[FRIAM] labels

[jon zingale]

"Peirce fuzzed the distinction between the empirical and the logical."

As far as I am concerned, systems of logic are wild and diverse. On FRIAM,
we often run explicitly into these distinctions (linear types, quantum
toposes) as well as implicitly (constructivist scoping and free will). A
surprising amount of the content we produce appears to me to be dialectical
explorations of these distinctions. For all the different systems that make
up me, I should expect to find non-equivalent logics at all levels. Logic at
whatever level is something to be discovered. Peirce believes logic to be
entangled in every experience, though I go a step further by saying logics.
How we resolve the geometric morphisms must be fascinating, but not
something immediately intuitive to me.

That I am able (in analogy to Turing machines) to operate across the
collection of all logics accessible to me doesn't mean that logics found at
every level are universal. To some extent, I believe that Logic (narrowly)
is in some sense the study of parts. For instance, whatever base I choose as
a domain of verification, that base may or may not be able to distinguish
parts distinguishable from the perspective of some other base.

Unlike abstract machines (where I feel some confidence), I am unsure how
logics are constrained by construction. When I reason about continuity, say,
whether or not continuity is a fact of the objective world, what must
logically be granted to me and how? A lot of work exists on the inheritance
structure of toposes under the name of doctrines, fundamentally an algebraic
theory. As exciting as it would be to get down to brass tacks and tackle
this body of work, I hear the cautionary words of those on list. What might
be lost in such an encoding (maximally stateful computations versus the
purely functional, for example)?At the end of the day, I feel some comfort
that historicity has done quite a bit of the work for me. I do not have to
be confronted by all possible logics, just those expressible by this finite
mass of flesh and desire.



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