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C.S. Peirce, Spencer Brown, & Me
Cf: Charles Sanders Peirce, George Spencer Brown, and Me
https://inquiryintoinquiry.com/2017/07/19/charlessanderspeircegeorgespencerbrownandme/ Dear Laws of Form Group, Here's an expanded version of my initial post to the old group. I'll use it partly as a test but also to anchor whatever posts from the original series still seem relevant and anything else I might have to say along the same lines. ⁂ James Bowery left a comment on my blog and opened a thread in the Yahoo! group devoted to discussing the mathematics of George Spencer Brown’s Laws of Form. I’ve been meaning to join that discussion as soon as I could work up the time and concentration to think about it — at long last I think I can do that now. I’ll use the above heading to blog any bits from my side of the conversation I think might serve a wider audience. It’s been a long time since I joined a new discussion group so I thought I’d start by posting a bit of the oldfashioned selfintro. Regards, Jon inquiry into inquiry: https://inquiryintoinquiry.com/ academia: https://independent.academia.edu/JonAwbrey oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 11
http://inquiryintoinquiry.com/2021/01/18/charlessanderspeircegeorgespencerbrownandme11/ All, There's a new “Laws of Form” group in town. James Bowery et al. have just revived the earlier group on a new platform and everything looks pretty handy so far. There's an honesttogoodness 60s vibe about it for me since it's wellknown to those in the know how Spencer Brown's work builds on Peirce's, not just because his calculus of indications resurrects aspects of Peirce's alpha level logical graphs but because the broader scope of his interests touched on inductive reasoning and the whole welter of knotty tangles in the pragmatics of communication, computation, concept formation which Ashby, Arbib, Bateson, Korzybski, R.D. Laing, McCulloch, Peirce, Polanyi, Watzlawick, and others probed in the matrix of quasiparadoxes and games people play with symbols. All of which inspires me to revise and extend the series of posts I shared with the old group a few years back, fixing in passing the large number of now broken links. Regards, Jon inquiry into inquiry: https://inquiryintoinquiry.com/ academia: https://independent.academia.edu/JonAwbrey oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 1
https://inquiryintoinquiry.com/2017/07/20/charlessanderspeircegeorgespencerbrownandme1/ All, Here's a piece of CSPGSB related biography I shared with the previous Laws of Form group when I signed on a few years ago. ⁂ It’s almost 50 years now since I first encountered the volumes of Peirce’s Collected Papers in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown’s Laws of Form in the Whole Earth Catalog and I sent off for it right away. I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, converting graphtheoretic data structures formed on their ideas to good purpose in the mechanics of its propositional reasoning engine. I thought it might contribute to a number of ongoing discussions if I could articulate what I think I learned from that experience. Regards, Jon


BAD T
Hi,
toggle quoted messageShow quoted text
Does anybody could help me on Luhmann's idea of Form and Medium? Is there any research discussed on such topic? Regards


