Earlier Discussion: http://comments.gmane.org/gmane.science.philosophy.peirce/15762 http://inquiryintoinquiry.com/2015/02/28/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-7/ http://inquiryintoinquiry.com/2015/04/13/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-comment-7-1/
Jeff, List, There appears to be a problem with the Gmane archive that I ordinarily use in search of lost times and thoughts out of mind … and this is the time of year when my brain runs out of steam anyway … and it may be a while before I can get completely up to speed on this subject again … so I'll just post a few thoughts off the top of my head … What prompted me to my series of comments on Selection 7 (chapt. 3 sec. 4) was a very important remark that Peirce made in passing, so smoothly so that it was all too easy to miss its significance, namely, this: <quote> The forms of general relatives are of infinite variety, but the following may be particularly noticed. Relatives may be divided into those all whose individual aggregants are of the form A : A and those which contain individuals of the form A : B. The former may be called concurrents, the latter opponents. </quote> As I commented before, this tells us that Peirce understands the distinction between general dual relatives and individual dual relatives, the individuals being “aggregated” or logically summed to form the generals, and that singling out special cases of general relatives in the way he does next is but a first rough cut toward a complete classification. This needs to be born in mind as we proceed toward the enumeration of triadic relations and beyond, especially as it affects the classification of triadic sign relations. Alright, that should recall some of the context. To be continued ... Jon On 6/24/2015 6:42 PM, Jeffrey Brian Downard wrote: > Jon, Lists, > > It appears that I somehow missed your May post on Chapter 3, so thank you for re-sending the link to comment 7.5. > You make quite a number of interesting points, one of which is future looking. You say: "Looking back from the > ascent we see that the two-point universe ... manifests a type of formal degeneracy (loss of generality) compared > with the three-point universe.... This is due to the circumstance that the number of “diagonal” pairs (in the > two-point case) exhibits symmetries that will be broken as soon as one adds another element to the universe." > > The diagram you offer at the end nicely illustrates how those symmetries are broken. I'm wondering if you might be > able to say a bit more about what kinds of symmetries are being broken -- and why those kinds of symmetries are lost > and not others. I feel that this should be obvious to me--and that I should be able to answer the question > myself -- by I'm finding it to be a bit of a challenge. > > --Jeff > > > Jeff Downard > Associate Professor > Department of Philosophy > NAU > (o) 523-8354 > ________________________________________ > From: Jon Awbrey [[email protected]] > Sent: Wednesday, June 24, 2015 12:42 PM > To: Jim Willgoose; Peirce List > Subject: [PEIRCE-L] Re: Survey of Relation Theory • 1 > > Thread: > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/16529 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/16535 > > Here is the series of blog posts on Chapter 3 (The Logic of Relatives) > in Peirce's 1880 “Algebra Of Logic” up to the point where I left off > on May Day. > > Preliminaries > http://inquiryintoinquiry.com/2015/01/30/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-preliminaries/ > > Selection 1 > http://inquiryintoinquiry.com/2015/02/01/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-1/ > > Selection 2 > http://inquiryintoinquiry.com/2015/02/03/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-2/ > > Selection 3 > http://inquiryintoinquiry.com/2015/02/11/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-3/ > > Selection 4 > http://inquiryintoinquiry.com/2015/02/12/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-4/ > > Selection 5 > http://inquiryintoinquiry.com/2015/02/15/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-5/ > > Selection 6 > http://inquiryintoinquiry.com/2015/02/16/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-6/ > > Selection 7 > http://inquiryintoinquiry.com/2015/02/28/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-7/ > > Selection 8 > http://inquiryintoinquiry.com/2015/03/12/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-8/ > > Comment 7.1 > http://inquiryintoinquiry.com/2015/04/13/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-comment-7-1/ > > Comment 7.2 > http://inquiryintoinquiry.com/2015/04/19/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-comment-7-2/ > > Comment 7.3 > http://inquiryintoinquiry.com/2015/04/23/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-comment-7-3/ > > Comment 7.4 > http://inquiryintoinquiry.com/2015/04/24/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-comment-7-4/ > > Comment 7.5 > http://inquiryintoinquiry.com/2015/05/01/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-comment-7-5/ > > Up to this point we are still dealing mainly with dyadic relations, > and as interesting as those may be, especially to a graph theorist, > the level of complexity we need to quicken semiotics does not come > into play until we reach the playing field of triadic relations. > > 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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