Talk:Laws of Form/Archive 2

Incidental Incremental Improvement Issues (I^4)

I will list here the issues that arise as we discuss improving this article toward the point where the coverage of Laws of Form (LOF), the book by George Spencer Brown and the corresponding formal system or system of forms, plus the necessary formal and historical connections to C.S. Peirce's "Logic of Relatives: Qualitative and Quantitative", including his Logical Graphs, in their dual interpretation as entitative graphs and existential graphs, his "Qualitative Logic" manuscripts, his alpha graphs, beta graphs, gamma graphs, along with whatever else comes along, will be more generally understandable and useful to the reader.

NB. Please excuse all the acronyms -- they're just how I keep track of things in my own mind and notes. Jon Awbrey 18:00, 22 December 2005 (UTC)

Query 1

• I guess the first issue that comes to mind is this: What's a good way to coordinate the content here with the closely associated and/or overlapping content in the Charles Peirce article?

I submit that HTML cross referencing works just fine here.202.36.179.65 11:31, 28 December 2005 (UTC)

• This may be more acutely critical since I also see a message saying that this article is approaching or already passed through some kind of "singularity of size" (SOS). Is that still an issue, or is it now an obsolete concern?

Wikipedia politely suggest that entries over 32KB in size are perhaps bigger than optimal. I hear tell that that can be ignored with impunity. The 32KB is the largest segment of HTML code I can edit in one bite on the iBook I use at home. The generic Windows system in my office has no such limitation.202.36.179.65 11:31, 28 December 2005 (UTC)

• Incidentally, how do I create a redirect from C.S. Peirce, which is the more usual name in logical and mathematical journals, not to mention large parts of the Peirce literature? Jon Awbrey 18:44, 22 December 2005 (UTC)

Wikipedia is committed to Charles Peirce. The entry Charles Sanders Peirce is deemed dead. If there is a way of creating and managing aliases for Wikipedia entries, I know nothing about it.202.36.179.65 11:31, 28 December 2005 (UTC)

I created a redirect for C.S. Peirce. Here's how it is done: Create a new page where you want to have a redirect. The easiest way to do this is follow a link like the one above (C.S. Peirce), or just use the search box to go to the page you want to create. type #REDIRCT and then a link to the page you want to be redirected to. In this case it was: #REDIRECT [[Charles Peirce]] -- Samuel Wantman 20:25, 6 March 2006 (UTC)

Query 2

Another issue that arose somewhere between my 2nd and 3rd reading of the articla has to do with the lower case acronym pa for primary algebra. The last thing I want to do here is institute any sort of paternity suit, so ... Philip, I guess I'll address this to you in particular, just in case you have any kind of "personal attachment" (PA) to this usage. But seriously, now, here're the problems that I'm having:

• To the mathematical community of interpretation, PA almost reflexively suggests "Peano Arithmetic", so I think I can see why you may have wanted to de-escalate the potential hash-clash there. But I'm not so sure that the lower register pa really does the trick, as you can't really hear the piano, in print or see the piano in normal speech -- no, I mean the other piano.

In my published work, I use "PA" to denote the primary arithmetic and "pa" the primary algebra. I write both in Helvetica, to very clearly demarcate them from the rest of the ms, which is in Palatino. I am quite aware that to many well versed in formal systems, PA brings to mind "Peano arithmetic," but you are the first to complain about this homonymy. GSB, William Bricken, and Jeffrey James have argued that one can derive the natural numbers from boundary methods, but doing so requires jettisoning A1 and exiting the PA. Hence the primary arithmetic and the Peano arithmetic are incompatible, and "PA" can refer to both with little risk of ambiguity.202.36.179.65 11:42, 28 December 2005 (UTC)

Okay, I was in a bit of a jolly mood that day, but the practical point that I'm trying to make is a bit like this. If I want to explain this to somebody at a party -- yes, I confess, I have -- or over a bad cellphone connection, or in some other noise-filled environ, then I can't depend on such nuances of fontology and intonation to 'make a distinction', as it were. Jon Awbrey 14:48, 29 December 2005 (UTC)

It is hard enough to exposit math and logic in writing. To expect, further, that they be communicable in speech is a Big Ask. To expect, even further, that they be communicable viva voce in a "noise-filled" environment" is simply too much. Formal systems require and deserve our quiet contemplation. I find speech so ineffective that I have found university lectures on such matters of little use; a lecture is an Index Sequential data structure, strongly dominated by Random Access structures, such as the printed page.202.36.179.65 15:59, 14 March 2006 (UTC)

• Be that as it may, the more serious problem that I'm having is this: My own experience expositing LOF and Peirce's various systems of logical graphs tells me that it's best to do it in very gradual stages. Jon Awbrey 19:56, 22 December 2005 (UTC)

