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[GBKR] What is the value of a weaker form of CG subsumption ?

by Damien Guichard

Hello CG-list, Thanks to László Babai graph isomorphism is known to be quasi-polynomial. Original paper : https://arxiv.org/abs/1512.03547 Live exposition : https://www.youtube.com/watch?v=r-nCYbX_Au0 This result generalizes well to hyper-graph isomorphism. Does that mean one could imagine a CoGUI version based around a weaker CG subsumption ? What would be the value of such a platform ? Regards, - damien -- Cet e-mail a été vérifié par le logiciel antivirus d'Avast. www.avast.com

1 year, 10 months

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Zeroth Law Of Semiotics

by Jon Awbrey

Cf: Zeroth Law Of Semiotics • Discussion 2 http://inquiryintoinquiry.com/2022/10/27/zeroth-law-of-semiotics-discussion… Re: Zeroth Law Of Semiotics https://inquiryintoinquiry.com/2015/07/30/zeroth-law-of-semiotics/ Re: FB | Charles S. Peirce Society https://www.facebook.com/groups/peircesociety/posts/2757776511024990/ ::: Joseph Harry https://www.facebook.com/groups/peircesociety/posts/2757776511024990?commen… <QUOTE JH:> “Meaning is a privilege not a right” would seem to be a meaningless proposition, since ‘privilege’ and ‘right’ are third-order evaluative, symbolic terms, while ‘meaning’ is a neutral second-order term, implying only existential individualized dynamic activity or process. Driving (a car) is a privilege not a right, but meaning is neither. </QUOTE> Dear Joseph, That may be too literal a reading for Zero‑Aster's poetic figure. If I read the oracle right, the contrast between “privilege” and “right” serves merely to mark the distinction between meanings optional and obligatory. Whether any hint of “private law” or “law unto itself” is intended or involved is something I would have to spend more time thinking about. Regards, Jon

1 year, 10 months

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Sign Relational Manifolds

by Jon Awbrey

Cf: Sign Relational Manifolds • 1 http://inquiryintoinquiry.com/2022/10/31/sign-relational-manifolds-1-2/ All, Riemann's concept of a manifold, especially as later developed, bears a close relationship to Peirce's concept of a sign relation. I will have to wait for my present train of thought to stop at a station before I can hop another but several recent discussions of geometry have brought this subject back to mind and I thought it might serve to drop off a few mail bags of related letters in anticipation of the next pass through this junction. Here are links to a set of excerpts from Murray G. Murphey (1961), “The Development of Peirce's Philosophy”, discussing Peirce's reception of Riemann's philosophy of geometry. Manifolds of Signs ================== https://web.archive.org/web/20150302021003/http://stderr.org/pipermail/inqu… https://web.archive.org/web/20150206000400/http://stderr.org/pipermail/inqu… https://web.archive.org/web/20150206000800/http://stderr.org/pipermail/inqu… https://web.archive.org/web/20150206000818/http://stderr.org/pipermail/inqu… Later developments of the manifold concept, looking to applications on the one hand and theory on the other, are illustrated by excerpts in the next two posts. Regards, Jon

2 years

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Abduction, Deduction, Induction, Analogy, Inquiry

by Jon Awbrey

Cf: Abduction, Deduction, Induction, Analogy, Inquiry • 31 https://inquiryintoinquiry.com/2022/10/14/abduction-deduction-induction-ana… Re: Scott Aaronson ( https://scottaaronson.blog/ ) ::: Explanation-Gödel and Plausibility-Gödel ( https://scottaaronson.blog/?p=6754 ) All, A general heuristic in problem solving suggests priming the pump with a stronger hypothesis. Applying that strategy here would have us broaden the grounds of validity, our notion of validation, from purely deductive proofs to more general forms of inference. Along that line, and following a lead from Aristotle, C.S. Peirce recognized three distinct modes of inference, called abductive, deductive, and inductive reasoning, and that way of thinking has even had some traction in AI from the days of Warren S. McCulloch on. At any rate I think it helps to view our questions in that ballpark. There’s a budget of resources and running thoughts on the matter I keep on the following page. • Survey of Abduction, Deduction, Induction, Analogy, Inquiry ( https://inquiryintoinquiry.com/2020/12/16/survey-of-abduction-deduction-ind… ) Regards, Jon

