Hi Kirsti, Clark: From the exchange: >> 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?
> No, CSP did not use traditional mathematical divisions into plane and solid > geometry, except as something to criticize. > Most modern logicians operate off of first order logical premise which roughly translate that logic is an algebra and algebra is a logic. Universality of meaning is, somehow or other, exchanged between algebraic symbols (signs) and logical symbols (signs). Do you believe this is possible? Do you find a method, a way, a path, a plausible conjecture that creates a bridge between algebra and logic? Many scholars (in many different fields) just assume that such a bridge exists, including CSP himself. No such bridge is known in chemistry, as far as I am aware. Of course, I agree with your assertion that > Whithin the realm of topology any plane or solid may be folded, streched and > shrunk (ect) ad infinitum. But without breaking the continuity of operations. > Thus a coffeecup and a doughnut appear as parts of SAME (as a process). (Although I would modify it slightly.) One logical consequence of the chemical symbol system is that atoms have volumes (Van der Waal’s constants in thermodynamics.) No generalized “folding, stretching, and shrinking” of these chemical symbols. Nor of chemical bonds. Chemical symbols represent a special form of logical constants that are subject to logical operations of other logical constants under the constraints of electrical attractors and repellers. That is what atomism is all about today. One of the conundrum that CSP’s logic (including his diagrams) brings to my mind is that the role of numbers is obscure and vague. How does anyone do science without numbers? Or, am I missing the point? Of course, to introduce numbers into his logic would effectively modify his notions about the role of continuity in logic and his view of the nature of chemical radicals. Tarski’s approach avoids this conundrum. See M. Malatesta, Primary Logic, 1997, Gracewing, for a detailed discussion of the history of logical forms, logical notations and Tarski’s linguistic consequences. Clark: These is a vast literature computational chemistry and it role in both stationary and transitional states. In fact my son had a paper in Science on such computations for the catalyst by gold of Carbon monoxide oxidation. Very sophisticated programs with beautiful graphics for showing molecular biological bindings are commercially available. Cheers Jerry > On Apr 6, 2016, at 3:07 AM, kirst...@saunalahti.fi > <mailto:kirst...@saunalahti.fi> wrote: > > Jerry, You wrote to me: > >> JLRC:"My purpose is mainly to align the logics in terms of Tarski’s >> meta-languages, but I will not address that here." > > KiM: If and when Tarski is your object of thought, my note is completely > irrelevant. > >> JLRC: 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? > >> > No, CSP did not use traditional mathematical divisions into plane and solid > geometry, except as something to criticize. He did re-arrange fundamental > geometry into three grades, first topology, second, perspectiv geometry, and > only after those comes meaasurement, etc. - The relation between topological > geometry and perspectival geometry are needed in order to make sensible, > meaningful and useful measurements. - This is how I have interpreted CSP. CSP > was not modern, he was definitely post-modern. > > Whithin the realm of topology any plane or solid may be folded, streched and > shrunk (ect) ad infinitum. But without breaking the continuity of operations. > Thus a coffeecup and a doughnut appear as parts of SAME (as a process). > > Tarski's metalanguages, on the other hand, appear to me definitely modern. > > In places, where you use the word "style", I would use "kind". Difference in > kinds has a different meaning than difference in styles, to my mind. But > apparently not to your mind? > > I was only talking of how to understand the graphical diagram from the ground > CSP had developed.