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 2
https://inquiryintoinquiry.com/2017/07/21/charlessanderspeircegeorgespencerbrownandme2/ All, Here's a lightly revised, linkrepaired edition of a previous post. ⁂ I’m making an effort to present this material in a more gradual and logical order than I’ve ever managed to do before. There are issues about the relationship between episodic and semantic memory that are giving me trouble as I try to remember how I came to look at things the way I do … but never mind that now. I’ll eventually get around to explaining the forces that drove me to generalize the forms of logical graphs from trees to cacti, as graph theorists call them, and how that made the transition to differential logic so much easier than it would have been otherwise, but I think it would be better now to begin at the beginning with the common core of forms introduced by CSP and GSB. Here’s a couple of articles I wrote for that purpose: Logical Graphs https://oeis.org/wiki/Logical_Graphs Propositional Equation Reasoning Systems https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems There are versions of those articles at several other places on the web which may be better formatted or more convenient for discussion: Logical Graphs (Wikiversity) https://en.wikiversity.org/wiki/Logical_graph Logical Graphs (Inquiry Blog) 1. https://inquiryintoinquiry.com/2008/07/29/logicalgraphs1/ 2. https://inquiryintoinquiry.com/2008/09/19/logicalgraphs2/ One big issue arising at the beginning is the question of “duality”. Both C.S. Peirce and Spencer Brown understood they were dealing with a “very abstract calculus”, one which could be interpreted for the purposes of ordinary propositional logic in two different ways. Peirce called the two different ways of interpreting the abstract graphs his “entitative” and “existential” graphs. He started out with a system of graphs he opted to interpret in the entitative manner but switched over to the existential choice as he developed his logical graphs beyond the purely propositional level. Spencer Brown elected to emphasize the entitative reading in his main exposition but he was very clear in the terminology he used that the forms and transformations themselves are independent of their interpretations. Table 1 at either of the locations linked below has columns for the graphtheoretic forms and the parenthesisstring forms of several basic expressions, reading them under the existential interpretation. Table 1. Syntax and Semantics of a Calculus for Propositional Logic a. https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Appendices#Table_1._Syntax_and_Semantics_of_a_Calculus_for_Propositional_Logic b. https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Cactus_Language_for_Propositional_Logic The Tables linked below serve to compare the existential and entitative interpretations of logical graphs by providing translations into familiar notations and English paraphrases for a few of the most basic and commonly occurring forms. Table A. Existential Interpretation https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Appendices#Table_A._Existential_Interpretation Table B. Entitative Interpretation https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Appendices#Table_B._Entitative_Interpretation Table C. Dualing Interpretations https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Appendices#Table_C._Dual_Interpretations Regards, Jon


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 3
https://inquiryintoinquiry.com/2017/07/31/charlessanderspeircegeorgespencerbrownandme3/ All, Here's the next installment in my biographical intro, with all the links repaired and the graphics upgraded. Re: Laws of Form https://groups.io/g/lawsofform/topic/c_s_peirce_spencer_brown/79916661 There are a number of “difficulties at the beginning” that arise here. I’ve been trying to get to the point where I can respond to James Bowery’s initial comments https://inquiryintoinquiry.com/2016/11/30/timetopologydifferentiallogic6/#comment33608 and also to questions about the relation between Spencer Brown’s imaginary logical values and the development of differential logic. The larger issue I see at this point has to do with the relationship between the “algebra” and the “arithmetic” of logical graphs. Peirce came right up to the threshold of discovering that relationship several times in his later work on existential graphs but never quite pushed it through to full realization. It was left to Spencer Brown to bring it to light. The relationship between Primary Arithmetic and Primary Algebra is discussed in the following article. Logical Graphs ( https://oeis.org/wiki/Logical_Graphs ) • Primary Arithmetic as Semiotic System https://oeis.org/wiki/Logical_Graphs#Primary_arithmetic_as_semiotic_system • Primary Algebra as Pattern Calculus https://oeis.org/wiki/Logical_Graphs#Primary_algebra_as_pattern_calculus The other issue has to do with my using a different J₁ than Spencer Brown. I believe I even called it J₁′ in the early days but eventually lost the prime as time went by. As far as I can remember, it initially had to do with negotiating between the systems of C.S. Peirce and Spencer Brown but I think I stuck with the variant because it sorts the types of change — modifying structure and moving variables — into different bins. Image Files =========== This Blog I₁ : https://inquiryintoinquiry.files.wordpress.com/2020/09/axiomi1.jpg I₂ : https://inquiryintoinquiry.files.wordpress.com/2020/09/axiomi2.jpg J₁ : https://inquiryintoinquiry.files.wordpress.com/2020/09/axiomj1.jpg J₂ : https://inquiryintoinquiry.files.wordpress.com/2020/09/axiomj2.jpg Oeis Wiki I₁ : https://oeis.org/wiki/File:Initial_I1.jpg I₂ : https://oeis.org/wiki/File:Initial_I2.jpg J₁ : https://oeis.org/wiki/File:Initial_J1.jpg J₂ : https://oeis.org/wiki/File:Initial_J2.jpg See also the discussions at the following locations. Logical Graphs • Formal Development https://inquiryintoinquiry.com/2008/09/19/logicalgraphs2/ Propositional Equation Reasoning Systems https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems Regards, Jon