I believe that the entry pretty much does as you prefer here.202.36.179.65 11:42, 28 December 2005 (UTC)

Well, I guess I'll start contributing a little more of what I have found preferable, and then we can talk about it with something less hypothetical in mind. Jon Awbrey 15:00, 29 December 2005 (UTC)

• Among other things, this means sorting out the "primary arithmetic" (PA) and the "primary algebra" (PA) from each other and introducing them to the reader or student in two distinct stages. I think you see the problem. One of the ways that I've addressed this problem in the past has been to dub the primary arithmetic "Par" and to dub the primary algebra "Pal", or fully capitalized variants thereof. What do you think? Could you live with that? Many Regards, Jon Awbrey 19:56, 22 December 2005 (UTC)

I italicized "pa" here simply out of a desire not to be typographically aggressive. If we are to deviate from the status quo, I would prefer keeping "pa" but writing it in bold rather than italics.202.36.179.65 11:43, 28 December 2005 (UTC)

Resonances in religion, philosophy, and science

Not sure where to put this note... but someone should seriously take a look at the wiki on Parmeides. ~wblakesx

You almost certainly mean Parmenides; I've added same today. --24.153.209.20 13:06, 22 August 2006 (UTC)

Actually, I think the section on Parmenides is almost completely mistaken. It's not particularly Parmenidean to distrust our senses. What's Parmenidean about LoF is early in the Introduction (?), he writes that everything conceivable is physically actual - which is one of Parmenides's central and most unusual claims. (I don't have a copy handy so can't give the actual quote.) --Gwern (contribs) 22:51 5 September 2009 (GMT)

Philip (?), For my part I find this sort of material personally fascinating, but I'm thinking that it might go better toward the end of the article, a rest from the formal rigors, as it were, especially given the problematic reception that this book has had over the years from a diversity of readers who do not appreciate diversity to the same extent. What do you think? Jon Awbrey 15:54, 4 January 2006 (UTC)

The shift you propose has been done (by someone other than me) and I like the result. Turning to LoF, I do not agree that its reception by readers has been problematic, or that it has had difficulty appealing to a diversity or readers. If anything, the serious problems with LoF are:

• Those who know logic and math dismiss it as "mere" Boolean algebra. They point to its confused assertions about set and type theory, and about metamathematics, and dismiss it out of hand;
• Its many readers who know little about formal systems are almost invariably overawed by its enigmatic and paradoxical assertions, concluding that there are rigorous grounds for abandoning rigor!

In the history of LoF, there are two near-tragedies.

1. When Spencer-Brown wrote LoF, Peirce's 1886 papers using the very notation GSB was proposing were mss gathering dust at Harvard. LoF cites vol. 4 of Peirce's Collected Papers, but GSB completely missed the 100+pp that volume includes on the existential graphs. The alpha graphs are isomorphic to the primary algebra; beta and gamma go further.
2. Shortly after LoF was completed, George Lakoff and others began building 2nd generation cognitive science. There are strong affinities between the "container image-schema" of Lakoff's Women Fire and Dangerous Things and LoF's "distinction." There are further affinities between LoF and Where Mathematics Comes From, a work which discusses possible cognitive origins of Boolean algebra, sentential logic, and elementary set theory in some detail. I am astonished that fans of GSB and fans of Lakoff are like ships passing in the night, except perhaps in that tiny part of the universe that lies between my ears ;<) On the other hand, a few Peircians do politely acknowledge LoF.202.36.179.65 17:00, 14 March 2006 (UTC)

Boundary of a boundary is zero

I deleted this remark:

A2 captures the essence of Wheeler's sentence "The boundary of a boundary is zero", quoted above.

Wheeler is referring to an axiom of algebraic topology that is very different in form from the law of crossing. Jon Awbrey 20:00, 10 January 2006 (UTC)

Wheeler almost surely had nothing Boolean in mind when he wrote "The boundary of a boundary is zero." And I do not doubt that he had topology in mind. But that does not necessarily invalidate my sentence to which you object. An important aspect of boundary mathematics is the way it points to all sorts of unwitting analogies and connections in the realm of abstraction. For the record, Lou Kauffman, a topologist and knot theorist, agrees with the sentence to which you object. Moreover, Boolean algebra can be grounded in elementary topology; for an exposition, see chpt. 2 of Rosser's 1969 monography on simplified independence proofs in set theory. A major unsolved problem is marrying boundary mathematics to the large corpus of topological mathematics, by either fleshing out what Rosser began in 1969, or by drawing on the laws of form to devise a non-set theoretic foundation for topology. The relation between the laws of form and topology must be clarified eventually, otherwise topologically literate mathematicians will sneer at our loose use of "boundary" and "distinction". The entry does not argue that the Laws of Form constitute an approach to 2 that is innocent of set theory, because to my thinking that is a working hypothesis, not a settled fact. Unlike many LoF fans, I have no real quarrel with the large body of academic work in math and logic. We can learn much from it, even it has missed some elementary insights.202.36.179.65 16:32, 14 March 2006 (UTC)

