<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class="">Dear Joe,</div>Think again please.<div class="">It is correct that one can see how boolean patterns arise from making distinctions (if one ignores the boundary places).</div><div class="">LoF is about distinctions and the book develops a formalism that can be interpreted as boolean, but even that formalism is not boolean, as it does take into account the mark itself, the indication itself. No boolean element is both an operator and an operand at the formal level. LoF does give guidance if you follow our extensions of it, to the meaning and construction of non-boolean logics. This is a special way to proceed and of course no one claims to have a whole theory of the world based on some non-standard logic. The point of Boolean logic is not to provide a complete model of the world. The point of Boolean logic is that it guides us in working with reasoning where it makes sense to use the law of the excluded middle, as in reasoning about your bridge game or reasoning about building a bridge. Another aspect of our work is the Flagg resolution where we can absorb paradoxical elements into the primary algebra by keeping their relations without introducing contradiction. This is accomplished not by letting go of excluded middle, but by changing substitution so that the special element (e.g an @ such that <@> = @) is substituted not locally but as a whole, either all instances of @ are changed, or none of them.</div><div class=""><br class=""></div><div class="">An example of making a non-boolean logic from LoF is to add @ with <@> = @ to the LoF arithmetic where we already have < > with <<>> =. , and <><> = <>. To obtain Lukasiewicz 3-valued logic we take <>@ = @<> = <> and @@= @ Then you have <@>@ = @@= @ and so law of excluded middle in the form <P>P = <> is not satisfied. One can start with this arithmetic and find the appropriate algebra and see that it does lead to 3-valued logic. </div><div class=""><br class=""></div><div class="">There are many variations. I just discovered that the variation where @@ cancels to the identity ( @@ = ) is a powerful calculus for telling whether certain tangle closures are connected or not connected! Will talk about this next week. This shows that “non-standard logics” are not neccessarily logics at all, but mathematical structures that can be used to see farther into complex situations. GSB liked to talk about the possibilities in using imaginary boolean values. This concept includes extended logics but is subtler than that. In the preface, he suggests comparing the liar paradox to the “paradox” of the square root of negative unity: ii = -1 —> i = -1/i. (If i = 1 then i = -1 and if i = -1 then i = 1).</div><div class=""><img apple-inline="yes" id="640FD123-928E-4D6F-9E95-57AF11C1011E" width="488" height="629" src="cid:B8F1EAED-D2CA-4F0B-8D87-B4FE1023BB01" class=""></div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">I imagine that this is also the sort of passage that some people find infuriating, since he sounds like he will deliver to you the </div><div class="">Theory of Everything and you ask - where is that? But the IDEA of the imaginary value is quite extraordinary and fruitful.</div><div class="">So I say, keep looking.</div><div class=""><br class=""></div><div class="">What I would like you to see, is that you can proceed on your own with this idea. The idea is to consider the the idea of a distinction and examine how the distinctions you make or may come to find/make influence what you are and what you do.</div><div class="">Every mathematical structure is made of certain distinctions and formalisms. This attitude asks you to not stop at the given formal constructions that you use either in your mathematics or in your intellectual work. Don’t stop! Keep looking at how any given ’thing’ you are working with is given to you. This is the underpinning of a dialectic approach.</div><div class="">At that point you are working with LoF.</div><div class=""><br class=""></div><div class="">An example I had emphasized earlier is the work on knotted DNA. Do you accept that photomicrograph and say oh! It is knotted! Well that was the point of the experiment - to produce a convincing argument and evidence that DNA molecules can be knotted. But then you have to ask - how was this magic trick accomplished? How did I “see” a Knotted DNA molecule? And then you go into all the detail about how the photomicrographs are prepared and the many many questions about how a micro object can or cannot be treated as though it were large and had topological properties! For example, at the quantum level, one cannot make exact copies of quantum states. This shows you that those DNA molecules are not pure quantum. But where do you draw the line?!</div><div class=""><br class=""></div><div class="">Personally, I think that it is better to keep probing rather than to adhere to some particular system of thought. Any given system of thought or formalism is open to questioning. Now you might then ask - how do you mathematicians proceed if you are always asking everything. The answer is the same as for game players - any given work is based on some rules adopted.</div><div class="">A nice example is L. E. J. Brouwer, the founder of intuitionistic logic. He began his career and became famous for such results as the Brouwer Fixed Point Theorem which used crucially the law of the excluded middle and was proved in a non-constructive way. After he changed his mind and adopted a constructivist philosophy, he could not support his early work.</div><div class="">The rest of the community continued to support it, but Hilbert, a staunch supporter of the Cantorial view, would not support, and in fact attacked Brouwer and checkmated his career. This is the frog and mouse battle of the mathematicians. One group plays a boolean game, another a different game. The problem with philosophy is that it sometimes becomes like a religion and people believe that one has to proceed this way and not that way. And so it goes.</div><div class="">Best,</div><div class="">Lou</div><div class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Jan 26, 2025, at 4:39 AM, <a href="mailto:joe.brenner@bluewin.ch" class="">joe.brenner@bluewin.ch</a> wrote:</div><br class="Apple-interchange-newline"><div class="">
