Hi Jon S, Gary R, List,
Let me try to simply matters considerably. It will involve a number of oversimplifications, but I'm hoping it might help to address some questions you are finding vexing. Let us compare three different sorts of discussions of universes, realms and categories: 1. The simple systems of formal algebraic and graphical logics--being developed as a part of mathematics 2. The phenomenological inquiries. 3. The semiotic inquiries. Peirce talks about three universes of experience as part of his phenomenological inquiries. In the early pages of "A Neglected Argument," the discussion of these universes is largely phenomenological in character. In the development of the formal systems of algebraic logic and existential graphs, Peirce builds various conceptions that model different universes of discourse and categories. In these different formal systems, the universes and modal notions are treated differently. For instance, the universes of discourse are handled differently in the alpha, beta, and the various systems of the gamma graphs. In the development of the semiotic theory, he uses the formal systems of logical for the purpose of refining the classifications and explanations of the sign relations and patterns of inference. At this point, he needs a philosophical interpretation of the mathematical models--including interpretations of what a sheet of assertion means in the context of the alpha graphs, the beta graphs, and the various versions of the gamma graphs. It might be helpful to think of the phenomenological inquiries concerning the three universes of experience as remarks concerning the more "global" features of our observations--where those observations are informing the classifications and philosophical explanations that being generated in the semiotic theory. Each of these three lines of inquiry--formal logic as a part of mathematics, phenomenological, and semiotic--are informing the others, but in different ways. For instance, in the context of the formal logic, Peirce sees no need to pick between the different ways of conceiving of the universes of discourse and the modal features of the assertions. The alpha system of graphs can make do with a much simpler version of a universe of discourse than is needed for the various systems of the gamma graphs. It isn't the case that one version is right or wrong. They are just different formal systems--like the different systems of numbers (e.g., rationals, reals, surreals) or different systems involving continuity (e.g., topology of one two or three dimensions, projective geometry, metrical geometries). Clearly, some of these different formal systems are more "basic" than the others in some senses, but we should remember that, in the final analysis, they are just different formal systems starting with different sets of initial definitions, postulates and axioms. We seek to build formal system that manifest virtues such as balance and symmetry, but even the systems that lack these virtues may be of some special interest for particular problems. Of course, when we move from these three forms of inquiry to metaphysics, we then need to press the question: what it the best explanation of the nature of what exists as objects and what is real as general? At this point, we can then make use of the prior work that has been done in the math, phenomenology and logic to address the questions of cosmological metaphysics that are so interesting--but hard to answer well. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Jon Alan Schmidt <jonalanschm...@gmail.com> Sent: Thursday, October 20, 2016 8:18 AM To: Peirce-L Subject: Re: [PEIRCE-L] Peirce's Logical Universes and Categories List: Following up on the post below--as I mentioned in the thread on Universes and Categories (was Peirce's Cosmology), I now notice that Peirce added the caveat that whether it is correct to assign Subjects to Universes and Predicates to Categories "is a question for careful study" (CP 4.545). He then proceeded to present a long and complicated analysis of propositions to explain why he found it unsatisfactory to view Universes as "receptacles of the Subjects alone" (CP 4.548). At least, I think he did ... CSP: Let us, at least, provide for such a [destined] mode of being in our system of diagrammatization, since it may turn out to be needed and, as I think, surely will. CSP: I will proceed to explain why, although I am not prepared to deny that every proposition can be represented, and that I must say, for the most part very conveniently, under your view that the Universes are receptacles of the Subjects alone, I, nevertheless, cannot deem that mode of analyzing propositions to be satisfactory. (CP 4.547-548) The second sentence here is key, but it is tough to decipher. I assume that "explain why" refers to the preceding assertion that a third mode of being will be needed. The rest is very muddled. What is the relevance of whether "every proposition can be represented"? What, specifically, did Peirce find "very convenient"? Most importantly, what "mode of analyzing propositions" could he not deem to be satisfactory? Am I right to take this as referring to "your view that the Universes are receptacles of the Subjects alone"? I think so, because Peirce went on to suggest, as an alternative, "the principle that each Universe consists, not of Subjects, but the one of True assertions, the other of False, but each to the effect that there is something of a given description." The rest of CP 4.548 is an analysis of two specific propositions using both methods, showing that the alternative is more correct. But this means that there are only two Universes, not three; and they consist of True and False assertions, not Ideas, Things/Facts, and Habits/Laws/Continua. Given the context, I gather that these may refer to the Sheet of Assertion and that which is fenced off from it by a cut. So apparently this passage is apparently not about the "Universes of Experience" at all! Peirce then came back to Categories in CP 4.549. CSP: I will now say a few words about what you have called Categories, but for which I prefer the designation Predicaments, and which you have explained as predicates of predicates. That wonderful operation of hypostatic abstraction by which we seem to create entia rationis that are, nevertheless, sometimes real, furnishes us the means of turning predicates from being signs that we think or think through, into being subjects thought of. As I also mentioned in the other thread, hypostatic abstraction enables us to convert predicates into subjects. Does this mean that even if we assign subjects to Universes and predicates to Categories, it turns out to be a distinction without a difference? CSP We thus think of the thought-sign itself, making it the object of another thought-sign. Thereupon, we can repeat the operation of hypostatic abstraction, and from these second intentions derive third intentions. Does this series proceed endlessly? I think not. What then are the characters of its different members? My thoughts on this subject are not yet harvested. I will only say that the subject concerns Logic, but that the divisions so obtained must not be confounded with the different Modes of Being: Actuality, Possibility, Destiny (or Freedom from Destiny). On the contrary, the succession of Predicates of Predicates is different in the different Modes of Being. Meantime, it will be proper that in our system of diagrammatization we should provide for the division, whenever needed, of each of our three Universes of modes of reality into Realms for the different Predicaments. Now we have "Modes of Being" or "modes of reality" that are identified as "three Universes" and correspond to "Actuality, Possibility, Destiny (or Freedom from Destiny)." We also have "Realms for the different Predicaments," which are what we used to call "Categories," but these divisions "must not be confounded with the different Modes of Being"; instead, "the succession of Predicates of Predicates is different in the different Modes of Being." Peirce leaves it at that ... and thus I am still confused about Universes and Categories. Regards, Jon On Wed, Oct 19, 2016 at 7:26 PM, Jon Alan Schmidt <jonalanschm...@gmail.com<mailto:jonalanschm...@gmail.com>> wrote: Jeff, List: JD: Relations of reference subsist between two subjects that belong to different categories of being. Referential relations subsist between subjects that belong to different universes of discourse. The passage that you quoted dates from 1903, before the shift in Peirce's theoretical framework that Jappy hypothesizes. How do we reconcile your summary here with the "Prolegomena" passage from 1906, which indicates that Subjects belong to Universes and Predicates belong to Categories? Which 1903 term corresponds to "Universes of Experience" in 1908--"categories of being" or "universes of discourse"? JD: I think that Peirce sometimes dropped the distinction between the realms of the logical categories and the realms of the universes in his later writings when he was examining matters of philosophical necessity and was operating as this very high level of the discussion. My impression--which may be incorrect--is that Peirce stopped talking about Categories altogether in his later writings, and only talked about Universes. Jappy specifically claims that "after 1906 Peirce never again employed his categories as criteria in the classification of signs," but I am not entirely sure that this is also true in other areas. JD: My ability to engage in these discussions has been limited due to my daughter's health issues. Prayers are ascending for your daughter, as well as for you and the rest of your family. 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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