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> 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> 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
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