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 - twitter.com/JonAlanSchmidt On Wed, Oct 19, 2016 at 5:08 PM, Jeffrey Brian Downard < jeffrey.down...@nau.edu> wrote: > 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: g...@gnusystems.ca [g...@gnusystems.ca] > Sent: Thursday, October 13, 2016 3:03 PM > To: peirce-l@list.iupui.edu > 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. >
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