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<span style="font-size: 13pt;" class="">Dear Pedro, Lou, Terry and All,</span>
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<span style="font-size: 13pt;" class="">At the end of his note of Jan. 23, Pedro wrote:</span>
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<span style="font-size: 13pt;" class="">"I assume this at the other extreme of logical underpinnings, sorry, but in my eyes it has some relation.."</span>
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<span style="font-size: 13pt;" class="">These logics to which I have seen recent reference, especially in connection with Spencer-Brown, are all Boolean. In addition, another recent note below suggests that the processes involved are "circular".</span>
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<span style="font-size: 13pt;" class="">I submit that what is happening before our eyes is "reductionism in action". With a stroke of the pen, large swaths of reality are excluded if they follow a non-Boolean logic of the kind proposed by Boole himself in his Appendix to the <em class="">Laws of Thought. </em></span>
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<span style="font-size: 13pt;" class="">My own interpretation insures me that opposites to it are present in your approaches also, but at most as minor perturbations that can be safely ignored since that presence is primarily potentialized, swept "under the rug".</span>
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<span style="font-size: 13pt;" class="">The dialectical approach, which I claim has its grounding in the <em class="">Laws of Physics, </em>and should be discussed as following them. There are inherent in such an approach the non-standard "logical underpinnings" that Pedro correctly states are missing. My problem with trying to defend my position and correct it for the "common good" is that it has never been attacked on specific grounds. </span>
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<span style="font-size: 13pt;" class="">The problem I have with LoF inspired reasoning is that it is hopelessly Hegelian, univocal. <em class="">"Ad</em> astra <em class="">per</em> <em class="">aspera</em>" preferably in vehicles built and operated by Musk. </span>
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<span style="font-size: 13pt;" class="">To conclude, applicable logical uderpinnings of your position, Pedro, exist, and it will be in a non- or anti-LoF approach that they may be found.</span>
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<span style="font-size: 13pt;" class="">Thank you and best wishes,</span>
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<span style="font-size: 13pt;" class="">Joseph</span>
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<span style="" class="">---------- Message d'origine ----------</span>
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De : Louis Kauffman <<a href="mailto:loukau@gmail.com" class="">loukau@gmail.com</a>>
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À : "Pedro C. Marijuán" <<a href="mailto:pedroc.marijuan@gmail.com" class="">pedroc.marijuan@gmail.com</a>>
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CC : fis <<a href="mailto:fis@listas.unizar.es" class="">fis@listas.unizar.es</a>>
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Date : 25.01.2025 18:03 CET
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Sujet : Re: [Fis] "Percepts" and self-reference and meaning - [chaotic issues]
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</div> Dear Pedro,
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I would like to speak to your question again.
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You ask about the nature of the subject/person (in the LoF dialogue and/or beyond that discussion).
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Certainly that book and our discussions in language presuppose a subject like us who can read and reason and make distinctions as we make them.
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We also look out on our worlds and see other makers of distinctions in a wider sense of the term - Bacteria, Eukaryotes, Multicellulars, Mammals and their Central Nervous System, and so on. And we are always looking at these through our own eyes, and thinking about the autonomy of such subjects. Indeed we think about and work with and live in our world recognizing the autonomy of other human subjects.
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And we know that our language is a communal construction.
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Yet we each, perhaps as a construction of that language, adhere to the notion of a personal subject.
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So the nature of “personal subject” is something that we can each explore and possibly communally via language and community.