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 4
https://inquiryintoinquiry.com/2017/08/06/charlessanderspeircegeorgespencerbrownandme4/ All, Two things that had a big impact on my studies of Peirce and Spencer Brown over the years were my parallel studies in mathematics and computer science. In the overlap between those areas came courses in logic, mathematical linguistics, and the theory of formal languages, grammars, and automata. My intellectual wanderings over a nineyear undergraduate career would take me through a cycle of majors from math and physics, to communication, psychology, philosophy, and a crosscultural liberal arts program, then back to grad school in mathematics. The puzzles Peirce and Spencer Brown beset my brain with were a big part of what drove me back to math, since I could see I had no chance of resolving them without learning a lot more algebra, logic, and topology than I had learned till then. Resources ========= Prospects for Inquiry Driven Systems https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#Bibliography Mathematical Notes https://oeis.org/wiki/User:Jon_Awbrey/Mathematical_Notes Regards, Jon


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 5
https://inquiryintoinquiry.com/2017/08/12/charlessanderspeircegeorgespencerbrownandme5/ All,  Continuing the salvage and update of posts lost when Yahoo! Groups defuncted.  That's just the way the internet cookie crumbles when capitalism incorpulent  takes over the web that a scienceminded ARPA once built at taxpayer expense. Peirce's Law Proof Animation https://inquiryintoinquiry.files.wordpress.com/2012/01/peirceslaw20animation.gif Here are blog and wiki versions of an article I wrote on Peirce’s Law, an axiom or theorem (depending on your choice of logical basis) which distinguishes classical from intuitionistic propositional calculus. Aside from its pivotal logical status it affords a nice illustration of several important features of logical graphs in the style of Peirce and Spencer Brown. Peirce’s Law ============ • Inquiry Blog ( https://inquiryintoinquiry.com/2008/10/06/peirceslaw/ ) • OEIS Wiki ( https://oeis.org/wiki/Peirce%27s_law ) • MyWikiBiz ( http://mywikibiz.com/Peirce';s_law ) • Wikiversity ( https://en.wikiversity.org/wiki/Peirce';s_law ) Here's another resource on the relationship between Classical and Intuitionistic Propositional Calculus: Propositions As Types Analogy • https://oeis.org/wiki/Propositions_As_Types_Analogy Regards, Jon


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 6
https://inquiryintoinquiry.com/2017/08/18/charlessanderspeircegeorgespencerbrownandme6/ Cf: Logical Graphs https://oeis.org/wiki/Logical_Graphs All, The formal system of logical graphs is defined by a foursome of formal equations, called “initials” when regarded purely formally, in abstraction from potential interpretations, and called “axioms” when interpreted as logical equivalences. There are two “arithmetic initials” and two “algebraic initials”, as shown below. Arithmetic Initials =================== Figure I₁ https://inquiryintoinquiry.files.wordpress.com/2020/09/axiomi1.png Figure I₂ https://inquiryintoinquiry.files.wordpress.com/2020/09/axiomi2.png Algebraic Initials ================== Figure J₁ https://inquiryintoinquiry.files.wordpress.com/2020/09/axiomj1.png Figure J₂ https://inquiryintoinquiry.files.wordpress.com/2020/09/axiomj2.png Spencer Brown uses a different formal equation for his first algebraic initial — where I use “a (a) = ( )” he uses “(a (a)) = ”. For the moment, let’s refer to my J₁ as J_1a and his J₁ as J_1b and use that notation to examine the relationship between the two systems. It is easy to see that the two systems are equivalent, since we have the following proof of J_1b by way of J_1a and I₂. a a oo  @ =======J1a {delete} oo  @ =======I2 {cancel} @ =======QED J1b In choosing between systems I am less concerned with small differences in the lengths of proofs than I am with other factors. It is difficult for me to remember all the reasons for decisions I made forty or fifty years ago — as a general rule, Peirce’s way of looking at the relation between mathematics and logic has long been a big influence on my thinking and the other main impact is accountable to the nuts and bolts requirements of computational representation. But looking at the choice with present eyes, I think I continue to prefer the {I₁, I₂, J_1a, J₂} system over the alternative simply for the fact it treats two different types of operation separately, namely, changes in graphical structure versus changes in the placement of variables. Regards, Jon


