I "Laws of Form" by G. Spencer-Brown (1969)

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"Laws of Form" by G. Spencer-Brown, published in 1969, is questioned for its relevance and utility in contemporary logic and mathematics, with some viewing it as a historical curiosity. While it has influenced various fields, including semiotics and consciousness research, its practical applications in logic and mathematics remain unclear. The discussion highlights the contrast with Boolean algebra, which is widely used and taught today. Some believe that future mathematicians may find new utility in Spencer-Brown's ideas, potentially reviving interest in the system. Overall, the book's impact appears limited, primarily attracting niche interest rather than mainstream adoption.
nomadreid
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I have received (unasked) a digital edition of "Laws of Form" (1969) by G. Spencer-Brown; I have glanced at it, and also at the Wikipedia article https://en.wikipedia.org/wiki/Laws_of_Form. OK, another logical system; logical journals (e.g. by ASL) are full of them, and I am not sure whether this one stands out (beyond having some fuzzy interpretations that made it a "cult classic", as Wiki states). Wiki lists people it has influenced, but my question is: has the system itself gone anywhere, been of any utility in the rest of logic or mathematics (or even philosophy, although this forum is not for that) since then? Is it, in other words, anything more than a historical curiosity?
 
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I think it was just another guidepost along the way to some better idea. The books listed were mostly written a few years after this one with the exception of one in 2011.

In contrast, Boolean algebra is in use everywhere and is still taught in CS classes.

This is not to say that some future mathematician won’t find some primal utility to his ideas and kick off a revolution. There was some mention of the provability of some famed math problems and so if someone were to use it for that means then it could become mainstream once again.
 
Thanks, jedishrfu.
 
nomadreid said:
I have received (unasked) a digital edition of "Laws of Form" (1969) by G. Spencer-Brown; I have glanced at it, and also at the Wikipedia article https://en.wikipedia.org/wiki/Laws_of_Form. OK, another logical system; logical journals (e.g. by ASL) are full of them, and I am not sure whether this one stands out (beyond having some fuzzy interpretations that made it a "cult classic", as Wiki states). Wiki lists people it has influenced, but my question is: has the system itself gone anywhere, been of any utility in the rest of logic or mathematics (or even philosophy, although this forum is not for that) since then? Is it, in other words, anything more than a historical curiosity?

The laws of form are still an area of interest, mostly to people interested in the foundations of logic, semiotics, consciousness research, psychology and sociology. Louis Kauffman (U Chicago topologist) has written many papers about LOF and other logical systems (see, for instance, Laws of Form, Majorana Fermions, and Discrete Physics at Researchgate)
 
Thanks very much, jdstarrett.
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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