Jeff, List: This is another post that I need to digest carefully. I have already been getting better acquainted with the Existential Graphs in recent days, so that should help. One immediate question is what connection (if any) there is between "universes of discourse" and "universes of experience"; Peirce only refers to the latter in "A Neglected Argument." And again, he never once mentions "categories" in that article, so I have a hard time drawing any conclusions about those from it.
Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sat, Oct 22, 2016 at 11:14 AM, Jeffrey Brian Downard < jeffrey.down...@nau.edu> wrote: > Gary R, Jon S, List, > > As far as I can tell, Peirce never stopped talking about the categories in > the context of the phenomenology or phaneroscopy. Furthermore, he never > stopped talking about the categories in the context of the semiotics. > > In fact, the phenomenological conception of the categories was a leading > idea that grew in importance and in its distinction (as compared to the > logical conception of the categories and the metaphysical conception of the > categories) from 1902 on. > > The classification of signs, objects, interpretants based on their modal > character and the modal character of the relations is grounded from early > to late on the division between possibles, existents and necessitates. The > explanations of the relations of determination, reference, representation, > signification, assurance, validity, and the like all hinge on this modal > division from beginning to end without waver. > > Having said that, I do see that Peirce was significantly rethinking the > relations between the quantifiers and the modal operators between 1903 and > the end. I don't see that he dropped the discussion of the modal categories > in the context of the formal logic in favor of trying to conceive of these > relations entirely in terms of universes and sub-universes of discourse. > Rather, he was actively experimenting and dramatically rethinking the > relations between them. > > Consider the rich explanations of the developments of the gamma graphs > that Don Roberts provides in chapters 5-7 of his monograph on the > existential graphs. One can nicely trace the development of the conceptions > by looking at the index and seeing how Peirce used the conceptions of > universes and categories at each of the major stages in the development of > the gamma graphs. > > While the developments are complex, let me summarize a few prominent sets > of ideas that Peirce experimented with between 1898 and 1910. Starting > in 1898, Peirce introduced developments of the lines that connect spots in > order to handle hypostatic abstraction, potentials and graphs of graphs. He > tried tapered thickened lines in order to deal with ordered sequences, > branches with numbered Rhos in order to express relations of different > orders of acidity, capital letters to represent selectives and spatially > ordered branching connections on numbered "carrots" for potentials to > handle relations between possibilities, abstractions and existent objects. > > Thus far, all of the major developments are experiments on the lines > connecting spots. He introduces a wavy line that goes around a symbol for > gamma expressions of the alpha graph, but that is not a special kind of cut > or boundary. Rather, it is just a way of highlighting the symbol (e.g., a > selective, an assertion, etc.) to say what it precisely expresses. In > Logical Tracts No. 2, Peirce introduced the dotted, wavy, and saw rims, but > these too were used to talk about the things inside the rims as different > kinds > of abstractions. They don't really introduce new kinds of boundaries into > the diagrammatic space that is the sheet of assertion. > > Having tried a lot of experiments on the lines connecting spots, he then > starts to experiment with variations on the cuts and scrolls to introduce > new kinds of boundaries. Already, in the early development of the cut, he > had already tried one variation on the continuous line forming a loop. In > place of a single line looping around an area to form a boundary between > two areas, he blackened in the area to represent the pseudograph as a way > of expressing that everything in that area is false, regardless of the kind > of possible expression that might be in that area. That is, it > obliterates that area entirely. That was a kind of limiting case in the > interpretation of the cut or scroll. > > Things change dramatically with the introduction of the tinctured graphs > in 1903. Now, we have the areas inside of cuts colored or shaded in some > way to distinguish between different ways of saying that something is > actually the case, or possible so, or different ways of being necessitated. > The introduction of the tinctures brings a whole host of complications and > complexities into the gamma graphs, and Peirce tries a number of different > approaches in order to bring more balance and harmony to the system. > > Without going into the details of what happens from 1906 and after, I > think we can already see that the introduction of the tinctures gives rise > to new kinds of interpretations of the colored or shaded areas. Instead of > having a sheet of assertion that represents a universe of discourse > consisting of individual actual objects and facts, where the cuts > separate areas into facts that are true and those that are false, the cuts > now have dramatically different meanings depending upon whether the area > inside, outside or the area of the cut itself is colored or shaded in some > way. From this point on, we need a dramatically different interpretation of > different universes--where those universes have modal characteristics. In > effect, the categories of possibles, actual existents and necessities are > still in the system, but they are being interpreted in terms of different > universes and sub-universes of discourse. The sub-universes are needed > because Peirce is now making distinctions between different kinds > and classes of possibles, actuals and necessities in the formal system > itself. > > The development of any system of mathematics is guided by a need to answer > questions that have proven to be intractable in some area of inquiry. So > too with the existential graphs. The primary purpose of developing > these mathematical systems of formal logic is to answer real questions in > philosophy, especially questions in the theory of semiotics. As such, the > gamma system are formal models that can be used for analytical purposes in > the semiotic theory to analyze propositions, inferences, their component > parts, and the relations that hold between them--both local and global. > > While Peirce was keenly interested in analyzing the validity of different > kinds of deductive inferences involving different sorts of modal claims, I > think he was even more keenly interested in having a mathematical set of > tools that could be used to analyze inductive and abductive inference and > the observations that inform such synthetic reasoning. (see Roberts, 100; > Ms 499(s)). > > So, let me venture an interpretative hypothesis. One of the guiding ideas > in the later development of the gamma graphs involved a set of remarkable > experiments in the use of different kinds of areas on the top and bottom of > the sheet of assertion, and between multiple pages within a larger book of > sheets. The introduction of two sides of a page and the introduction of > multiple sheets in a book was driven, in part, by an interest in having a > formal system that would be sufficiently rich to enable us to analyze > inductive and abductive reasoning. > > As such, the late developments in the gamma graphs may very well represent > a concerted effort to rethink the different ways that one might represent > different universes of discourse and categories of possibility, actuality > and necessity--where this exploration was being done with an eye to solving > longstanding philosophical problems in applying the universes of discourse > and the modal categories of possibility, actuals and necessity to the > accounts of abductive and inductive inference. > > So, in "The Neglected Argument", Peirce may very well be examining--on an > observational basis--the different ways that we might think about the > phenomenological account of the universes and categories in common > experience for the sake of refining his explanations of how the logical > conceptions of the universes of discourse and categories should be applied > to those abductive inferences that give rise to our most global hypotheses. > > --Jeff > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 >
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