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 7
https://inquiryintoinquiry.com/2017/08/21/charlessanderspeircegeorgespencerbrownandme7/ All, Here's an icebreaker on the question of logical boundaries ... A statement P that implies both Q and ¬Q is called a false statement, and anyone can prove anything at all from a false statement, as we all too frequently observe on the political front these days. There is however a reasonable way of handling boundaries, for instance, as illustrated by the circumference of a region in a venn diagram, and that is by means of differential logic. I’ve been tortoising my way toward the goal line of explaining all that, and it’s going a bit slow, but there’s a gentle introduction at the other end of the link below, if you wish to achilles ahead. Differential Propositional Calculus • Part 1 https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1 Regards, Jon


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 8
https://inquiryintoinquiry.com/2017/08/22/charlessanderspeircegeorgespencerbrownandme8/ Re: Boundary Logic For me, the heart of the matter is “what is the purpose of logic and what is the purpose of mathematics and what is their relationship?” There are semiotic situations which appear to violate the initial conditions of logic but there are ways of approaching them without reducing our brains to jelly from the getgo. Charles S. Peirce, following on Aristotle’s negotiation of the boundary between logic and rhetoric, developed his theory of triadic sign relations in large part to manage just these sorts of situations. I’m determined to keep my gnosis close to the grinstone for the time being but here is a smattering of old notes which give a hint as to Peirce’s way of approaching the question. C.S. Peirce on “General” and “Vague” https://oeis.org/wiki/User:Jon_Awbrey/EXCERPTS#Excerpt_6._Peirce_.28CP_5.448.29 https://cs.nyu.edu/pipermail/fom/2009March/thread.html#13437 1. https://cs.nyu.edu/pipermail/fom/2009March/013437.html 2. https://cs.nyu.edu/pipermail/fom/2009March/013446.html 3. https://cs.nyu.edu/pipermail/fom/2009March/013448.html Regards, Jon


Jon,
We are sentient beings inside a large, but finite Universe. The Laws of Form tell us that there can be no distinction without intent or motive. How can we determine the motive of the Creator of the Universe? The answer is that the CotU would have to cause an artifact or artifacts to appear in the Universe that would tell us His motive. He would have to structure that artifact so that when GSB finally came around to "discovering" the Laws of Form, it would be obvious that is was the correct artifact to use. I postulate that the artifact is the Hebrew Scriptures which tell us that the CotU created an "inhabited World" full of living things, and living beings. That He created "Man" as a Living Being that He could work with to develop His Universe. That He arranged the evolution of the Universe so that the Beings who believe in Him and follow His Commandments would be separated from those who believe they know better. My advice is to everyone is to stay as close to the Scriptures as is possible when exploring the motives of the CotU. I am advocating this as a matter of "Science" not "Religion" and as a way of identifying "False Science" and "False Religions" that will lead one to Perdition. For example, any "science" that postulates a Universe without "Motive" is a "False Science". Here is what I have written on this so far. My next topic will be to "for any boundary, to recross is not to cross." It turns out that this has sociological and salvational implications Best regards, Lyle. https://www.scribd.com/document/470732777/UnifiedTheoryofEverything


