[FRIAM] PM-2017-MethodologicalBehaviorismCausalChainsandCausalForks(1).pdf

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This is exactly my problem with understanding tonk as both a bi-adjoint functor and NOT causing problems in logics that disallow transitivity. The only way I can feel around the problem is to allow multiple types of consequence. But it, and this discussion, pick at a fundamental problem I have with the way everyone discusses function composition. It seem to rely fundamentally on sequentiality. Everywhere we assume things like commutativity and transitivity, it seems to sequentialize it. But this flies smack in the face of how I experience reality, as pervasively parallel. The tricks we use to handle parallelism in computation feel like cheap magic tricks, stilted, inelegant, ham-handed abominations.

Or maybe I'm simply insane. This is probably a stupid post and I should delete it. Pfft. I'm going to lunch.

On 2/10/21 12:12 PM, jon zingale wrote:
> The screening-off case appears to me to be that we cannot distinguish
> extensionally (in cases of probability 1 causality) a path like:
> 
> a, a => b, b => c ⊢ a, a => c ⊢ c
> 
> from
> 
> a, a => b, b => c ⊢ b, b => c ⊢ c
> 
> what effectively amounts to transitivity. I don't really know about the term
> screening-off, but I gather it has to do with this inability to distinguish.
> Of course, I could be way off.
> 
> [Ӕ] The cartesian closed condition (CCC) is always available for debate, and
> could easily be a point of contention (or block to understanding). A
> wonderful example of how broken the CCC can be is explicated in the text
> "Applied Category Theory" by Spivak (no not that Spivak) and Fong. To
> summarize the point made there:
> 
> A material category includes objects like H20, 2Na, 2NaOH+H2, etc... This
> collection yields a symmetric monoidal category that is not closed because
> of an interesting technicality that arises often in functional programming
> paradigms, something called currying:
> 
> A x B -> C ~  A -> (B -> C)
> 
> or as it appears in formal logic:
> 
> a ^ b => c ⊢ a => (b => c)
> 
> In words, a function that takes *a pair of things to a thing* corresponds to
> a function that takes *a thing and returns a function that takes a thing and
> returns a thing*. An example would be that I can write a function (+) which
> takes a pair of numbers and returns a number: (+) 2 5 = 7 and this will
> correspond to a function: (+ 2) 5 = 7 Which takes a 5 and returns a 7. The
> (+ 2) isn't a number in its own right, but something that waits for a number
> to do a thing. The authors go on to talk about this correspondence wrt a
> material category.
> 
> We can have: 2H20 + 2Na -> 2sNaOH + H2 (Sorry for the lack of subscripts),
> and this expression would correspond to:
> 
> 2H20 -> (2Na -> (2sNaOH + H2)), while (2Na -> (2sNaOH + H2)) doesn't
> correspond to any material, it does correspond to a potential reaction, with
> two water molecules unlocking that potential. What is novel here, to me, is
> the doubling of the word *potential*, that of something near to happening
> with concepts like electrical potential (functional) giving rise to
> lightning.


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