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In the book LoF and in the literature of cybernetics there is talk of the “observer”, as though we knew what this meant.
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We do not know.
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And not knowing, we can regard this notion as subject (sic) for research.
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To ask about the nature of the observer is the same (I suggest) as to ask about the nature of distinction.
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Best,
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Lou
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On Jan 23, 2025, at 1:30 PM, Pedro C. Marijuán <<a class="" href="mailto:pedroc.marijuan@gmail.com">pedroc.marijuan@gmail.com</a>> wrote:
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Dear Lou and FIS Colleagues,
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Let me ask you just a couple of questions on the subject implicit in your distinction scheme. I assume it is human, an enlightened logician. And this person makes use of an unfettered system of perception --jumping then from percepts to concepts, as you say, and achieving a higher state of consciousness and problem solving via emptiness and the Heart Sutra. Right? No thought collective instances are intervening or involved, at least directly. And no ostensible limitations are precluding advancement of thought... And about other possible 'distinctional' subjects, i.e. non-human subjects --Bacteria? Eukaryotes? Multicellulars? Mammals and their Central Nervous System?
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One could state, too succinctly, that any of these living entities have adapted to their niche by abducing or intercepting ad hoc information flows, which in the basis become sort of molecular-recognition distinctions that are processed in successive steps and finally elaborated into meanings that adaptively change the ongoing behavior and selfproduction processes. So... it is about surviving via the information flows adaptively catched from the niche, which in the human case is a social niche.
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Further, we humans have developed an amazing knowledge system of several thousand disciplines, where distinctions pile up on distinctions, assembled into theoretical constructs, experimental methods and multifarious approaches. The actual ways and means to move within that gigantic tangle have been pragmatism, traditions, and bureaucracy. Lots of the latter as we know well from the institutions in charge of knowledge handling. Right. But nowadays we have a new invitee to the chaotic "Fiesta of Knowledge": AI.
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In what extent this new invitee will get free of the most conspicuous knowledge limitations of our individual minds? What kind of information flows will enter into its gut and what kind of new 'meanings' will be produced? Unfortunately, almost nobody is interested in the nuclear matter that has forced us into a Babel of spattering disciplines, into unending explanatory/'translatory' exchanges: our entrenched cognizing limitations. We prefer, and take refuge into, the security of the well-framed 'microscope'.
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I assume this at the other extreme of logical underpinnings, sorry, but in my eyes it has some relation...
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Best--Pedro
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El 20/01/2025 a las 8:46, Louis Kauffman escribió:
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Dear Jason,
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I have already answered this in some other ways, but lets try again.
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Diagrams
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(a) A diagram is not particularly static. It could be a movie or an injunction to make a movie.
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It could be a dance or a ritual, a temple or a war.
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That is how you might view the diagrams about topology of DNA recombination.
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And it is in that mode that diagrammatic work and the possibility of creating a diagram from the “microword” by electron microscopy, led to the understandings about
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Knotted DNA and topological enzymes. These in turn have had an effect at some medical levels since if your topo enzymes do not work, your cells cannot divide and you die.
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<a class="" href="https://urldefense.com/v3/__https://www.excedr.com/resources/topoisomerase-overview*:*:text=In*20pharmaceuticals*2C*20topoisomerases*20are*20used,anticancer*20therapeutics*20other*20than*20chemotherapy__;I34lJSUlJSUlJSU!!D9dNQwwGXtA!VN3_KOI3NVnHHrQCUBhk-CmKe_3eXVjVC6CDnsTgT_aqTDe_YRSaOTbYTVnZXUUn-RfO2h_ygvadEF65$">https://www.excedr.com/resources/topoisomerase-overview#:~:text=In%20pharmaceuticals%2C%20topoisomerases%20are%20used,anticancer%20therapeutics%20other%20than%20chemotherapy</a>.
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So here you have a real example of how diagrammatic topological mathematics is closely allied with applications that can save lives.
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(b) For the design of quantum algorithms and all things quantum field theoretic we use diagrams quite intensively.
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The same is true for working out the reactions that lead to the bomb. So diagrams can also be used to kill en masse, as can all of language.
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(c) Written language is a work of diagrams. Those little characters you string together are stylized diagrams, rather static by themselves. And if you live in China or Japan your
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Language is an incredible pastiche of diagrams.
