Jon, Gary F, List, How might we think about the relationship between the categories and the universes? First, let's note that he uses these terms in a number of different ways in different contexts. For instance, in the Harvard Lectures of 1903, he provides a phenomenological account of the universal categories that are found in all possible experience. In other places, such as his work on algebraic and diagrammatic systems of logic, he provides a logical account of the categories and universes that employed when making assertions and drawing inferences. In what follows, I will focus on the latter distinction (hence the change in the subject heading for this post).
For the sake of clarity, let's start by focusing our attention on one place where he talks about categories and universes. Here is what Peirce says about relations of reference and referential relations on the opening pages of "Nomenclature and Division of Dyadic Relations": The broadest division of dyadic relations is into those which can only subsist between two subjects of different categories of being (as between an existing individual and a quality) and those which can subsist between two subjects of the same category. A relation of the former kind may advantageously be termed a reference; a relation of the latter kind, a dyadic relation proper. A dyadic relation proper is either such as can only have place between two subjects of different universes of discourse (as the membership of a natural person in a corporation), or is such as can subsist between two objects of the same universe. A relation of the former description may be termed a referential relation; a relation of the latter description, a rerelation. (CP 3.573). Notice what he says about relations of reference and referential relations. 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. For my part, I think Peirce is engaged a discussion the way that he plans to handle these sort of relations in (1) his formal systems of algebraic logic and existential graphs (both of which are mathematical systems of logic) and (2) in his speculative grammar and critical logic as two parts of his semiotic theory. His aim is to rethink the mathematical systems so that he can then use them as tools in his philosophical inquiries in semiotics. He sees that there are a number of problems with the systems that Kempe and Schroder have developed, and he is draw on the obvious shortcomings in these two formal systems for the sake of gaining insight into how he might further develop his own systems--especially the existential graphs. While there are a number of difficult issues that he is trying to grapple with in this essay, it seems to me that one of the prominent concerns is how to handle the quantifiers and modal operators in these logical systems. In particular, I think he is worrying about the relationships between the realms that the quantifiers and modal operators each range over in the different sorts of assertions that make use of such logical conceptions. He adds the following remark about his limited aims in this essay: The author's writings on the logic of relations were substantially restricted to existential relations; and the same restriction will be continued in the body of what here follows. A note at the end of this section will treat of modal relations. (CP, 3.574) He sees the limitations that are involved in restricting the formal systems to existential relations. Now that he is ready to make the move from the alpha and beta systems of the existential graphs to the gamma system, he is trying to sort through the thorny issues involved in understanding the realms over which different sorts of modal assertions (e.g. it is logically necessary that, it is metaphysically necessary that, it is physically necessary that, etc.) range over, and it is not obvious what will be needed once we allow the formal system to express operations of hypostatic abstraction so that the predicates that are formed on the basis of such operations may themselves be treated as objects for further inquiry. Given the fact that such predicates may themselves have the character of what is possible or what is a necessary rule, we now have a system where the quantifiers may range over objects having different modal characteristics. Here is a point that he makes about modal dyadic relations in the appended part of the essay: Dyadic relations between symbols, or concepts, are matters of logic, so far as they are not derived from relations between the objects and the characters to which the symbols refer. Noting that we are limiting ourselves to modal dyadic relations, it may probably be said that those of them that are truly and fundamentally dyadic arise from corresponding relations between propositions. To exemplify what is meant, the dyadic relations of logical breadth and depth, often called denotation and connotation, have played a great part in logical discussions, but these take their origin in the triadic relation between a sign, its object, and its interpretant sign; and furthermore, the distinction appears as a dichotomy owing to the limitation of the field of thought, which forgets that concepts grow, and that there is thus a third respect in which they may differ, depending on the state of knowledge, or amount of information. To give a good and complete account of the dyadic relations of concepts would be impossible without taking into account the triadic relations which, for the most part, underlie them; and indeed almost a complete treatise upon the first of the three divisions of logic would be required. (3.608) The issue Peirce is highlighting here is a problem for any system of mathematics—including systems of algebraic logic and the existential graphs. How should the systems be constructed so that they embody the growth of the very concepts that are being modeled in the systems? Peirce describes the special problems that crop up when we move back and forth between quantifiers and the modal operators that extend over the realms of physical objects that might stand in relations of necessity or contingency and quantifiers and modal operators that range over logical conceptions and relations when he makes the following remark about some assertions that Dr. Carus has made: Yet philosophical necessity is a special case of universality. But the universality, or better, the generality, of a pure form involves no necessity. It is only