Jeff, List: I guess my point is that the only reason why we can *isolate *relate, correlate, and the relation between them is because there is an underlying order; that is what enables us to *distinguish *these things as individuals at all.
I deliberately avoided using the relation of brother as an example because it entails other relations--one is older, both A and B are in the relation of son to some C, etc. Left and right do require an observer for orientation, but "next to" does not; likewise being on the same surface and similarity. These relations are not "ordered" in the sense of priority or sequence, but they do require an underlying order, or we would not be able to pick them out at all. Regards, Jon On Sun, Nov 6, 2016 at 12:03 AM, Jeffrey Brian Downard < [email protected]> wrote: > Jon, List, > > From a logical point of view, when we study some relation--such as the > dyadic relation of A is brother of B--we are isolating the relate, the > correlate, and the relation between them. We understand that the things > standing in the position of relate and correlate will typically have many > internal relations among the parts that make them up. We also understand > that the things in the position of relate and correlate may stand in a > variety of different external relations to other things. But, when we > analyze this particular relation of being a brother, we ignore those other > relations. That is, we ignore such things as the fact that one might be > taller than another or that one might be more social than the other. > > We do the same thing, I take it, when we are engaged in a phenomenological > analysis of something that has been observed. Phenomenological analysis > works in manner that is analogous to logical analysis. Peirce explicitly > says, for instance, that we do not attend to the parts of the spots. The > fact that, in reality, the two spots on the page are arranged so that one > is the left to the other brings in another kind of relation involving an > observer. In relation to that observer, one is to the right and one is to > the left really. But Peirce has isolated the relation of "being on the same > surface." > > Let's consider a limiting kind of relation: C is similar to D. The > relation of being on the same surface is a similarity, if I am not > mistaken. Does such a relation of similarity involve some sort of order > that holds between the relate and the correlate? There is a relation, but > is it ordered? > > --Jeff > > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 > ________________________________________ > From: Jon Alan Schmidt [[email protected]] > Sent: Saturday, November 5, 2016 5:05 PM > To: Jeffrey Brian Downard > Cc: Peirce-L > Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was > Metaphysics and Nothing (was Peirce's Cosmology)) > > Jeff, List: > > Just thinking out loud here ... Do two random spots on a page have a > relation? If not, then this example is not pertinent; but if so, is it > accurate to say that they have no order? Doesn't the fact that they occur > on the same piece of paper--like, say, chalk marks on a blackboard--entail > that there is order in some sense? Again, I see that they are not > "ordered" in terms of having a hierarchy or sequence, but in fact one will > be to the left of the other, one will be above the other, etc. If we > rotate the page 180 degrees, then these relations will be reversed from our > point of view, but the spots will still exhibit the same order because of > the underlying paper. As long as they are potential spots, they "cannot be > placed in any particularly regular way," as Pierce said; but once they are > actual spots, they now have been placed in a particularly regular way, and > are distinguishable only because of the order that is manifested in their > relations. > > Regards, > > Jon > > On Sat, Nov 5, 2016 at 6:10 PM, Jeffrey Brian Downard < > [email protected]<mailto:[email protected]>> wrote: > > Jon, Gary R, List, > > First, let me point out that my comments were meant as interpretation of > how Peirce is coming at these questions about the character of dyadic and > triadic relations from the side of math (including formal logic), > phenomenology and semiotics. I am not making any metaphysical claims about > what, really presupposes what. My aim was to hold off on those sorts of > questions--at least for now. > > In response to your claim that all dyads are, in some way or another, > organized, I tend to disagree. Let's take one of Peirce's examples from > "The Logic of Mathematics" as a starting point. If you put two spots on a > page, they are not ordered. As soon as you say that one is the left of the > other, or that one is above the other, you are comparing them with respect > to some third thing. > > Here is the passage: "Two phenomena, whose parts are not attended to, > cannot display any law, or regularity. Three dots may be placed in a > straight line, which is a kind of regularity; or they may be placed at the > vertices of an equilateral triangle, which is another kind of regularity. > But two dots cannot be placed in any particularly regular way, since there > is but one way in which they can be placed, unless they were set together, > when they would cease to be two. It is true that on the earth two dots may > be placed antipodally." (CP 1.429) > > If you take a pair of things as a collection within the mathematical > system of set theory, the pair can be treated as an unordered set, or as an > ordered set. The character of the set as a whole is, itself, some third > thing. As such, the character of the set may be characterized in terms of a > general rule of order between the members--or a set may not impose such an > ordered rule on its members. > > In the case of a dyad of identity, we have a dyad that consists of two > instances of the same thing. Setting aside some temporal or spatial > framework, the dyad of identity is unordered. Some mathematical collections > allow multiple instances of the same thing (e.g., multiple instances of the > number 1), but the postulates of most set theories do not allow multiple > members that are identical. > > There is a short discussion within the context of formal logic of > unordered collections of two or three things CP 4.345. He calls such > relations doublets and triplets, whereas he calls the ordered collections > dyads and triads. > > I must admit that this pretty thin evidence for my claim that some dyads > (or doublets in the context of the system of logic he is developing at > 4.345) may not involve an ordered relation, but it is what I have to offer > at this point. I don't see textual evidence for the claim that every sort > of relation--of any kind--always involves some kind of order or another. > Having said that, Peirce is typically considering limiting kinds of cases > in order to clarify some matter that is at hand. In order to get a better > understanding of different sorts of order, considering relations that are > unordered may be helpful. > > Looking ahead, preserving the conceptions of unordered relations may help > us explain how things (e.g., some undifferentiated possibilities) which > lack order might come to get ordered. After all, the presence of order--of > any kind--is one of the things that needs to be explained. > > Given the fact that we're now looking at RLT, I think it makes sense to > hold off on the Minute Logic--at least for now. > > --Jeff > > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354<tel:928%20523-8354>
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