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

[jon zingale]

Nick,

I would say, yes. Frank's point is that if I have a causal chain of the form
A -> B -> C, where the arrow is strict causation, then B screens (or
filters, or blocks) knowledge about A at C. EricS' point is that (given
cartesian closedness[Ӕ]), there is a relationship that allows one to
transform between implication statements and conjunction statements.

We are likely ok with statements with forms:
a, a => b ⊢ b
a, a => b ⊢ a ^ b

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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