > > > > Gary > > > as late as 1909 Peirce was still trying (apparently without success) > > > to get Lady Welby to study Existential Graphs. And the graphs he sent > > > her to study look pretty much the same as the graphs he introduced in > > > the Lowell Lecture 2: nested cuts, areas defined by the cuts, and no > > > shading. > > > > That failure may have been one of the inspirations for the 1911 version, > which he addressed to one of her correspondents. > > > > >> [JFS] The rules are *notation independent*: with minor adaptations > > >> to the syntax, they can be used for reasoning in a very wide range of > > >> notations... > > > > > > [GF] This does not explain why Peirce was dissatisfied with algebraic > > > notations (including his own) and invented EGs for the sake of their > > > optimal iconicity > > > > On the contrary, simplicity and symmetry enhance iconicity and > generality. See the examples in http://jfsowa.com/talks/visual.pdf : > > > > 1. Shading of negative phrases in English (slides 28 to 30) and the > > application of Peirce's rules to the English sentences. > > > > 2. Embedded icons in EG areas (Euclid's diagrams, exactly as he drew > > them) and the option of inserting or erasing parts of the diagrams > > according to those rules (slides 33 to 42). > > > > 3. And the rules can be generalized to 3-D virtual reality. I couldn't > > draw the examples, but just imagine shaded and unshaded 3-D blobs > > that contain 3-D icons (shapes) with parts connected by lines. I'm > > sure that Peirce imagined such applications when he was writing > > about stereoscopic equipment (which he could not afford to buy). > > > > Gary > > > “Peirce said that a blank sheet of assertion is a graph. Since it's a > > > graph, you can draw a double negation around it.” — Eh? How can you > > > draw anything around the sheet of assertion, which (by Peirce’s > > > definition) is unbounded?? > > > > But note Jeff's comments about projective geometry and topology (which > Peirce knew very well): > > > > Jeff > > > My reason for picking this example of a topological surface is that it > > > provides us with an example of a 2 dimensional space in which a path > > > can be drawn all of the way "around" the surface... > > > > Yes. And that infinite space bounded by its infinite circle can be mapped > -- point by point -- to a finite replica on another sheet. > > In any case, the formal logic does not depend on the details of any > representation. We can just use the word 'blank' to name an empty sheet of > assertion or any finite replica of it. > > > > Gary > > > I’m reluctant to apply topological theories to EGs if they’re going to > > > complicate the issues instead of simplifying them. > > > > For a mathematician, Jeff's method is an enormous simplification. > > Finite boundaries in mathematics and computer science are always a > nuisance. But when you're teaching EGs to students, you can just use the > word 'blank' for an empty area. A pseudograph is just an enclosure that > contains a blank. > > > > Gary > > > John appears to regard all graphs, all partial graphs and all areas as > > > being on the sheet of assertion. But Peirce says explicitly that > > > neither the antecedent nor the consequent of a conditional can be > > > scribed on the sheet of assertion... > > > > My diagrams (with or without shading) are isomorphic to Peirce's. > > Talking about sheets doesn't generalize to other logics or to 3-D icons. > It makes the presentation more complex and confusing. > > > > Kirsti > > > I attended Hintikka's lectures on game theory in early 1970's. > > > No shade of Peirce. I found them boring. > > > > Game theoretical semantics (GTS) is just a mathematical theory. > > As pure mathematics, Peirce would not object to it. > > > > Kirsti > > > it hurts my heart and soul to read a suggestion that Peirce's > > > endoporeutic may have or could have been a version of Hintikka's game > > > theoretical semantics. > > > > Jon > > > Peirce's explanation of logical connectives and quantifiers in terms > > > of a game between two players attempting to support or defeat a > > > proposition, respectively, is a precursor of many later versions of > > > game-theoretic semantics. > > > > Risto Hilpinen (1982) showed that the formal theory of Peirce's > endoporeutic is equivalent to GTS. As a formal theory, Peirce would have > no objection to GTS or to any proof of formal equivalence. > > > > Peirce's motivation was the similarity to his theory of inquiry: > > a dialog between two parties, one who proposes a theory and one who is > skeptical. The proposer is trying to find evidence for it, and the skeptic > is trying to find evidence against it. > > > > Hintikka's applications had some similarities and some differences. > > But that's a topic that goes beyond the EG issues. > > > > 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 > peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L > but to l...@list.iupui.edu 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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