Hello Lists, Following Peirce's classification of the different kinds of molecules that can be built from the combinations of dyads and triads that he provides in "The Logic of Mathematics", we should be able to sort out what kinds of dyadic and triadic relations obtain within and between the subjects that comprise the three correlates in a genuinely triadic relation that is governed by the laws of fact, and we should be able to say what is special about the case where the rules are mechanical in character. Having done this, we should be able to take the next step and sort out what is different in the case of the relations that obtain within and between subjects in a thoroughly genuine triadic relation involving representation.
Peirce is using this classification of kinds of relations in order to show us the possible connections that may obtain for each of the classes that he is considering--where they are being sorted along lines of relative genuineness and degeneracy. Just out of curiosity, Jon, do you take Peirce to be saying that the 3! kinds of logical relations that hold when we analyze a conception like A gives B to C is a point that applies to all genuinely triadic relations of any sort, or that it holds only for those that are thoroughly genuine, or for all genuinely triadic relations except those that are thoroughly genuine? My assumption is that Peirce is making this point as part of an argument that genuine triads can't be reduced to the component dyads that hold between the three correlates. The question is: what kind of combination or mediation is found where we have a genuinely triadic relation. This leaves open the question of what kind of combination or mediation is found in thoroughly genuine triads. Peirce makes a distinction that I find helpful for sorting through questions of this sort. In the notes he later made on his early essay on the new list of the categories, he says: "By logical relations, I mean those in respect to which all pairs [of] objects in the universe are alike; by hemilogical relations those in respect to which there is in reference to each object in the universe only one object (perhaps itself) or some definite multitude of objects which are different from others; while the alogical relations include all other cases. The logical and hemilogical relations belong to the old class of relations of reason, while relations in re are alogical. But there are a few not unimportant relations of reason which are likewise alogical. In my paper of 1867, I committed the error of identifying those relations constituted by non-relative characters with relations of equiparance, that is, with necessarily mutual relations, and the dynamical relations with relations of disquiparance, or possibly non-mutual relations. Subsequently, falling out of one error into another, I identified the two classes respectively with relations of reason and relations in re." (CP, 1.567) In our discussions of Frederik's book thus far, we've circled around the following kind of question a number of times: what are the differences between the relations that hold when something is governed by a general rule where the rule determines things in a mechanical way and the kinds of relations that obtain when the general rule determines things as a representation that functions as a purpose? I've pointed to one place where Peirce says that the difference between what is a living process and what is really just a mechanical process is better framed in terms of the kinds of dyadic and triadic relations that hold in each case. It is a better way of framing the issue because the latter kind of question is something that we can make clearer. As such, I'd like to put some weight on Peirce's distinction between a genuinely triadic relation that is governed by a law of fact and a thoroughly genuine triadic relation that is govern by a representation that is functioning as a purpose. Anyone have suggestions for how we might more clearly articulate the differences between a genuinely triadic relation that is under a general law of fact, and a thoroughly genuine triadic relation that is determined by the representation of a purpose? --Jeff Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354 ________________________________________ From: Jon Awbrey [[email protected]] Sent: Wednesday, February 04, 2015 1:40 PM To: Edwina Taborsky; Peirce List Subject: [PEIRCE-L] Re: Six Ways Of Looking At A Triadic Relation ⌬ 1 Thread: JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15622 ET:http://permalink.gmane.org/gmane.science.philosophy.peirce/15623 Edwina, As often happens I do not understand enough of your language to make much reply. Peirce says "these six sentences express one and the same indivisible phenomenon" and that much I understand to the extent that it resonates with several important lessons of my math and scientific training over the years, for example, to be on guard against the errors of "Grammar Reified As Metaphysics". That doesn't mean there are no truths of being, it just means that we have to think very critically about the metaphysical assumptions that seem to come "ready made" out of language. As far as I can understand your statement that "the reality of Mind as represented in the modal categories differentiates them by function", it doesn't appear to say anything more than what I already stipulated, namely, that those six variations on the same logical theme are "grammatically and rhetorically different". Of course the mind imagines that nuances of expression correspond to substantial differences, but that's a matter that has to be tested. Regards, Jon On 2/4/2015 2:36 PM, Edwina Taborsky wrote: > I'm not sure, Jon, what your point is, in this post. Although there may be > six 'mechanical' ways of relating three > 'logical subjects', the reality of Mind as represented in the modal > categories differentiates them by function. > > Edwina > > ----- Original Message ----- From: "Jon Awbrey" <[email protected]> > To: "Peirce List" <[email protected]> > Sent: Wednesday, February 04, 2015 1:45 PM > Subject: [PEIRCE-L] Six Ways Of Looking At A Triadic Relation ⌬ 1 > > >> Post : Six Ways Of Looking At A Triadic Relation ⌬ 1 >> http://inquiryintoinquiry.com/2015/02/04/six-ways-of-looking-at-a-triadic-relation-%e2%8c%ac-1/ >> Posted : February 4, 2015 at 1:00 pm >> Author : Jon Awbrey >> >> Peircers, >> >> Here's a triadic factoid from the 1903 Harvard Lectures on Pragmatism >> that raises a number of important questions for me. I isolated Peirce's >> observation about the "ordinary logic of relations" from the context of his >> remarks that follow, partly in order to render the puzzle more striking. >> There's better copy on my blog, and I'll copy out more as I get time. >> >> --- >> >> A triadic relation has 3! = 6 ''converses'', six grammatically and >> rhetorically different ways of representing what is >> logically the same information. Peirce illustrates the situation as >> follows, with six variations on the theme of giving. >> >> <blockquote> >> >> So in a triadic fact, say, for example >> >> A gives B to C >> >> we make no distinction in the ordinary logic of relations between the >> ''subject nominative'', the ''direct object'', and >> the ''indirect object''. We say that the proposition has three ''logical >> subjects''. We regard it as a mere affair of >> English grammar that there are six ways of expressing this: >> >> A gives B to C >> A benefits C with B >> B enriches C at expense of A >> C receives B from A >> C thanks A for B >> B leaves A for C >> >> These six sentences express one and the same indivisible phenomenon. >> >> </blockquote> >> >> References >> >> * Peirce, C.S., “The Categories Defended”, Harvard Lectures on Pragmatism : >> Lecture 3 (MS 308, delivered on 9 April >> 1903). Published in Collected Papers (CP 5.66–81, 88–92, in part), Harvard >> Lectures (HL 167–188), Essential Peirce : >> Volume 2 (EP 2, 160–178). >> >> * Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1–6, >> Charles Hartshorne and Paul Weiss (eds.), vols. >> 7–8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, >> 1931–1935, 1958. Volume 5 : Pragmatism and >> Pragmaticism, 1934. (Cited as CP). >> >> * Peirce, C.S., Pragmatism as a Principle and Method of Right Thinking : The >> 1903 Harvard Lectures on Pragmatism, >> Patricia Ann Turrisi (ed.), State University of New York Press, Albany, NY, >> 1997. (Cited as HL). >> >> Peirce, C.S., The Essential Peirce : Selected Philosophical Writings, Volume >> 2 (1893–1913), Peirce Edition Project >> (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1998. >> (Cited as EP 2). >> >> Add a comment to this post: >> http://inquiryintoinquiry.com/2015/02/04/six-ways-of-looking-at-a-triadic-relation-%e2%8c%ac-1/#respond >> -- 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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