Jon Awbry, Edwina, list,
Just an addition that underscores the vital importance of trying to overcome the dyadic reductionism. The reduction of triadic to dyadic relations is endemic in all kinds of organisations when questions of responsibility arise. A child is in danger in education or care and almost all involved professionals and managers tend to restrict their responsibility to just one aspect to the detriment of the object in focus, i.e. the child. If the parents keep their eyes on their child a serious conflict is to be expected. However in the resulting procedures it is not the welfare of the child that is at stake, but the process that runs between organisation and parents. This comes down to such a shift in object of interpretation that it can be rightfully said that the original object, the child, gets lost. What started as a difference between the immediate objects of a given dynamical objects, results in the shift to another dynamical object. This may be the condition humane as Edwina states, but we ought to try to overcome this existent condition. I value Jon's mathematical/logical approach to and further development of Peirce. Since I am much more focussed on semiotics, our immediate objects differ, but in the measure that our conception of the respective aspects of Peirce's thought is adequate, we are adding to our respective understanding of the ultimate dynamical object. I could write similar words on the work of many other list members. The architectonic of the sciences identifies the relations in a general way, it is up to us ( interpreters of Peirce) to find out how the different layers can be combined in a more practical way. We ourselves must realize that we are not exempt from the temptations of dyadic thinking, and taking our fallible immediate object of peirce's appraoch conceived as a dynamical object as our utopia. best, Auke van Breemen Op 21 oktober 2019 om 14:26 schreef Edwina Taborsky <edwina.tabor...@gmail.com>: ----- Original Message ----- From: Edwina Taborsky tabor...@primus.ca mailto:tabor...@primus.ca To: , @, @, @, Validation failed for: Laws Of Form Group lawsoff...@yahoogroups.com mailto:lawsoff...@yahoogroups.com , @, @, @ Sent: Mon 21/10/19 8:21 AM Subject: Fwd: Re: [PEIRCE-L] Re: The Difference That Makes A Difference That Peirce Makes Jon Awbrey, list Thanks for your post. I'd say that reductionism of triadic relations, i.e., of mediated complexity, to absolutist and dyadic ways of thinking is almost a default position of human beings. We can see this in the cyclic emergence of utopian ideologies, which move the mediated Relation to the Absolute and set it up as a Universal Force; and in the equally common view of simple dyadic mechanical ideologies, which remove mediation and insert simple direct-contact linear causality. There are many examples in our history - our human history of fundamentalist religious and political ideologies - which, because of removing mediation, require total emotional commitment and/or physical force to maintain. And our simple mechanical causality which reduces informational processes to local dyadic relations. The fact that life functions within that irreducible triadic process, in a way, moves the human individual to being part of the process rather than leading it or intervening with it - and we humans want to have control. Therefore, we move to Absolutist and Dyadic perspectives, where we feel we can intervene with the Absolute and the Dyadic Forces. Edwina On Mon 21/10/19 7:54 AM , Jon Awbrey jawb...@att.net mailto:jawb...@att.net sent: All, One of the more disconcerting developments, I might even say "devolutions", I've observed over the last 20 years has been the general slippage back to absolutist and dyadic ways of thinking, all of it due to the stubborn pull of unchecked reductionism, a failure to comprehend the relational paradigm, especially triadic relations, their irreducibility, and its consequences. With all that in mind, I'll return to a point in our earlier discussions, add a bit more on the concept of closure, and continue from there to its bearing on the pragmatic maxim. > Cf: The Difference That Makes A Difference That Peirce Makes : 23 > At: > https://inquiryintoinquiry.com/2019/09/20/the-difference-that-makes-a-difference-that-peirce-makes-23/ > > A fundamental question in applications of mathematical logic > is the threshold of complexity between dyadic (binary) and > triadic (ternary) relations, in particular, whether 2-place > relations are universally adequate or whether 3-place relations > are irreducible, minimally adequate, and even sufficient as > a basis for all higher dimensions. > > One of Peirce's earliest arguments for the sufficiency > of triadic relative terms occurs at the top of his > 1870 "Logic of Relatives". > > Cf: > https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview > Cf: https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1 > Cf: > https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1#Selection_1 > > > > The conjugative term involves the conception of "third", > the relative that of second or "other", the absolute term > simply considers "an" object. No fourth class of terms exists > involving the conception of "fourth", because when that of "third" > is introduced, since it involves the conception of bringing objects > into relation, all higher numbers are given at once, inasmuch as the > conception of bringing objects into relation is independent of the > number of members of the relationship. Whether this "reason" for the > fact that there is no fourth class of terms fundamentally different > from the third is satisfactory or not, the fact itself is made > perfectly evident by the study of the logic of relatives. > (Peirce, CP 3.63). > > > > Peirce's argument invokes what is known as a "closure principle", > as I remarked in the following comment: > > What strikes me about the initial installment this time around is > its use of a certain pattern of argument I can recognize as invoking > a "closure principle", and this is a figure of reasoning Peirce uses > in three other places: his discussion of "continuous predicates", his > definition of "sign relations", and in the "pragmatic maxim" itself. > > * https://oeis.org/wiki/Continuous_predicate > * https://oeis.org/wiki/Sign_relation > * https://inquiryintoinquiry.com/2008/08/07/pragmatic-maxim/ > > In mathematics, a "closure operator" is one whose repeated application > yields the same result as its first application. > > If we take an arbitrary operator A, the result of applying A > to an operand x is Ax, the result of applying A again is AAx, > the result of applying A again is AAAx, and so on. In general, > it is perfectly possible each application yields a novel result, > distinct from all previous results. > > But a closure operator C is defined by the property CC = C, > so nothing new results beyond the first application. > Cf: The Difference That Makes A Difference That Peirce Makes : 24 At: https://inquiryintoinquiry.com/2019/09/22/the-difference-that-makes-a-difference-that-peirce-makes-24/ The concepts of "closure" and "idempotence" are closely related. We usually speak of a "closure operator" in contexts where the objects acted on are the primary interest, as in topology, where the objects of interest are open sets, boundaries, closed sets, etc. In contexts where we abstract away from the operand space, as in algebra, we tend to say "idempotence" for the detached application CC = C. (If I recall right, it was actually Charles Peirce's father Benjamin who coined the term "idempotence".) At any rate, I'll have to mutate the principle a bit to cover the uses Peirce makes of it. Regards, Jon ----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
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