rsmyth64
Lyle, I took a quick glance at your scribd document. I don't agree with a couple of things: 1. You write, "For a particular theory or hypothesis to become socially accepted, experiments usually need to be repeated by other investigators. This research is easy to arrange if the experiment supports, or advances the currently acceptable “scientific” theory. However, when a particular theory reaches the status of scientific dogma, then any experiment that questions the dogma will be hard to conduct and if it is conducted then the experimenter being treated as a heretic to a religious system." (p. 2) Here you are trying to argue that science is equivalent to religion. There is nothing that is farther from the truth. You are correct about entrenched theory becoming "dogma" or, what Thomas Kuhn, in his THE STRUCTURE OF SCIENTIFIC REVOLUTIONS, would call a paradigm. But if you read Kuhn  and if you haven't yet, you really need to, as it provides a basic understanding of how science works that your writing lacks  you would see that the scientific method provides a process for coming to a consensus around the emergent paradigm that challenges the old dogma. He provides many excellent examples. The problem with religion is that you could argue all you want with someone about an assertion/belief, providing as much evidence as you can, and still not change his/her mind... I should point out that the example of calling out a "global warming denier" that follows this passage (especially in examining at time frame as short as 18 years) as an example of "scientific dogma" or "the religion of science" is incredibly problematic. 2. You write, "The most important original source is the Holy Scriptures themselves. Once you begin to believe
in the Bible as the Word of the CotU, you will begin to read and study it under the guidance of the Presence (aka Spirit) of the CotU. This is not a religious assertion. This is a scientific assertion of how the universe actually works." (p. 4) It is not religious assertion to say that the Bible is the Word of the CotU? This is a "scientific assertion of how the universe actually works"?!! If it's scientific, there would be an experimental basis for proving it right or wrong, or replicating the process. I hesitate to comment on this, for I suspect that these topics lie far outside of the interests of most people in this group. Richard
On Wednesday, January 27, 2021, 02:20:56 PM EST, Lyle Anderson <lylephone@...> wrote:
[Edited Message Follows] Jon,We are sentient beings inside a large, but finite Universe. The Laws of Form tell us that there can be no distinction without intent or motive. How can we determine the motive of the Creator of the Universe? The answer is that the CotU would have to cause an artifact or artifacts to appear in the Universe that would tell us His motive. He would have to structure that artifact so that when GSB finally came around to "discovering" the Laws of Form, it would be obvious that is was the correct artifact to use. I postulate that the artifact is the Hebrew Scriptures which tell us that the CotU created an "inhabited World" full of living things, and living beings. That He created "Man" as a Living Being that He could work with to develop His Universe. That He arranged the evolution of the Universe so that the Beings who believe in Him and follow His Commandments would be separated from those who believe they know better. My advice is to everyone is to stay as close to the Scriptures as is possible when exploring the motives of the CotU. I am advocating this as a matter of "Science" not "Religion" and as a way of identifying "False Science" and "False Religions" that will lead one to Perdition. For example, any "science" that postulates a Universe without "Motive" is a "False Science". Here is what I have written on this so far. My next topic will be to "for any boundary, to recross is not to cross." It turns out that this has sociological and salvational implications Best regards, Lyle. https://www.scribd.com/document/470732777/UnifiedTheoryofEverything


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 9
https://inquiryintoinquiry.com/2017/08/22/charlessanderspeircegeorgespencerbrownandme9/ Re: Boundary Logic A wider field of investigation opens up at this point, spanning the diversity of interactions among languages we use, and systems of signs in general, to the thoughts ever streaming through our heads, to the universes we talk and think upon, from Plato’s Heaven to Gaia’s Green Earth to the Tumbling Galaxies Beyond. The complexities in play when we consider a domain of Signs, a domain of Ideas, and a domain of Objects all wound up in relationship to one another is what Peirce’s “semiotics” or theory of sign relations is all about. Viewing the enterprise of logic within the broader frame of semiotics not only gives us more insight into its means and ends but affords us more “elbow room” for carrying out its operations. To make a long story short, we don’t have to “escape language” because we don’t live inside any language or system of signs, even if we get so confused sometimes as to think we do. We live in that wider world of reality and only use languages and other systems of signs to describe what little we can of it. Regards, Jon