• JA: I know exactly what Wheeler is referring to, and will get you a standard ref when I get time. There is no analogy here because the formal properties are totally different. The boundary operator in algebraic topology has the properties d0 = 0, dd = 0, so all higher powers of d are 0, whereas the operator () has the form, (()) = blank, ((())) = (), and so odd and even powers alternate beyween () and blank. Jon Awbrey 16:33, 14 March 2006 (UTC)

In my view, this controversy points out the need to flesh out an intriguing little 2x2 table in Shoup's website, one claiming that changes to I1 and I2 yield finite numbers, sets, and multisets. The Holy Grail for me is a unified boundary formalism for lattices, number systems up to real analysis, sets, point set topology, and discrete math. Perhaps even groups and categories.202.36.179.65 17:27, 14 March 2006 (UTC)

I have drawn Lou Kauffman's attention to the difference of opinion aired in this section. He agrees that there is a useful analogy between A2 and the boundary operator of algebraic topology. If all powers of d are 0, then d and 0 can be seen as interpreting (), in which case d0=0 and dd=0 are both instances of A1. So if linking A2 and algebraic topology is a mistake, I say replace A2 with A1. In any event, there is a crying need for a boundary reformulation of group and lattice theory. Doing so will afford much insight.202.36.179.65 10:00, 16 September 2006 (UTC)

Speculation on Spencer-Brown's sources

• JA: Your statements about Spencer-Brown's sources remain for the time being in the realm of wholly unsourced speculation. I'm told that they have moderately adequate libraries at Cambridge and Oxford, and transatlantic aeronautic transport was commonly available to the average scholar even in those primitive times. There were microfilm editions of Peirce's Nachlass at many university libraries in the early 70's just from my personal acquaintance. But the essentials of Peirce's graphical systems are abundantly clear from what is found in CP, and Spencer-Brown evinced a clear insight into their character. Jon Awbrey 17:28, 14 March 2006 (UTC)

LoF was completed in 1967 and published in 1969. The Peirce Nachlass was microfilmed in 1964. Did any British university library have a copy of this microfilm before 1967? I rather doubt it, if only because to this day Peirce studies have been weak in the UK. Did Spencer-Brown fly to Boston and spend 1-2 weeks in the Harvard's Houghton Library and find there the Peirce mss that were completely unknown until Carolyn Eisele published an important excerpt in 1976? I rather doubt it, because the Robin catalogue of the Nachlass was published only in 1967. Without that catalogue, GSB would have had no idea where to look in the vast Nachlass. How many British libraries acquired a copy of the Univ. of Mass Press edition of the Robin catalogue before 1968? Meanwhile, Spencer-Brown's Cross notation was well established in lectures he gave beginning in 1963, if not earlier. If Spencer Brown had any awareness of Peirce's graphical logic, he's kept very very quiet about that fact for now 40 years. LoF reveals that GSB, when writing LoF, was aware of Peirce's Collected Papers because LoF cites vol. 4 of said papers. Ironically, that volume is the one containing 115pp devoted to the existential graphs. If the initials of the primary algebra included what Peirce called (De)Iteration, I would suspect that GSB could have appropriated aspects of the existential graphs without attribution. But the initials of LoF betray GSB's close reading of Huntington's postulates, not Peirce's graphical logic.202.36.179.65 10:14, 16 September 2006 (UTC)

Are abbreviations like 'LoF' & 'pa' necessary?

Most book articles don't require one-shot acronyms. It's not clear that they're useful here. It seems like a self-important bias to tax readers with new jargon. It's not obvious why this:

LoF argues that the pa reveals striking connections among logic, Boolean algebra and arithmetic, and the philosophy of language and mind.

...would be preferable to this:

"Laws of Form argues that the primary algebra reveals striking connections among logic, Boolean algebra and arithmetic, and the philosophy of language and mind."

--AC 06:57, 10 October 2006 (UTC)

pa seems to be an especially poor abbreviation, given that primary arithmetic and primary algebra both have the initials pa. Pdturney 13:10, 10 October 2006 (UTC)

I agree with Pdturney and AC; pa is a poor abbreviation. Make it primary algebra, the length is easily compensated for by gained clarity. Apart from that most sincere thanks and congratulations for the huge improvements this page has seen in the last 2 years or so. I think this will be a most valuable starting point for research into both the fundamentals and the history of both logic and mathematics. RBF, 13 October 2006