2 years, 1 month

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Re: Theme One Program • Exposition

by Jon Awbrey

Cf: Theme One Program • Exposition 5 https://inquiryintoinquiry.com/2022/06/23/theme-one-program-exposition-5/ All, Lexical, Literal, Logical ========================= Theme One puts cactus graphs to work in three distinct but related ways, called their “lexical”, “literal”, and “logical” uses. Those three modes of operation employ three distinct but overlapping subsets of the broader species of cacti. Accordingly we find ourselves working with graphs, files, and expressions of lexical, literal, and logical types, depending on the task at hand. The logical class of cacti is the broadest, encompassing the whole species described above, of which we have already seen a typical example in its several avatars as abstract graph, pointer data structure, and string of characters suitable for storage in a text file. Being a “logical cactus” is not just a matter of syntactic form — it means being subject to meaningful interpretations as a sign of a logical proposition. To enter the logical arena cactus expressions must express something, a proposition true or false of something. Fully addressing the logical, interpretive, semantic aspect of cactus graphs normally requires a mind-boggling mass of preliminary work on the details of their syntactic structure. Practical, pragmatic, and especially computational considerations will eventually make that unavoidable. For the sake of the present discussion, however, let’s put a pin in it and fast forward to the logical substance. Regards, Jon

2 years, 1 month

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Theory and Therapy of Representations

by Jon Awbrey

Cf: Theory and Therapy of Representations • 5 https://inquiryintoinquiry.com/2022/09/05/theory-and-therapy-of-representat… Re: R.J. Lipton and K.W. Regan https://rjlipton.wpcomstaging.com/about-me/ ::: Legal Complexity https://rjlipton.wpcomstaging.com/2022/09/04/legal-complexity/ <QUOTE> I do not pretend to understand the moral universe; the arc is a long one, my eye reaches but little ways; I cannot calculate the curve and complete the figure by the experience of sight; I can divine it by conscience. And from what I see I am sure it bends towards justice. 🙞 Theodore Parker https://web.archive.org/web/20200302045624/https://books.google.com/books?i… </QUOTE> All, The arc of the moral universe may bend toward justice — let's hope it does. For the logic of laws to converge on justice may take some doing on our part. Regards & Happy Labor Day, Jon

2 years, 2 months

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Cybernetics, Semiotics, Inquiry Driven Systems

by Jon Awbrey

Cf: Survey of Cybernetics • 2 http://inquiryintoinquiry.com/2022/09/08/survey-of-cybernetics-2/ All, There's an updated Survey of my blog posts pertaining to Cybernetics on the page linked above. It includes the selections and commentary I've posted so far on Ashby's Intro, which I hope to get back to one of these days, plus two series of posts reflecting on the governance of social systems in the light of cybernetic and semiotic principles. Here's the links for the series on Theory and Therapy of Representations. https://inquiryintoinquiry.com/2016/03/13/theory-and-therapy-of-representat… https://inquiryintoinquiry.com/2016/12/19/theory-and-therapy-of-representat… https://inquiryintoinquiry.com/2019/12/19/theory-and-therapy-of-representat… https://inquiryintoinquiry.com/2019/12/20/theory-and-therapy-of-representat… https://inquiryintoinquiry.com/2022/09/05/theory-and-therapy-of-representat… Regards, Jon

2 years, 2 months

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Basal Ingredients Of Society

by Jon Awbrey

Basal Ingredients Of Society • Prologue https://inquiryintoinquiry.com/2015/09/01/basal-ingredients-of-society-prol… All, I settled on the acronym BIOS to suggest the vital elements of life in society, a life in association with others, and not just any association but one whose flickers of life are sustained for more than a few vicissitudes of history. Sustainability in that life requires democracy, a society based on a distinctive form of social compact. Best Regards on this Day of Contemplation, Jon

2 years, 2 months

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Re: [PEIRCE-L] Peirce's "Proof" of Pragmatism

