Talk:Laws of Form/Archive 1

Older discussions and comments
Philip Meguire, 22.10.05: I am now the author of most of this entry, while being none of mathemacian, logician, or philosopher. I respect the Laws of Form, seeing them as a major simplification of the 2 element Boolean algebra (2) and of the truth functors of elementary logic. The formalism should be extendable to arbitrary finite Boolean algebras and to first order logic. In any event, the primary algebra could greatly simplify the teaching of logic to nonspecialists, such as philosophy majors, electrical engineers, and computer scientists.

About Spencer-Brown's bolder claims, I reject some (e.g., his belief that LoF eliminates any need for type or set theory) and am thoroughly agnostic about others (e.g., imaginary truth values could revolutionize mathematics and electrical engineering).


 * Philip, I offer my very sincere congratulations on your mathematically rigorous treatment of Spencer-Brown's work. You've done a great piece of work yourself -- similarly respectful of LoF, the calibre of this article had previously been something that I could not even reference.  Please stay flexible and with us as this continues to evolve.  The article may need a separate section to discuss the philosophical and even theological implications of LoF, but there are critical points in your very well done discussion that provide segue and foundations for this future section. Again...very nicely done.  --AustinKnight 19:59, 28 October 2005 (UTC)

Philip Meguire, October 31. I have taken the liberty of editing your additions. I teach university and find it very natural to edit other people's writing.


 * Well done, again. I didn't like the interruption of flow myself, and was clearly too focused on the segue opportunity presented by the "first distinction" dialogue.  I've reedited to somewhat 'sandwich' the ineffable allusions via both a re-assertion of the linkage with the "first distinction" and the LoF Notes section for Chapter 12. --AustinKnight 14:27, 31 October 2005 (UTC)

Philip Meguire. I've expanded your discussion of Confucianism by including my favorite quote from the Analects.


 * The article seems complete to me except with regard to one important dimension: LoFs dialogues on the imaginary.  I don't necessarily disagree with you, Philip, that "G." overreached, but at the same time he was dealing with the imaginary, and so one clear characteristic of that 'set' is that it is boundless.  Given that imaginary numbers are quite "real," it'd be interesting and perhaps valuable to capture S-B's thoughts in our article re. the imaginary, while at the same time sticking to a rigorous mathematical treatment of it.  Philip, do you think you could you take a shot at this? --AustinKnight 14:28, 7 November 2005 (UTC)

Philip Meguire, November 7. I have concluded that LoF strongly overstates the value of imaginary truth values for logic, mathematics, and engineering. Moreover, what chpt. 11 of LoF seems to groping after was anticipated by the work of the Russian logician Bochvar (Russian original 1939, English translation 1981). I am happy to let someone else add a section summarizing chpt. 11 and mentioning possible extensions (I have yet to encounter work building on LoF in a serious way; the nearest exceptions are the curious books by Nathan Hellerstein). Incidentally, the imaginary numbers are no more boundless than the reals. Granted, complex numbers are two dimensional, but Cantor showed that complex numbers have the same order of infinity as the reals.


 * Quite right...I should have stated "infinite" vs. "boundless." My computer science/math days are long ago and more than a bit rusty.


 * I am intrigued by the nature of imaginary numbers and sense (right or wrong) more than a bit of resonance in other matters of the rational mind and the demonstrated limitations thereof. I am hopeful that Spencer-Brown is at least conceptually onto something with respect to the coupling of: (1) the concept of the distinction as the root of cognition, and (2) the concept of an imaginary dimension to logic.


 * Clearly, imaginary numbers are already of value in the real world...I'm hopeful that the extension of white/black binary logic can benefit from their counterpart. I'll take a shot at this, perhaps.  If so, the creaking hinges of mathematical thinking that you hear will be entirely my own fault. --AustinKnight 13:54, 9 November 2005 (UTC)

In 1963 I attended a lecture series given by Brown (as then known) at University College London. This article considerably extends the content of that series; I guess the lectures were a try-out for the book.

Brown referred to his work on the control of lifts (elevators) as a significant driver in the development of the Laws.

