Jon, John, Kirsti, List: First, Ok, I found the passages. My source was Roberts, Existential Graphs of CSP, p.26. Roberts cites 3.469 and 4.561.
Now to the philosophical issues and the perplexity of number theory as matter. This post should be contrasted with FS views of the role of diagrams in CSP’s writings. John: Since ammonia is a very small molecule with a small number of electrical parts, 14 to be exact, it has been deeply studied from a physical-mechanical perspective. The usual chemical representation is as a planar figure,as a representation of empirical measurements. Approximations from both quantum theory and molecular mechanics suggest a ‘flattened” TETRAHEDRAL structure, not a plane. In gas phase, the spectra data suggests that NH3 molecule flips back and forth, above and below the plane of the nitrogen nucleus, much like an umbrella flipping by strong wind. Electrically, the 14 particles are distinguished as 4 nuclei and 10 electrons. The polar opposites (nuclei and electrons) are arranged in a lattice like pattern to form an electro-neutral lattice like object. Thus, from a modern chemical perspective, NH3 is more perplex than the simple structure of introductory textbooks,. But, CSP did not have access to such data and could not have taken it into consideration. Nevertheless, the underlying concept of representation of chemical structures as stationary objects remains the same today, the same since Dalton’s precedence of 1806. It is this stationary image of whole-part relations that give chemistry its scientific identity and CSP’s logic of the particular. This stationarity of representation of numbers is, of course, one of the critical mathematical and philosophical separations of CSP’s logic from modern physical thought, where “to be is to be a variable”. Kirsti: May I re-align your wording a bit? My purpose is mainly to align the logics in terms of Tarski’s meta-languages, but I will not address that here. The meta-languages of interest here geometry, matter, number, space and time. First, geometry. Plane geometry terms: point, line, plane, closed surfaces, (triangles, squares, pentagons,…) Solid geometry - spheres, tetrahedrons, irregular forms (soccer balls and the like). Mathematical dimensionality, in its traditional form bridges plane and solid geometry - 1,2,3,..,N. Did CSP ever use traditional mathematical dimensionality in describing logic? A three dimensional tetrahedron plays a critical role in the extension of chemical thought as a mode of "filling space”. (This concept has deep inferences and deeper implications!) Compare, ammonia (NH3) with methane (CH4). The latter has five nuclei and ten electrons. The five nuclei and eight of the ten electrons can be arranged in a regular lattice-like perplex structure. The other two electrons appear to be irregular in this geometric representation. AS a consequence of these formula and similar formula, Nitrogen is assigned a valence of three and carbon a valence of four. (It is that simple!) Methane is spatially represented as a tetrahedron with the carbon atom IN THE GEOMETRIC SPATIAL CENTER. It is symmetric around the center point of the carbon nucleus. (The potential for planar asymmetry is intrinsic to the valence of four of carbon and introduces the concept of “handedness" into chemical thought. Again, this is another major distinction between the conceptualization of physical and chemical thought as a consequence of valence.) CSP’s diagram, as shown by Roberts, is a diagram on a surface with a central nitrogen and the three attached hydrogens as “spokes”, forming a unity. It is not a directed graph (not a graph of mathematical category theory.) The intent of this brief post was to shed some light on why I found the passage cited by Roberts of great interest and why I questioned Jon’s enhancements to CSP’s artwork. I hope I succeeded. Some of my generalizations in relation to certain weaknesses of CSP’s style. The philosophical conjecture is that CSP used number theory in many ways, not just the simple arithmetic of addition, subtraction, multiplication, division, roots and exponents. He sought to include CHEMICAL number theory within his mathematical logic. As well as chemical memory. His general approach to logic is characterized by his efforts to do so. Latter, Lesniewski followed the percepts of CSP, but Tarski rejected this logical style of thought and separated formal logical terms into meta-languages (see: Malatesta, The Primary Logic, 199. Modern chemical and biological logic follow both the Poles. The notation of the perplex number system captures the Lesniewski - Tarski duality. This is the "difference that makes a difference” and separates CSP's metaphysics of logic from other formal logics, other systems of beliefs about the nature of thought, such as those proposed by FS. Cheers Jerry By the way, these remarks are a further example of my simplistic metaphysics: The union of units unifies the unity. > On Apr 5, 2016, at 3:50 AM, [email protected] > <mailto:[email protected]> wrote: > > John & al > > I have a suggestion for what is missing. By mistake, I sent my suggestion > only to Jerry. But perhaps you and Jon are interested in it, as well. - So > I'll copy my note below: > > Jerry, > > I have not studied this particular triad CSP has presented. - BUT > two-dimensional diagrams never present triadicity to completion. Tree > dimensions are needed. And even then TIME is needed as the fourth dimension, > IF any reaction is to be grasped as a process. > > Try imagining the diagram in a three-dimensional space. - Triadicity is not > about triangles (as defined in plane geometry) ). - Then you will end up with > a tetraed. > > Any tetraed has FOUR turning points, four edges, as well as four triangular > planes. Projective geometry is thus needed in order to present a diagram > showing the hidden one, too. > > And then the dimension of TIME. - Phillip J. Davis & Reuben Hersh (1980) in > 'Mathematical Experience' deal with some of the mathematical problems > involved. (They do not understand triadicity, unfortunately). > > Best wishes, > > Kirsti > > > > > John Collier kirjoitti 5.4.2016 07:41: >> Thanks for the context, Jerry. I am not familiar with the passage, but >> it does seem, by your account, to be peculiar at best. I would agree >> that the standard representation of NH3 puts all of the nodes (the >> endpoints, or perhaps the branches, representing hydrogen atoms and >> the centre the nitrogen atom). This is a structure of relations, and I >> see no reason why it would need to be interpreted as a third. That is >> quite unlike the triple relation of the sign, unless we are missing >> something here, I have no idea what it might be. Your explanation >> seems plausible to me, given Peirce's (near) obsession with threes, >> but it is also such an obvious error that I can't help but wonder if >> we are missing something. >> John Collier >> Professor Emeritus and Senior Research Associate >> University of KwaZulu-Natal >> http://web.ncf.ca/collier <http://web.ncf.ca/collier> >>> -----Original Message----- >>> From: Jerry LR Chandler [mailto:[email protected]] >>> Sent: Tuesday, 05 April 2016 6:24 AM >>> To: Peirce List >>> Subject: Re: [PEIRCE-L] Re: Systems Of Interpretation >>> Jon, John: >>> Thanks, Jon. >>> The question I raised was in order to seek alternative interpretations of >>> CSP’s >>> diagram of a chemical structure, ammonia. (NH3) >>> He showed it as a triad. The nitrogen atom was in the middle of the three >>> hydrogens, each at the end of a spoke. NOT a triangle. >>> But, the chemical atoms are all of the nature and co-exist as relatives. >>> So, >>> four atoms but only a triad. >>> Why? >>> My feeling is that CSP wanted a triad so that he made one. >>> This is not a satisfactory inquiry into a diagrammatic assertion. >>> Cheers >>> Jerry >>> > On Apr 3, 2016, at 5:04 PM, Jon Awbrey <[email protected]> wrote: >>> > >>> > Peircers, >>> > >>> > Questions about the meaning of the “central hub” in the “three-spoked” >>> > picture of an elementary sign relation have often come up, just >>> > recently among Jerry Chandler's questions and a question Mary Libertin >>> > asked on my blog. >>> > Maybe the answer I gave there can help to clear that up: >>> > >>> > http://inquiryintoinquiry.com/2016/03/31/systems-of-interpretation-%E2 >>> > %80%A2-5/#comment-32800 >>> > >>> > The central “spot”, as Peirce called it [in his logical graphs], is >>> > located on a different logical plane, since it is really a >>> > place-holder for the whole sign relation or possibly for the >>> > individual triple. Normally I would have labeled it with a letter to >>> > indicate the whole sign relation, say L, or else the individual >>> > triple, say ℓ = (o, s, i). >>> > >>> > Regards, >>> > >>> > Jon >>> > >>> > On 3/31/2016 1:24 PM, Jon Awbrey wrote: >>> >> Post : Systems Of Interpretation • 5 >>> >> http://inquiryintoinquiry.com/2016/03/31/systems-of-interpretation-%e >>> >> 2%80%a2-5/ >>> >> Date : March 31, 2016 at 10:24 am >>> >> >>> >> Subthread: >>> >> MB:http://permalink.gmane.org/gmane.science.philosophy.peirce/18534 >>> >> >>> EVD:http://permalink.gmane.org/gmane.science.philosophy.peirce/18540 >>> >> >>> JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/18552 >>> >> JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/18553 >>> >> JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/18554 >>> >> >>> >> Mike, Val, Jerry, List, >>> >> >>> >> Here is the revised edition of my last comment on the order issue. >>> >> (I am hoping I can get to the rest of Jerry's questions eventually.) >>> >> >>> >> Figure 2. An Elementary Sign Relation (and see attached) >>> >> https://inquiryintoinquiry.files.wordpress.com/2016/03/awbrey-awbrey- >>> >> 1999-elementary-sign-relation.gif >>> >> >>> >> An elementary sign relation is an ordered triple (o, s, i). >>> >> It is called ''elementary'' because it is one element of a sign >>> >> relation L ⊆ O × S × I, where O is a set of objects, S is a set of >>> >> signs, and I is a set of interpretant signs that are collectively >>> >> called the ''domains'' of the relation. >>> >> >>> >> But what is the significance of that ordering? >>> >> >>> >> In any presentation of subject matter we have to distinguish the >>> >> natural order of things from the order of consideration or >>> >> presentation in which things are taken up on a given occasion. >>> >> >>> >> The natural order of things comes to light through the discovery of >>> >> invariants over a variety of presentations and representations. >>> >> That type of order tends to take a considerable effort to reveal. >>> >> >>> >> The order of consideration or presentation is often more arbitrary, >>> >> making some aspects of the subject matter more salient than others >>> >> depending on the paradigm or perspective one has chosen. >>> >> >>> >> In the case of sign relations, the order in which we take up the >>> >> domains O, S, I or the components of a triple (o, s, i) is wholly >>> >> arbitrary so long as we maintain the same order throughout the course >>> >> of discussion. >>> >> >>> >> Regards, >>> >> >>> >> Jon >>> >> >>> > >>> > -- >>> > >>> > academia: http://independent.academia.edu/JonAwbrey >>> > my word press blog: http://inquiryintoinquiry.com/ >>> > >>> > >>> > ----------------------------- >>> > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON >>> PEIRCE-L to this message. PEIRCE-L posts should go to >>> [email protected] >>> . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] >>> with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at >>> http://www.cspeirce.com/peirce-l/peirce-l.htm . >>> > >>> > >>> > >>> > > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > <mailto:[email protected]> . To UNSUBSCRIBE, send a message not to > PEIRCE-L but to [email protected] <mailto:[email protected]> with the > line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm > <http://www.cspeirce.com/peirce-l/peirce-l.htm> . > > > >
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