John,
Many thanks for those links to the Pietarinen pieces, which I hadn't seen before. The one at http://www.digitalpeirce.fee.unicamp.br/endo.htm, or at least the first section of it (headed "Preliminaries") is a very helpful summary of the basics of EGs as they are presented in the Lowell lectures. The rest of that article, and the whole of the other one, seems concerned mainly with claiming Peirce's work as a precursor of more recent developments in mathematics, mainly model and game theories. I'm sure that these pieces, like your own presentations of EGs, are of great value to people who are more or less well versed in formal logic but know little or nothing about Peirce or about the history of logic. Some of us who are now studying EGs as a component of the Lowell lectures, though, are a very different audience: we are more or less well versed in Peircean philosophy but know little or nothing about current trends in formal logic. For you, formal logic is a branch of mathematics; for us, though, mathematics is not what Peirce called a "positive science" - and therefore not a branch of philosophy, as logic is: "Logic is a branch of philosophy. That is to say it is an experiential, or positive science, but a science which rests on no special observations, made by special observational means, but on phenomena which lie open to the observation of every man, every day and hour" (CP 7.526). >From the perspective that I'm taking in this study of the Lowells, Peirce is very clear that EGs are a tool for studying deductive reasoning, which is itself a phenomenon familiar to everybody, although a given person may not practice it every day and hour, or even be aware that he practices it at all. This part of the study does draw mainly on mathematics, because the objects of attention in pure mathematics are wholly imaginary (see Lowell 2.8!) and deduction - unlike other parts of the inquiry cycle - works exactly the same with imaginary objects as it does with real, observable, measureable objects. Logic as a whole, like other positive sciences such as physics (and phenomenology!), makes use of mathematical reasoning, but if EGs are relegated entirely to the realm of pure mathematics, we lose the experiential element of their meaning. This is why I don't find it helpful to consider the Lowell presentation of EGs as merely a crude and confused form of more recent developments in mathematics. By the way, in the part of MS 455 which I've omitted from my online publication of Lowell 2 (as explained yesterday), there is this interesting 'aside' by Peirce: "Here we have the three signs [of the alpha part] defined purely in terms of logical transformations from them and to them without one word being said about what the signs really mean. They are left to be applied to whatever there may be that corresponds to them. This is the Pure Mathematical point of view, a point of view far from easy to a person as imbued with logical notions as I am." Gary f. -----Original Message----- From: John F Sowa [mailto:s...@bestweb.net] Sent: 3-Nov-17 00:21 To: peirce-l@list.iupui.edu Subject: Re: Fw: [PEIRCE-L] Lowell Lecture 2.6 Gary F, There are two separate issues here: (1) the isomorphism between Peirce's 1911 system and his earlier presentations; and (2) the relationship between Peirce's endoporeutic and GTS. About #1, the issues are clear for first-order logic (Alpha + Beta): every graph drawn according to the 1903 or 1906 rules can be converted to one according to the 1911 rules by shading the negative areas. The rules of inference are also equivalent: a proof by one set of rules is also a valid proof by the other rules. There is one point about the scroll, which Peirce does not mention in 1911 as distinct from a nest of two ovals. But that point has no effect on any of the graphs or any proof. Therefore, I regard the 1911 rules as a cleaner, simpler, and more elegant version of his earlier treatment. But I believe that this simplicity is a major *improvement* because it makes the rules more general and more flexible. (As I summarized in my previous note.) Re graphist and interpreter: Peirce wrote many versions over the years, in some of them the two parties cooperated and in others they were more competitive. See the comment by Pietarinen below: > 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 Peirce wrote many fragmentary remarks about the dialog, most of which were unpublished. Pietarinen has a summary of the various passages: <http://www.digitalpeirce.fee.unicamp.br/endo.htm> http://www.digitalpeirce.fee.unicamp.br/endo.htm For a more systematic treatment, see the following by Pietarinen: <https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=16&cad=rja&ua ct=8&ved=0ahUKEwjH9b2dqKHXAhUp8IMKHfP-Bo44ChAWCDQwBQ&url=https%3A%2F%2Fdialn et.unirioja.es%2Fdescarga%2Farticulo%2F4729798.pdf&usg=AOvVaw1DgzAp3gS_pYb_5 wiN9gu5> https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=16&cad=rja&uac t=8&ved=0ahUKEwjH9b2dqKHXAhUp8IMKHfP-Bo44ChAWCDQwBQ&url=https%3A%2F%2Fdialne t.unirioja.es%2Fdescarga%2Farticulo%2F4729798.pdf&usg=AOvVaw1DgzAp3gS_pYb_5w iN9gu5 >From page 2: > Peirce coined a plethora of names... assertor and critic, concurrent > and antagonist, speaker and hearer, addressor and addressee, scribe > and user, affirmer and denier, compeller and resister, Me and Against-Me... Pietarinen also said "these names can easily be confused with one another." That's why I chose the terms proposer and skeptic, which seem to be clearer and more memorable. The skeptic is willing to be persuaded, but only after checking all the details. Summary: Peirce's ideas and terminology were in flux. He didn't have the advantage of modern computers and the 20th c. techniques of recursive functions and game-playing programs. But his notion of a dialog with two parties collaborating and/or competing keeps recurring in all those discussions. My specification of the game (URL below) is based on familiarity with software for playing games like chess. Peirce did not have that experience, but I believe that he would agree with the method. John __________________________________________________________________ >From page 18 of <http://jfsowa.com/pubs/egtut.pdf> http://jfsowa.com/pubs/egtut.pdf In modern terminology, endoporeutic can be defined as a two-person zero-sum perfect-information game, of the same genre as board games like chess, checkers, and tic-tac-toe. Unlike those games, which frequently end in a draw, every finite EG determines a game that must end in a win for one of the players in a finite number of moves. In fact, Henkin (1961), the first modern logician to rediscover the game-theoretical method, showed that it could evaluate the denotation of some infinitely long formulas in a finite number of steps. Peirce also considered the possibility of infinite EGs: "A graph with an endless nest of seps [ovals] is essentially of doubtful meaning, except in special cases" (CP 4.494). Although Peirce left no record of those special cases, they are undoubtedly the ones for which endoporeutic terminates in a finite number of steps. The version of endoporeutic presented here is based on Peirce's writings, supplemented with ideas adapted from Hintikka (1973), Hilpinen (1982), and Pietarinen (2006)... What distinguishes the game-theoretical method from Tarski's approach is its procedural nature. One reason why Peirce had such difficulty in explaining it is that he and his readers lacked the vocabulary of the game-playing algorithms of artificial intelligence... [Follow the URL for the details.]
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