when the form is materialized that the distinction between necessity and freedom makes itself plain. These ideas are, therefore, as it seems to me, of a mixed nature. CP 6.592 (also see CP 5.223) To put the idea in simpler terms, I think Peirce is pointing out that the quantifiers and the modal operators range over pretty much the same realms (i.e., the widest realm of all that is possible) when we move up to the level of philosophical necessity (i.e., the laws of logic and the laws of metaphysics). So, to address a question that Jon S and Gary F posed a bit ago, 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. He saw that the distinction could be dropped because, at this high level “philosophical necessity is a special case of universality.” --Jeff PS My ability to engage in these discussions has been limited due to my daughter’s health issues. As such, I will try to jump in when I am able but may be absent from the discussion for some time when these more personal matters are more pressing. Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________________ From: [email protected] [[email protected]] Sent: Thursday, October 13, 2016 3:03 PM To: [email protected] Subject: RE: [PEIRCE-L] Peirce's Cosmology Jon, Gary R et al., I’ve been away for a couple of days and haven’t yet caught up with the discussion. However I’ve done a bit of searching through Peirce’s late texts to see whether I could confirm your suggestion that Peirce “seems to have shifted toward discussing "Universes" rather than "categories.” I found a couple of extended discussions of the difference between “Categories” and “Universes,” one in the “Prologemena” of 1906. But I also found two other places where Peirce writes of “the three Universes”: the long letter to Welby of Dec. 1908 (EP2:478 ff.) and a 1909 letter to James (EP2:497). He doesn’t refer to Categories in these letters, so that would seem to support your suggestion. I found very little that uses either term from 1909 on. I see that Gary R. has corrected me on my reference to the ‘ur-continuity’, and I’ll leave any further comments on that until I catch up with the thread. Gary f. From: Jon Alan Schmidt [mailto:[email protected]] Sent: 11-Oct-16 15:08 To: Gary Fuhrman <[email protected]> Cc: [email protected] Subject: Re: [PEIRCE-L] Peirce's Cosmology Gary F., List: GF: I think it would be less of a stretch to identify the contents of those Universes as Firsts, Seconds and Thirds, i.e. as subjects or objects in which Firstness, Secondness, and Thirdness (respectively) inhere. I have generally been reluctant to talk about Firsts/Seconds/Thirds, rather than Firstness/Secondness/Thirdness. I am not sure that the former terminology is completely appropriate and consistent with Peirce's usage, especially late in his life, although I am open to being convinced otherwise. In fact, he seems to have shifted toward discussing "Universes" rather than "categories," perhaps in order to emphasize that they are objective constituents of reality, not mere labels that we apply to organize our experience. GF: This leaves open the possibility of identifying one of the categories as Creator of all three Universes. Peirce's statement was not that one of the categories created all three Universes, but that all three Universes--or at any rate, two of the three--have a Creator who is independent of them. I take this to mean that the Creator might not be entirely independent of one of the three Universes. Of course, my basic argument is that Peirce unambiguously described God as "pure mind" and the Universe that corresponds to Thirdness as that of "Mind," so the alignment seems pretty clear. GF: To me it seems logical enough to regard this insubstantial Being, this capacity, as the Creator of all three Universes. Again, it is not that the Creator is identified with one Universe or its contents, it is that He might not be entirely independent of one Universe. And "mere capacity for getting fully represented" does not strike me as equivalent to "capacity for creation," especially of other Universes. In "A Neglected Argument," the only description of a Universe that mentions the other two is that of the third. GF: This would be somewhat analogous to regarding abduction as Creator of the hypothesis which, my means of deduction, creates a theory which through inductive testing becomes more and more substantial. As we all know, abduction is the only source of new ideas; perhaps Firstness is the only source of Ideas. Likewise we might regard the dreamer as Creator of the dream and of the fact of the dream and of whatever might be predicated of it (i.e. of its meaning, if it has any). But abduction is not the creator of the hypothesis, it is the reasoning process by which a person creates the hypothesis. Reasoning is thought, which is Thirdness. Peirce characterized a person as a symbol or as a continuum, both of which are Thirdness. Likewise, the dreamer who creates the dream, the fact of it, and whatever might be predicated of it is a person (again, Thirdness). GF: But I think you will agree that possibility is the logical equivalent of Firstness, not Thirdness. Peirce at this stage in his thinking often identified continuity with generality, and he wrote c.1905 that “The generality of the possible” is “the only true generality” (CP 5.533). So I don’t think continuity is confined to Thirdness ... This brings up one of the great puzzles for me in Peirce's writings. He steadfastly associated possibility with Firstness and continuity/generality with Thirdness, but his mathematical definition of a continuum evolved toward the notion of an infinite range of indefinite possibilities. Is a continuum of possibilities more properly considered to be an example of Thirdness (as a continuum) or Firstness (as possibility)? Should we perhaps distinguish possibility as Firstness from potentiality as Thirdness? If so, on what basis? GF: ... and I think Gary Richmond has argued that the ur-continuum or tohu bohu represented by the blackboard in Peirce’s famous cosmology lecture is the first Universe, which comprises “vague possibilities.” >From browsing through the List archives, I took Gary R. to be suggesting that >the blackboard or "ur-continuum" is Thirdness, consistent with my initial post >in this thread. Perhaps he can weigh in on this himself. Regards, Jon Alan Schmidt - Olathe, Kansas, USA
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