Yes indeed Brent!
Tts a very tough problem, and exactly what I've been critizing
Bayesianism for. That's what I've been going on about when I talked
about how Bayesianism can only fully deal with *Shannon Information* ,
it can't fully handle the *meaning* (semantics) of the information.
So how do we ascribe meaning to mere formalism?
Remember the story of John Boole. He developed a means of reasoning
about thinking, by matching up the abstract concepts of *algebra* with
concrete concepts of *mental logic*. In large part, his ideas were
the foundation for Bayesianism.
Enter the story of Marc Geddes ;)
Like Boole, I’m trying to extend logic further meaning by matching up
abstract concepts with concrete logical concepts. In particular, it
is highly suspicious that there appears to be a remarkably close
match-up between the concepts of *category theory* and the concepts of
*analogy formation*. What is even more remarkable, no one but me
seems to have noticed ;)
So, the meaning is obtained by matching the abstract concepts to the
Let’s look once again at the close match between an *analogy*, and a
*functor* from category theory:
First, observe the definition of an analogy:
" Analogy is both the cognitive process of transferring information
particular subject (the analogue or source) to another particular
target), and a linguistic expression corresponding to such a
Go to the definition of a functor from category theory:
"Given two categories C and D a functor F from C to D can be thought
of as an *analogy* between C and D, because F has to map objects of C
to objects of D and arrows of C to arrows of D in such a way that the
compositional structure of the two categories is preserved"
So we can match the meaningful concept (ie 'analogy') to the abstract
concept (ie 'functor', from category theory)
It useful to look at the story of George Boole once again, because he
developed computer logic precisely by performing these sorts of match-
ups between abstract algebra (meaningless) and basic mental logic
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