Gary F, Jon S, List,
In order to ground the suggestions I made in a text, consider what Peirce says in MS 518 about the sheet of assertion. This manuscript is part of a larger project to explain the connections between the first principles of logical algebra and the EG. §1. As the fundamental transformations of any algebra, if strict logical method is desired, choose indecomposable transformations. But an indecomposable transformation is either an omission or an insertion, since any other may be analyzed into an omission followed by an insertion. §2. The algebraic symbols are written on the surface of paper, wherein it is assumed that a surface is capable of representing every logical relation. That the surface must be capable of iconically representing every logical relation is not evident; and though it is true, I shall not here have occasion to prove it. We provide ourselves, therefore, with a surface which we call the sheet of assertion; and pretend to hold ourselves responsible for the truth of whatever we may write upon it. But as long as it remains blank we are irresponsible. Hence, the first rule of transformation will be Rule I. The whole of what is written on the sheet of assertion may be erased, without danger of falsehood. Here is the passage I find particularly suggestive: "That the surface must be capable of iconically representing every logical relation is not evident; and though it is true, I shall not here have occasion to prove it." So, instead of saying that a diagrammatic system of logic depends upon certain relations being invisible, I would say that the system makes clear to us not only what has been explicitly asserted on a sheet--but also what can be asserted that is consistent with what has been thus far. As such, the blank sheet iconically represents all that is logically possible (1) at each indeterminate point and (2) on the surface as a whole within the given system of logical hypotheses. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: g...@gnusystems.ca <g...@gnusystems.ca> Sent: Monday, April 8, 2019 7:22 AM To: peirce-l@list.iupui.edu Subject: RE: [PEIRCE-L] Phaneroscopy and logic Jeff, Jon, Thanks for your comments, all helpful! Though I may need more time to study yours, Jeff, and see how it relates to phaneroscopy. I recall that Michael Polanyi wrote a book on The Tacit Dimension. Maybe that’s a good name for what the blank sheet of assertion represents. Gary f. From: Jeffrey Brian Downard <jeffrey.down...@nau.edu> Sent: 7-Apr-19 17:49 To: peirce-l@list.iupui.edu Subject: Re: [PEIRCE-L] Phaneroscopy and logic Gary F, Jon S, List, GF: The iconicity of EGs avoids such verbal inconsistency by minimizing the use of words; but the system only works as a representation of Thought if we recognize the absence of lines as a mode of connection. The system appears to involve invisible icons! Instead of describing the relations under consideration in terms of what is invisible, I would stress Peirce's point, made several times in NDDR, to the effect that the representation of every logical relation implies something about some type of inverse of the relation. Without getting into the details of the matter, allow me to gesture in the direction of the broader ideas that are in play. In saying that a relation of agent and patient holds between relate and correlate that stand as dynamical dyads, it follows that the relation is not merely one of dyadic reference, and that is not a mere referential relation, and that is not a mere dyadic identity, etc. In other words, every assertion of some relation involves indefinitely many implications about what is and is not possible with respect to the converse of the relation--and so too with all other relations that are composed of such relations. Peirce takes the time to provide a nomenclature system inspired by the system used in organic chemistry in order to spell out what is and is not involved in the inverse or converse of progressively richer sorts of relations. What follows from the blank sheet of assertion? At every possible point where there is no assertion, the open space has implications that extend to any and every kind of relation that might, within a given system (e.g., such as the gamma graphs) be written on the sheet. As such, every possible point on any sheet of assertion involves all of the possible assertions that could be made at any point that are consistent with what is written elsewhere. If nothing has yet been scribed and the sheet is blank, that leaves a lot of possibilities. What should we say about an assertion involving three nested cuts? For all of those points outside the outmost cut, there is no fourth or fifth cut. So too for the areas inside of the cuts. In addition to expressing what is positively the case, each assertion written in diagrammatic form also expresses--and thereby allows us to see--what is and is not possible in terms of the converse relations. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Jon Alan Schmidt <jonalanschm...@gmail.com<mailto:jonalanschm...@gmail.com>> Sent: Sunday, April 7, 2019 1:06 PM To: peirce-l@list.iupui.edu<mailto:peirce-l@list.iupui.edu> Subject: Re: [PEIRCE-L] Phaneroscopy and logic Gary F., List: Just a few quick responses to some of your comments over the last couple of days. GF: I hesitated over your statement that “a definition can only serve as an Immediate Interpretant,” because I don’t think that applies to a term defined for use in pure mathematics ... Yes, I had in mind mainly linguistic Semes that purport to represent real Objects. A definition in pure mathematics is more of a hypothetical stipulation GF: But it took me a while to recognize that the absence of lines is also a mode of connection, as Peirce says above, and that both of these are “degenerate Secundan,” i.e. symmetrical dyadic relations in which there is no reaction of one correlate upon the other where one is relatively active and the other relatively passive. I agree that neither correlate is active or passive with respect to the other--that is what makes these relations symmetrical rather than asymmetric--but I think that it would be misleading to say on this basis that there is no reaction between them at all. On the contrary, coexistence is precisely a form of reaction--"existence is that mode of being which consists in the resultant genuine dyadic relation of a strict individual with all the other such individuals of the same universe" (CP 6.336; 1908). GF: The iconicity of EGs avoids such verbal inconsistency by minimizing the use of words; but the system only works as a representation of Thought if we recognize the absence of lines as a mode of connection. The system appears to involve invisible icons! I suggest that the Icons in question are invisible because their Objects are likewise invisible; i.e., invisibility is one of the respects in which the absence of lines resembles the mode of connection that constitutes coexistence. Recall that the blank Phemic Sheet represents "all that is tacitly taken for granted between the Graphist and Interpreter, from the outset of their discussion" (CP 4.553; 1906). That which is taken for granted--like coexistence as a relation that everything in the Universe has with everything else in the Universe--is invisible, unless and until we deliberately attend to it. GF: But you are quite right to point out that this usage of “empirical” is “a much broader notion of the term than often is used by classical British empiricists as well as contemporary empiricists of a more analytical orientation.” It is also much broader than the usage of Comte and the Positivists. This is essentially the thesis of Aaron Bruce Wilson's book, Peirce's Empiricism: Its Roots and Its Originality, which I recently reread. It is quite informative as far as tracing the historical and philosophical background against which Peirce was operating. Unfortunately, in my view Wilson makes some rather fundamental errors when it comes to Peirce's Semeiotic, most notably in his treatment of the Immediate Object. Regards Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt<http://www.LinkedIn.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt<http://twitter.com/JonAlanSchmidt>
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