Lyle Anderson
Dear Richard,
You are the second person who has had an adverse reaction to that paragraph. The other was Stan Tenen who let me review early drafts of his book "The Alphabet That Changed the World." That is where I first encountered George SpencerBrown and "Laws of Form." He wasn't able to get beyond what he said was an attack on "Science," so coupled with your reaction, I think I will take that out. Thank you. My study of science of Neurolinguistic Programming tells me that "the meaning of the communications it the response it elicits." The response I am seeking is to have people consider the idea that the Hebrew Scriptures are the main way that the Creator of the Universe communicated His motive for creating the Universe. Trying to do this without evoking religious stereotypes and prejudices is hard. For example, I have been struggling with having to describe "the cross." It is the Second Axiom in Laws of Form. Without it there is nothing. How can I convey the idea that when Jesus said, "Pick up your Cross, and follow me" He was making a mathematical statement? I would appreciate any ideas or suggestions that you , or anyone in the group, might have on how to do that. Answering the question "Why are we here?" is the only thing that has lasting importance. Best regards, Lyle


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 10
https://inquiryintoinquiry.com/2017/08/25/charlessanderspeircegeorgespencerbrownandme10/ All, With any formal system it is easy to spend a long time roughing out primitives and reviewing first principles before getting on to practical applications, and logical graphs are no different in that respect. But the promise of clearer and more efficient methods for solving realistic problems is what led me to the visual calculi of Peirce and Spencer Brown in the first place, so my aim through all our rehearsal of rudiments is to make a bridge to applications a few steps closer to what the real world throws our way. I’ve been thinking how to make the transition from basic ingredients of logical graphs and laws of form to slightly more interesting examples, still “toy worlds” as AI folk call them but suggestive to some degree of what might be possible in the long run. I’ll spend a few days gathering assorted examples I’ve worked up before and try presenting those. Regards, Jon


Lyle Anderson
This Thesis, "Systematic Analysis of Algorithms" that I wrote forty years ago may be of interest to the group. I found an algorithm for systematically analyzing Jonassen's and Knuth's celebrated "Trivial Algorithm Whose Analysis Isn't" by introducing (on page 42) a new kind of "delta function" that I modestly called the Anderson Delta. This new delta function is closely related to the Kronecker and Dirac delta functions, except that its domain is a Boolean space with possible values True and False. The Anderson delta maps the Boolean space into the numbers 0 and 1.
I am still amazed what we were able to do with PDP8 based word processors and spinwriter "printers". https://digitalcommons.uri.edu/cgi/viewcontent.cgi?article=2175&context=theses