by John F Sowa

Jeff, Your questions about Peirce's proof of pragmatitiicsm are important. Jeff> I tend to think the later writings often build on the earlier. As such, I wonder what the later proof borrows by way of premisses from the arguments developed in the 1903 Harvard Lectures on Pragmatism. Once that is clearer, we can then ask what might have been added to the later argument by way of additional premisses. Peirce's ideas were constantly evolving up to the very end. He frequently went back to earlier ideas, but always with some new insights or directions from his later developments. For pragmaticism, his 1903 Harvard and Lowell lectures were an important starting point. And the word 'prolegomena' in 1906 is an important clue. An interesting occurrence in December 1902: Carus published a new English translation of Kant's "Prolegomena to any future metaphysics" and Peirce published a notice of it in the Nation in June 1903. -- he must have been reading (or rereading) it around the same time as he was preparing those Lectures. Peirce must have read it (in German) during the time that he and his father were studying Kant. After Kant finished the first edition of KdrV (or CdrV as Peirce preferred to refer to it), he wrote the short Prolegomena as an intro and overview of the questions that he tried to answer in the first edition of the K(C)drV. Those questions were the prelude to his second edition, which he finished a few years later. Although Peirce had criticized some of Kant's fundamental assumptions, he always had a high regard for Kant, and he cited him frequently throughout CP. And he had a very high regard for Kant's questions, which are the main topic of his own Prolegomena. If you (a) read Kant's questions and (b) read Peirce's writings from 1903 onwards, you can see a strong influence of Kant's questions on Peirce. In fact, Peirce's 1903 classification of the sciences seems to be part of Peirce's answers to K's three transcendental questions. Even stronger evidence for Kant's influence is Peirce's 1906 Apology for Pragmaticism, which is written as a prelude to a series of articles he planned for the Monist. Unfortunately, he ran into difficulties around 1909, which led him to the series of ten MSS on "Assurance" (R661 to R670) from 1910 to 1911. There's much more to be said about all these issues. I recommend an article about Peirce's Apology by Max Fisch (1982) and reprinted in a book by Fisch in 1986. In that article, Max F. wrote that methodeutic is a key topic that Peirce was addressing in his planned proof. I agree. And I also believe that there were two reasons why Peirce stopped in 1909: (1) problems with phaneroscopy as a science egg (R645) and (2) problems with logic, which were the reason for his ten studies (R661 to R670) from 1910 to 1911. These are the reasons for major revisions that Peirce made in 1911 and 1912. It's sad that he was converging on important new ideas just when he had that accident in 1911 followed by the cancer. There is, of course, much more to say about all these issues. And as Max Fisch also said, that's why we need all of Peirce's late MSS available in suitable formats. As Peirce's late letters show -- he was thinking very hard about all these issues. And he didn't hesitate to make major revisions when necessary. John

2 years, 2 months

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Theme One Program • Jets and Sharks

by Jon Awbrey

Cf: Theme One Program • Jets and Sharks 1 http://inquiryintoinquiry.com/2022/08/25/theme-one-program-jets-and-sharks-… All, It is easy to spend a long time on the rudiments of learning and logic before getting down to practical applications — but I think we've circled square one long enough to expand our scope and see what the category of programs envisioned in Theme One can do with more substantial examples and exercises. During the development of the Theme One program I tested successive implementations of its Reasoning Module or Logical Modeler on appropriate examples of logical problems current in the literature of the day. The PDP Handbook of McClelland and Rumelhart set one of the wittiest gems ever to whet one's app‑titude so I could hardly help but take it on. The following text is a light revision of the way I set it up in the program's User Guide. Example 5. Jets and Sharks ========================== The propositional calculus based on the minimal negation operator ( https://oeis.org/wiki/Minimal_negation_operator ) can be interpreted in a way resembling the logic of activation states and competition constraints in one class of neural network models. One way to do this is to interpret the blank or unmarked state as the resting state of a neural pool, the bound or marked state as its activated state, and to represent a mutually inhibitory pool of neurons A, B, C by the proposition (A , B , C). The manner of representation may be illustrated by transcribing a well-known example from the parallel distributed processing literature (McClelland and Rumelhart 1988) and working through a couple of the associated exercises as translated into logical graphs. Displayed below is the text expression of a traversal string which Theme One parses into a cactus graph data structure in computer memory. The cactus graph represents a single logical formula in propositional calculus and this proposition embodies all the logical constraints defining the Jets and Sharks data base. Display. Theme One Guide • Jets and Sharks • Log File https://inquiryintoinquiry.files.wordpress.com/2022/08/theme-one-guide-e280… To be continued … References ========== • McClelland, J.L. (2015), Explorations in Parallel Distributed Processing : A Handbook of Models, Programs, and Exercises, 2nd ed. (draft), Stanford Parallel Distributed Processing Lab ( https://web.stanford.edu/group/pdplab/ ). Online ( https://web.stanford.edu/group/pdplab/pdphandbook/ ), Section 2.3 ( https://web.stanford.edu/group/pdplab/pdphandbook/handbookch3#x7-320002.3 ), Figure 2.1 ( https://web.stanford.edu/group/pdplab/pdphandbook/jetsandsharkstable.png ). • McClelland, J.L., and Rumelhart, D.E. (1988), Explorations in Parallel Distributed Processing : A Handbook of Models, Programs, and Exercises, MIT Press, Cambridge, MA. “Figure 1. Characteristics of a number of individuals belonging to two gangs, the Jets and the Sharks”, p. 39, from McClelland (1981). • McClelland, J.L. (1981), “Retrieving General and Specific Knowledge From Stored Knowledge of Specifics”, Proceedings of the Third Annual Conference of the Cognitive Science Society, Berkeley, CA. Resources ========= • Theme One Program • User Guide https://www.academia.edu/5211369/Theme_One_Program_User_Guide • Example. Jets and Sharks https://inquiryintoinquiry.files.wordpress.com/2022/08/theme-one-guide-e280… https://inquiryintoinquiry.files.wordpress.com/2022/08/theme-one-guide-e280… Regards, Jon

2 years, 2 months

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