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(d) Actually all of mathematics is a pastiche of diagrams for all sorts of conceptual and calculational purposes.
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(e) I refer you to C.S. Peirce for the role of diagrams and signs in thought.
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(f) The greatest masters of diagrams in Cybernetics were Strafford Beer and Humberto Maturana. Perhaps you see some value in their work.
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(f) The GUI that began with Mac and infiltrated PC is the
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diagrams of finitely nested boxes
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that are the basis of the distinctions and indications of LOF.
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LOF is about distinctions and indications.
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Its diagrams are just a particular representation of that.
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Mac uses these diagrams and never had to pay any royalties to GSB.
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Religion
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(g) The Heart Sutra explains clearly how to use the unmarked state (emptiness) to solve all human problems.
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That it has not been applied to this end is not the fault of either GSB or the Buddha.
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(h) I am aware that no matter what I say,
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someone will complain
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about something
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that comes up for them
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when we get near to no-thing.
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That is the nature of it.
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Believe it or not,
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I am not an advocate of the absolute binary distinction.
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It is in contrast to what cannot be said.
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See the quote below that fell into my email from Malcolm Dean.
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<span class="" style="font-size: x-small; font-style: italic;"><a class="" href="https://urldefense.com/v3/__https://books.google.com/books?id=oI9hwgEACAAJ__;!!D9dNQwwGXtA!VN3_KOI3NVnHHrQCUBhk-CmKe_3eXVjVC6CDnsTgT_aqTDe_YRSaOTbYTVnZXUUn-RfO2h_yggIa9BkE$">https://books.google.com/books?id=oI9hwgEACAAJ</a> </span><a class="" href="https://urldefense.com/v3/__https://bleuje.com/mp4set/2019/2019_25.mp4__;!!D9dNQwwGXtA!VN3_KOI3NVnHHrQCUBhk-CmKe_3eXVjVC6CDnsTgT_aqTDe_YRSaOTbYTVnZXUUn-RfO2h_ygkOzwPOE$" target="_blank" rel="noopener">GIF by <span class="gmail-il">Etienne</span> <span class="gmail-il">Jacob</span></a><em class=""> used to illustrate Bits forming an Information process.</em>
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"The <strong class="">tentative and non-black-and-white nature of categorization</strong> is inevitable, and yet <strong class="">the act of categorization often feels perfectly definite and absolute</strong> to the categorizer, since many of our most familiar categories seem on first glance to have <strong class="">precise and sharp boundaries</strong>, and this naïve impression is encouraged by the fact that people’s everyday, run-of-the mill use of words is seldom questioned; in fact, every <strong class="">culture constantly, although tacitly, reinforces the impression that words are simply automatic labels that come naturally to mind and that belong intrinsically to things and entities</strong>. If a category has fringe members, they are made to seem extremely quirky and unnatural, suggesting that nature is really <strong class="">cut precisely at the joints by the categories that we know</strong>. The resulting illusory sense of the <strong class="">near-perfect certainty and clarity of categories</strong> gives rise to much confusion about categories and the mental processes that underlie categorization. The idea that category membership always comes in shades of gray rather than in just black and white <strong class="">runs strongly against ancient cultural conventions</strong>and is therefore disorienting and even disturbing; accordingly, it gets swept under the rug most of the time."
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(i) Oh, and what did you think Hofstader was about?
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Did you think that he was bragging about the clarity and perfection of logic?
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He was telling you the story of how logic in the hands of human understanding
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slayed the Jabberwock of the completeness of formality.
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Don’t worry. You are not the only one who did not listen.
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We sell you fake word makers to do your job.
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And in the year of our T, you can buy cryptocurrency, watches and bibles from your leader.
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<em class="ydp72b1ecb8yiv5762753745">"<a class="ydp72b1ecb8yiv5762753745" href="https://urldefense.com/v3/__https://gutenberg.net.au/ebooks01/0100021.txt__;!!D9dNQwwGXtA!VN3_KOI3NVnHHrQCUBhk-CmKe_3eXVjVC6CDnsTgT_aqTDe_YRSaOTbYTVnZXUUn-RfO2h_yglukToEj$" target="_blank" rel="noopener">It was one of those pictures</a> which are so contrived that the eyes follow you about when you move."</em>
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Best,
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Lou
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