( Nothing about Tarski.) > > Just dismiss my note, if it has no appeal to you! > > Cheers, Kirsti > > > Jerry LR Chandler kirjoitti 5.4.2016 18:13: >> 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 UNIT_y. >>> On Apr 5, 2016, at 3:50 AM, kirst...@saunalahti.fi >>> <mailto:kirst...@saunalahti.fi> 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> [1] >>> -----Original Message----- >>> From: Jerry LR Chandler [mailto:jerry_lr_chand...@icloud.com >>> <mailto:jerry_lr_chand...@icloud.com>] >>> 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 <jawb...@att.net >>>> <mailto:jawb...@att.net>> 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 >> <http://inquiryintoinquiry.com/2016/03/31/systems-of-interpretation-%E2> >>> [2] >>>> %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 >> <http://inquiryintoinquiry.com/2016/03/31/systems-of-interpretation-%e> >>> [3] >>>>> 2%80%a2-5/ >>>>> Date : March 31, 2016 at 10:24 am >>>>> Subthread: >>> MB:http://permalink.gmane.org/gmane.science.philosophy.peirce/18534 >>> <http://permalink.gmane.org/gmane.science.philosophy.peirce/18534> >>> [4] >>> EVD:http://permalink.gmane.org/gmane.science.philosophy.peirce/18540 >>> <http://permalink.gmane.org/gmane.science.philosophy.peirce/18540> >>> [5] >> JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/18552 >> <http://permalink.gmane.org/gmane.science.philosophy.peirce/18552> >>> [6] >>> JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/18553 >>> <http://permalink.gmane.org/gmane.science.philosophy.peirce/18553> >>> [7] >>> JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/18554 >>> <http://permalink.gmane.org/gmane.science.philosophy.peirce/18554> >>> [8] >>>>> 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- >> <https://inquiryintoinquiry.files.wordpress.com/2016/03/awbrey-awbrey-> >>> [9] >>>>> 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 >>>> <http://independent.academia.edu/JonAwbrey> [10] >>>> my word press blog: http://inquiryintoinquiry.com/ >>>> <http://inquiryintoinquiry.com/> [11] >>>> ----------------------------- >>>> 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 <mailto:peirce-L@list.iupui.edu> >>> . To UNSUBSCRIBE, send a message not to PEIRCE-L but to >>> l...@list.iupui.edu <mailto: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 >>> <http://www.cspeirce.com/peirce-l/peirce-l.htm> [12] . >> ----------------------------- >> 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 <mailto:peirce-L@list.iupui.edu> . To UNSUBSCRIBE, >> send a message not to >> PEIRCE-L but to l...@list.iupui.edu <mailto: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 >> <http://www.cspeirce.com/peirce-l/peirce-l.htm> [12] . >> Links: >> ------ >> [1] http://web.ncf.ca/collier <http://web.ncf.ca/collier> >> [2] http://inquiryintoinquiry.com/2016/03/31/systems-of-interpretation-%E2 >> <http://inquiryintoinquiry.com/2016/03/31/systems-of-interpretation-%E2> >> [3] http://inquiryintoinquiry.com/2016/03/31/systems-of-interpretation-%e >> <http://inquiryintoinquiry.com/2016/03/31/systems-of-interpretation-%e> >> [4] http://permalink.gmane.org/gmane.science.philosophy.peirce/18534 >> <http://permalink.gmane.org/gmane.science.philosophy.peirce/18534> >> [5] http://permalink.gmane.org/gmane.science.philosophy.peirce/18540 >> <http://permalink.gmane.org/gmane.science.philosophy.peirce/18540> >> [6] http://permalink.gmane.org/gmane.science.philosophy.peirce/18552 >> <http://permalink.gmane.org/gmane.science.philosophy.peirce/18552> >> [7] http://permalink.gmane.org/gmane.science.philosophy.peirce/18553 >> <http://permalink.gmane.org/gmane.science.philosophy.peirce/18553> >> [8] http://permalink.gmane.org/gmane.science.philosophy.peirce/18554 >> <http://permalink.gmane.org/gmane.science.philosophy.peirce/18554> >> [9] https://inquiryintoinquiry.files.wordpress.com/2016/03/awbrey-awbrey- >> <https://inquiryintoinquiry.files.wordpress.com/2016/03/awbrey-awbrey-> >> [10] http://independent.academia.edu/JonAwbrey >> <http://independent.academia.edu/JonAwbrey> >> [11] http://inquiryintoinquiry.com/ <http://inquiryintoinquiry.com/> >> [12] http://www.cspeirce.com/peirce-l/peirce-l.htm >> <http://www.cspeirce.com/peirce-l/peirce-l.htm>
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