https://livrepository.liverpool.ac.uk/3101665/1/Spencer%20Brown%20submission%20(1)%20(1).pdfLaws of Form responds to a long-standing mathematical paradox relating to infinite series of numbers. At the end of the nineteenth century, the founder of set theory, Georg Cantor, found that the infinite is itself differentiated, with different infinite series coming in different sizes. Moreover, if one counted all the infinite series, one would again find an infinite series, but one whose number, including itself when counted, must be larger than any countable (cardinal) number (Davis, 2000, p. 67). This problem led Russell to consider paradoxes in logic and the membership of sets: Extraordinary sets are self-including, such as ‘a set of all things not sparrows.’ This set itself also belongs to all things not being sparrows. Ordinary sets, on the other hand, have no such self-referentiality, for instance the set: ‘all things that are sparrow’ which, clearly, does not include the ‘set’ itself. But what about a set containing all ordinary sets? Would that not at once have to be larger than the number of all the sets it contains, as it, itself, is one such set (Davis, 2000, p. 67)? As Russell (1919, p. 136) states:
The comprehensive class we are considering, which is to embrace everything, must embrace itself as one of its members. In other words, if there is such a thing as “everything,” then, “everything” is something, and is a member of the class “everything.”
Whitehead and Russell’s (1910) Principia Mathematica proposes a stopgap intervention by excluding paradoxes from the domain of logic: sets cannot be members of themselves!.
Spencer Brown’s biography placed him directly into this debate, having worked with the two foremost logicians of the time, Russell and Wittgenstein. His solution to the problem was formed when he worked on practical electrical and engineering assignments.
LoF's mystical and declamatory prose and its love of paradox make it a challenging read for all.
Ok, I'm seeing a re-work of Boolean logic with a sort of pseudo-Hegelian dialectic thing going on.
A poor idealist's Tractatus? — Banno
The pdf I linked won't allow quotes.
2. My keyboard does not have the cross symbol. — unenlightened
I'm not a logician, mathematician, or electrical engineer, but I am somewhat informed on the philosophical concept of Form. Especially as it applies to essential or causal Information --- To Enform : the act of creating recognizable forms : designs ; patterns ; configurations ; structures ; categories. Generic Information begins in the physical world as mathematical ratios (data points ; proportions, 1:2 or 1/2) in a starry sky of uncountable multiplicity. Hence, we begin by clumping cosmic complexity into symbolic zodiac signs relating to local significance. In an observing mind, that raw numerical data can be processed into meaningful relationships (ideas ; words). Or, in a mechanical computer, those ratios are analyzed reductively into either/or (all or nothing) numerical codes of digital logic : 100%true vs 0%true. This is probably the most elemental form of categorization, ignoring all degrees of complexity or uncertainty.I’ve noticed ‘Laws of Form’ but when I tried reading it, found it quite daunting. Maybe we should start a discussion group on it. — Quixodian
Construction
Draw a distinction.
Content
Call it the first distinction.
(you don't have to agree, I'm just giving shape to the way the axioms work with a familiar example.) — unenlightened
Something I'm stuck on, from a first reading of the first two chapters, is the distinction between letting and calling. I think I have to read "Let" as "Call a function" or something like that. It's naming an instruction rather than naming a distinction. — Moliere
I get a different shape? — bongo fury
Assertion and negation, basically? — bongo fury
Leon-Konrad---Roots%252C-Shoots%252C-Fruits-%2528paper%2529.pdfIt’s worth thinking about the ‘dictums’ in terms of Laws of Form – for they put the ineffable at the heart of the operation. ‘You can’t have a blue universe,’ I can hear him say. Of course you can’t. If you’re proposing a blue universe, then you’re also, by definition, expressing the contradictory of a ‘non-blue universe’ at the same time. Since there can only be one universe, the whole idea is preposterous.
ibid.It’s a key difference that applies to logic – with Boole committing a logical fallacy by indicating ‘the universe’, as 1 and nothing as 0, as Boole does, when introducing his binary approach to algebraic logic. 1 and 0 are both marks on the page, but he does not acknowledge the space in which they stand. In Boole’s thought – and, I would argue, in Luhmann’s, 1 and 0 are both marks. They’re contradictory terms, but the underlying unity isn’t acknowledged. Both Luhmann and Boole mark the unmarked state. Thus, in Boole’s work, and in Luhmann’s, it appears as a mere sign: [*]
Spencer-Brown never makes this error. He symbolises it the unmarked state by making it equivalent to the piece of paper it is written on: [*]
'Let' is a command from on High. This how it shall be henceforth. 'Let x be the number of angels that can dance on the head of a pin. 'Let' happens outside the formal system to create it. 'Call' is an action that happens inside the the system. You can call the distinction into being by making the distinction, that is by writing the sign. and If you write it twice in a row you call and recall. — unenlightened
For 2 I think we could use brackets, thus:
[ ], [[ ]], [[ ] [ ]], [a], [[[a] [[b] [c]] [ ]] Not very clear, and it might be better to alternate square and curly by depth, thus:
[{ } { }], [{[a] [{b} {c}] { }] — unenlightened
Reading Chapter 1-2 (for some reason I'm finding them linked as I read this the first time -- like I can't talk about chapter 1 without chapter 2, and vice versa) again I can see the opening of 2 as a re-expression of Chapter 1, like The Form needed to be explicated before talking about forms out of the form, and the form takes as given distinction and indication which it also folds together as complementary to one another. — Moliere
But this is where I really got lost entirely: What is going on from "Depth" to "Pervasive space", or are these concepts that, like the first chapter, will become elucidated by reading chapter 3? Like a puzzle unfolding? — Moliere
If there's a easy link to figuring out how to embed multiple crosses, jgill, I'd be happy if you could pass it along because it does look prettier, and if I can figure out the syntax it's probably not that hard to embed multiple crosses. — Moliere
but perhaps the way to understand is to read through first, and then go back and worry at the terms when you have a grasp of the 'idea of the game'. and all this 's' and 'c' is just a way of talking about
The idea of the game, at first, anyway, is that the stop light is on when the train is in the tunnel and off when the train is not in the tunnel. Mark, or no mark. And that game is what comes next. — unenlightened
My hope, in the long run, is to offer strings which people can simply copy-paste with clear delineations for plug-and-play. — Moliere
'that the universe comes into being when a space is severed or taken apart' — Wayfarer
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