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 14
https://inquiryintoinquiry.com/2021/01/31/charlessanderspeircegeorgespencerbrownandme14/ Re: C.S. Peirce, Spencer Brown, and Me • 11 https://inquiryintoinquiry.com/2021/01/18/charlessanderspeircegeorgespencerbrownandme11/ Re: Laws of Form https://groups.io/g/lawsofform/topic/c_s_peirce_spencer_brown/79946926 ::: Dirk Baecker https://groups.io/g/lawsofform/message/24 <QUOTE DB:> Watzlawick's request for a pragmatic calculus of communication up to now was never appropriately answered. W. Barnett Pearce and Vernon E. Cronen (Communication, Action, and Meaning : The Creation of Social Realities, 1980) did important studies on this as did Anthony Wilden (System and Structure : Essays in Communication and Exchange, 1972), but we still lack it. </QUOTE> Dear Dirk, Watzlawick's request for a pragmatic calculus of communication recalls McCulloch's earlier question whether the human capacity for insightful learning and reasoning demands a grasp of transdyadic relations, or not. <QUOTE McCulloch> But the problem of insight, or intuition, or invention — call it what you will — we do not understand, although many of us are having a go at it. […] Tarski thinks that what we lack is a fertile calculus of relations of more than two relata. I am inclined to agree with him, and if I were now the age I was in 1917, that is the problem I would tackle. ⁂ That process of insight by which a child learns at least one logical particle, “neither” or “not both”, when it is given only ostensively — and one must be so learned — is still a little beyond us. It may perhaps have to wait for a potent logic of triadic relations, but I now doubt it. (McCulloch, p. 15). </QUOTE> The way I see things today, my motto would be “Context Precedes Calculus” if I had to sum it up as briefly as possible. In other words, the first order of business is finding the right context for understanding the phenomena and problems at hand. As far as the human capacity for conversing with nature and our fellows goes, pragmatic thinkers informed by Peirce would no doubt point to the context of triadic sign relations and declare, “Eureka! This Must Be the Place.” References ========== • McCulloch, Warren S. (1961), “What Is a Number that a Man May Know It, and a Man, that He May Know a Number?”, Ninth Alfred Korzybski Memorial Lecture, General Semantics Bulletin, Numbers 26 and 27, pp. 7–18, Institute of General Semantics, Lakeville, CT. Reprinted in Embodiments of Mind, pp. 1–18. Online: 1. http://www.vordenker.de/ggphilosophy/mcculloch_whatisanumber.pdf 2. http://www.generalsemantics.org/wpcontent/uploads/2011/04/gsb2627mcculloch.pdf • McCulloch, Warren S. (1965), Embodiments of Mind, MIT Press, Cambridge, MA.


Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 15
http://inquiryintoinquiry.com/2021/02/05/charlessanderspeircegeorgespencerbrownandme15/ Re: C.S. Peirce, Spencer Brown, and Me • 11 https://inquiryintoinquiry.com/2021/01/18/charlessanderspeircegeorgespencerbrownandme11/ Re: Ontolog Forum https://groups.google.com/g/ontologforum/c/8HfnSonFrY ::: Michael DeBellis https://groups.google.com/g/ontologforum/c/8HfnSonFrY/m/h97uRlBEAgAJ <QUOTE MDB:> I've just started taking Peirce seriously in the last year or so and some of his more complex ideas still aren't completely clear to me but here goes: Has anyone come up with an OWL upper model (i.e., something like the upper models in Cyc and BFO) based on Peirce's work? I've come to appreciate Peirce as a major figure in the history of logic, information theory, semiotics, etc. but I've never quite been able to map his ideas into a logical model in OWL. I'm not sure if this is because trying to do so isn't consistent with what Peirce is trying to do or just that I still haven't grasped his ideas completely. Or perhaps the subset of FOL that OWL supports isn't powerful enough to map to Peirce. At an initial reading it seems like there should be a good fit because (at least as I understand it) one of Peirce's core ideas of symbols (as opposed to icons or indexes) seems like a perfect fit to the triple model (Subject Predicate Object) that is the foundation (RDF/RDFS) for OWL. Would like to know your opinions on this. </QUOTE> Dear Michael, Google still reminds me I spent some time on the RDFLogic List ( https://lists.w3.org/Archives/Public/wwwrdflogic/ ) back around the turn of the millennium (January 2001 ) ( https://www.w3.org/Search/Mail/Public/search?hdr1name=from&;hdr1query=Jon+Awbrey&indexgrp=Public_FULL&indextype=t&typeindex=wwwrdflogic&resultsperpage=40&sortby=dateasc ). I was especially intrigued by the prospect of using triples as a fundamental data structure. Now the (subject, verb, object) triples of RDF and the (object, sign, interpretant) triples of Peirce's semiotics are ostensibly different data types in their concrete descriptions but that may not obstruct integration too much if the triples are defined abstractly enough and implemented polymorphically enough. As far as I can remember, though, the concrete connotations tended to get in the way of crosscultural or transsilo communication at that time. That is not, however, the largest obstacle to harmonizing the logic of Peirce with the ways of FOL as she is spoke today. I'll take that up when I next get a chance ... Regards, Jon

