Gary F., Jon, List, In a discussion of elementary relatives, you ask: "Perhaps correlates which are not relations are 'individual relatives'?"
Here is a nice passage from "On an Improvement in Boole's Calculus of Logic: "There are in the logic of relatives three kinds of terms which involve general suppositions of individual cases. The first are individual terms, which denote only individuals; the second are those relatives whose correlatives are individual: I term these infinitesimal relatives; the third are individual infinitesimal relatives, and these I term elementary relatives." CP 3.95 In the preceding paragraph, Peirce makes the following point: "If we call a thought about a thing in so far as it is denoted by a term, a second intention, we may say that such a term as 'any individual man' is individual by second intention. The letters which the mathematician uses (whether in algebra or in geometry) are such individuals by second intention. Such individuals are one in number, for any individual man is one man; they may also be regarded as incapable of logical division, for any individual man, though he may either be a Frenchman or not, is yet altogether a Frenchman or altogether not, and not some one and some the other." This discussion of individual terms, infinitesimal relatives and elementary relatives is found in the context of a discussion of a system of formal logic. I take this to be, first and foremost, an inquiry in mathematical logic. The crucial move, I take it, is that Peirce is building a mathematical system that has the character of a second intentional system of formal logic. What happens when we include the kinds of abstractions that involve taking terms--like numbers--that are used first and foremost as pure indexes that are put into relations of one-to-one correspondence with some collection of individuals (such as a collection of spots on a page), and we then treat the mathematical signs themselves as individuals? This abstractive move gives us an individual that has the character of an elementary relative. It is elementary in the sense that it is not amenable to any further logical division. That is, we can't logically divide the indexical "2" that was put into correspondence with a couple of individual spots on the page any further. It is an individual of a special sort. While there may be, as Qunie suggests in Word and Object, rabbit time slices, there are no number time slices--are there? This is true even when we are talking about a specific use of "2" as an index that is put into a relation of correspondence. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________________ From: [email protected] [[email protected]] Sent: Thursday, December 03, 2015 9:31 AM To: 'Peirce List' Subject: RE: [PEIRCE-L] Elementary Relatives or Individual Relatives Jon, This doesn't explain “the difference between relations proper and elementary relations” (which you said was "critically important to understand"), because the latter term is itself used in a specific "technical sense" by Peirce in the places you cite. It doesn't help to understand which “technical sense” of the word you have in mind. My guess is that what’s confusing some of us in understanding triadic relations is that some of them relate correlates which are themselves relations. (Perhaps correlates which are not relations are “individual relatives”?) Gary f. -----Original Message----- From: Jon Awbrey [mailto:[email protected]] Sent: 2-Dec-15 22:30 Peircers, As I wrote before, I used the phrase "relations proper" merely to emphasize that I was talking about relations in the technical sense. Another common idiom to the same purpose would be "relations, strictly speaking". As for "elementary relatives", Peirce uses this term in the 1870 Logic of Relatives. See, for example, CP 3.121ff and a later remark at 3.602ff. See Also: ☞ https://www.google.com/search?hl=en&as_q=Peirce&as_epq=Elementary+Relative And toward the end of this section: ☞ http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction#Operational_Representation Regards, Jon > Gary, all, > > I used the phrase “relations proper” to emphasize that I was speaking > of relations in the strict sense of the word, not in any looser sense. > I have been reading Peirce for almost 50 years now and I can't always > recall where I read a particular usage. In the 1970s I spent a couple > of years poring through the microfilm edition of his Nachlass and read > a lot of still unpublished material that is not available to me now. > But there is no doubt from the very concrete notations and examples > that he used in his early notes and papers that he was talking about > the formal objects that are variously called elementary relations, > elements of relations, individual relations, or ordered tuples. > > I did, however, more recently discuss a number of selections from > Peirce's > 1880 Algebra of Logic that dealt with the logic of relatives, so I can > say for a certainly that he was calling these objects or the terms > that denote them by the name of “individual relatives”. > … > > On 11/27/2015 12:42 PM, [email protected]<mailto:[email protected]> wrote: >> Jon, >> >> If it’s critically important to understand the difference between >> “relations proper” and “elementary relations”, can you tell us what >> that difference is, or point us to an explanation? These are not >> terms that Peirce uses, so how can the rest of us tell whether we understand >> them or not? Being unfamiliar with those terms does not indicate lack of >> understanding of the important concepts they signify. >> >> Gary f. >> >> From: Jon Awbrey [mailto:[email protected]] Sent: 27-Nov-15 11:16 >> >> Gary, all, >> >> It is critically important to understand the difference between >> relations proper and elementary relations, also known as tuples. >> >> It is clear from his first work on the logic of relative terms that >> Peirce understood this difference and its significance. >> >> Often in his later work he will speak of classifying relations when >> he is really classifying types of elementary relations or single tuples. >> >> The reason for this is fairly easy to understand. Relations proper >> are a vastly more complex domain to classify than types of tuples so >> one naturally reverts to the simpler setting as a way of getting a foothold >> on the complexity of the general case. >> >> But nothing but confusion will reign from propagating the categorical error. >> >> Regards, >> >> Jon -- academia: http://independent.academia.edu/JonAwbrey my word press blog: http://inquiryintoinquiry.com/ inquiry list: http://stderr.org/pipermail/inquiry/ isw: http://intersci.ss.uci.edu/wiki/index.php/JLA oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache
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