I kept my lecture notes. The purpose of this 'discussion' entry (Feb, 2005) is to offer a view of my course notes, as background material for anyone who may be examining the early history of the subject. This is the web site:

http://www.tooke-picarel.co.uk/LoF/

Richard H. Pickard, Norwich, UK

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Richard Shoup has published an interesting article elaborating upon the imaginary values. At the end of the article there is a nice overview of correspondences between classical circuit notation, Boolean Algebra and the Calculus of Indications aka Laws of Form. 

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If anybody feels compelled to elaborate upon the self-referential forms - please do. The reference to Spencer-Browns talk in 1973 is, unfortunately, the best I'm up to at the moment. I think it necessary to at least give a hint to this element of the "Laws of Form" which is crucial to many a discussion about "paradox" and the still lingering theory of types.

Unmarked state
This should be merged in (it was on an orphan page). Charles Matthews 07:51, 7 October 2005 (UTC)

Criticism
What does the "Resonance in religion & philosophy" have to do with Laws of Form? LoF is a formal system for logic. The "Resonance..." section quotes from a collection of religious texts that appear to have no relationship with LoF. Maybe someone could make the connection clearer. Or conversely maybe they could tell me why there aren't similar discussions in articles for other branches of logic? sigfpe Nov 1, 2005

Concerned Cynic, Nov. 4 2005. Adding the section "Resonance" is Austin Knight's preference. Once I committed to humouring him in this respect, I added the quotes from Genesis, Confucius and the rectification of names, Royce, and Wheeler.

Syntactically, the Laws of Form are no more than a streamlining of the Boolean algebra 2 and propositional logic in equational form, and monadic predicate logic. The Laws are not isomorphic to first order logic, but I am confident they can (and will) be made so.

Relation to LoF? That book reveals that Spencer-Brown believes in some God, and that he was very much caught up in the bohemian Zen mysticism (Alan Watts, Suzuki, etc.) of a half century ago. Add to that a fascination with the enigmatic Wittgenstein (popular among persons educated at Oxbridge 40-60 years ago) and Ronald Laing (the radical psychiatrist), and you can see why LoF became a cult classic (a phrase that Austin Knight will not let me include in the article!).

That God, logic, and order in the natural and human world are interconnected was argued by, e.g., Plato, Aristotle, some Chinese classics, Aquinas, Leibniz, Kant, the late Whitehead, Charles Hartshorne, and the curious American analytic philosopher Richard Milton Martin (whose Wikipedia entry I wrote). -- User:132.181.160.61

In the U.S., at least, usage of the term "cult" of any form is highly pejorative...with good reason, as we have had some truly nasty ones. It also implies some sort of at least loosely-formed organization, of which there certainly is nothing substantial for LoF that I am aware of.

As my original notes indicated, there is little avoiding of such topics around the ostensibly mathematical writings of Spencer-Brown. As User:132.181.160.61 notes in the article, S-B was highly paradoxical in his writings...sometimes to the point of being virtually opaque, but clearly with the intent of such ties as noted above.

BTW, I predicted this section at least as much as contributed to it, but did not create it. Someone else did using the original title "Analogies," and I thought to replace that with the term "Resonance" as a sort of homage to Spencer-Brown...whose work I also very much respect.

As to ties with LoF: User:132.181.160.61's list of reknown philosophers who would tie these topics together also goes, of course, into all of those currently listed in "Resonance." Historically, these topics are wedded by quite a substantial collection of individual thinkers and belief systems. It'd be intellectually dishonest to assert otherwise. Specific, referenceable ties to LoF, as also indicated in the article, include the language surrounding the "first distinction" and the Notes to Chapter 12. --AustinKnight 23:38, 2 November 2005 (UTC)

User:132.181.160.61 = Philip Meguire! I added Royce and Wheeler.

The 'History' tab above provides a good bit of clarity re. editors. It really is best to sign all 'Talk' work via the 2nd button from the right at the top of an 'Edit' page. Cheers, --AustinKnight 04:18, 4 November 2005 (UTC)

Featured Article? Perhaps.
This was a very enjoyable article on an enjoyable book. Many of us have been influenced by it. Congratulations to those of you who have improved it. Ancheta Wis 16:35, 5 November 2005 (UTC)

Lead section
Would it be possible to conver this into prose? - Ta bu shi da yu 14:42, 22 December 2005 (UTC)

Funny You Should Mention It (FYSMI)
I am wikiworkinup to a rewrite, but will need to discuss much before I do. Maybe later today. Jon Awbrey 15:06, 22 December 2005 (UTC)