Is Boundary Logic interesting?

Discussion in 'Physics & Math' started by arfa brane, Aug 21, 2018.

  1. iceaura Valued Senior Member

    That would make it identical with the representation of "false".
    Instead, one can extend the BL notation and arithmetic to include - and assign a truth value to - self referential statements. Which Brown does, in LoF.
    It appears to clear up a confusion.
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  3. arfa brane call me arf Valued Senior Member

    This confusion you speak of. Is it related at all to how LoF appears to make "nothing" into something, even saying it's ok to say A is nothing, and maybe (A) (B) is too, etc.

    How do you make a mark or define a boundary, a thing that obviously has structure, in nothing? This to me is the strongest criticism I can level at the notation, and still it works.

    may the Void be with you.
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  5. parmalee peripatetic artisan Valued Senior Member

    I see it the other way round: LoF is characterized by not making nothing into "something", i.e., by the very action of not designating nothing with a symbol--naming what can't be named. At first, this seems kinda unfamiliar, in the context of logic systems at least (though not so with iconic systems), but it correlates more readily with other fields--from semiotics to anthropology to philosophy (I'm thinking mostly non-analytic schools, here--esp. Continentals from Agamben to Derrida, or neo-Wittgensteinians like Diamond, Cavell, et al) to ethology (again, Uexkuell's umwelt).

    W. Bricken

    Let the Void-space be your canvas.
    Last edited: Sep 12, 2018
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  7. arfa brane call me arf Valued Senior Member

    From this, I get the idea that the semantic rule: (( )) =
    . . . is not labeling the void, but something else. I also assume it calls into question what the "=" means.

    I can interpret the rule ( ) ( ) = ( ) as saying "making the same distinction twice is the same as making it once", or somesuch. Or I can think of it as a reduction rule.
    I can leave the whole void thing alone as long as I don't have an expression which evaluates (reduces) to nothing.

    Say I have:
    1. ( ) ( ) = ( )
    1a. ( ( ) ( ) ) = ( ( ) )
    2. ( (( )) ) = (( ( ) )) = ( )
    => ( ) ( ) = ( (( )) ) = (( ( ) ))

    Bricken says I'm allowed to use symbols to label any expression, any combination that follows the rules. So he's saying labeling (( )) is allowed.
    Indeed the operations of involution: ((A)) = A, occlusion: (( )A) = (( )), and pervasion: (A) A = ( ) A, don't seem to make sense unless A is an expression which is either "( )", or "(( ))".
    Something happens when you introduce symbols to an otherwise iconic "language"; not recognising this (never mind characterising what exactly changes) is also a mistake--labeling "nothing", or writing "This sentence doesn't exist", are logical mistakes (perhaps you need to make them). Clearly the sentence in quotes does exist; it took me some time and energy to type it out, it has an information content, but logically it's a contradiction or a lie.
  8. iceaura Valued Senior Member

    It means "interchangeable in all defined expressions", basically.
    Grounding interpretations of symbols in instruction, action, and the like - rather than static states of being - brings clarity to BL. imho
    Which may be why the step from arithmetic to algebra is explicitly recognized and justified, and a chapter devoted to it, in LoF.
    These issues and questions of yours are dealt with, explicitly, in LoF among other places.
    It has one of the truth values available in the space of self referential statements.
    The interpretation of "existence" in logical arguments, and therefore in the arithmetic and algebra of BL, is complex - again, LoF addresses that issue (not thoroughly).
    Last edited: Sep 13, 2018
  9. parmalee peripatetic artisan Valued Senior Member

    Again, I'm seeing echoes of Wittgenstein here: meaning is use. Our ability to define something with abstractions is irrelevant; rather, our ability to use the term correctly, in a meaningful way, is what matters.

    It seems the biggest obstacle here, and Bricken mentions this repeatedly as do commentators on LoF, is a lack of familiarity.
  10. arfa brane call me arf Valued Senior Member

    What does LoF say about such things as inductive proofs of program correctness?

    Would it be useful to the task of finding so-called loop invariants? This isn't a straightforward thing to do, usually. It's something people do because it's a hard problem. If a boundary algebra simplifies things, maybe it would make it easier to derive an invariant.

    I notice LoF isn't a hot topic, there are only a handful of authors. Louis Kauffman is one (he's a topologist, knot theory etc). What I've read of Kauffman's writings on LoF is sometimes a bit too metaphysical for me. In fact the metaphysical "cosmic implications" are quite a common theme.

    Another topic I uncovered is that of imaginary logical values: the "square root" of not, say. Again not many logicians have written a whole lot about it.
    Last edited: Sep 17, 2018 at 9:30 PM
  11. parmalee peripatetic artisan Valued Senior Member

    There seemed to have been a lot more stuff on LoF on the net up to the early/mid-aughts. I honestly don't know what become of all that stuff, but, yeah, Louis Kauffman's page provides a fair number of links, as do the enolagia pages-- -- compiled by Randall Whitaker. From what I can tell, he seems to have salvaged a lot of stuff that had disappeared from the net.

    I think you'll find more stuff that interests you on Kauffman's page; Whitaker's links seem to be more of the systems theory, cybernetics, Maturana/Varela, and psychoanalytics variety--not to mention some John Lilly stuff (you know, the dolphin and isolation tank guy--he was a bit of a nutter, but some of his work is quite substantive). I'm certainly partial to the latter stuff (from work philosophy (mostly continental), anthropology, critical animal studies, and so forth, but I can certainly appreciate that a lot of people tend to regard that a nonsensical crap

    Edit: Just a suggestion, when reading the latter stuff (or even some of Kaufmann's), try to abandon some preconceptions, and or biases, about the metaphysical and "cosmic implications. " Most of this work seems pretty grounded, and pretty free of woo. Fields like semiotics, and biosemiotics, and zoosemiotics, and so forth, have kinda gotten a bad rap. Some of it deserved, frankly, but by no means all. The field emerges largely from Peirce, de Saussure, Uexkuell, et al, don't let the mentions of Lacan or Barthes, for instance, cloud your judgement.

    In the notes to chapter 11 (with the flip-flop circuit), Brown notes that the circuit, which was used by British Railways, suggests that the application may in fact be the first instance of imaginary values used for such a purpose. He writes:

    LoF, p. 123 (in the copy I've got).
    Last edited: Sep 18, 2018 at 12:56 AM

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