[FOM] Turing machines, algorithms, and category theory
paul at personalit.net
Wed May 3 17:09:01 EDT 2017
[NOTE: Includes corrections.]
On 5/1/17 00:08, Patrik Eklund wrote:
> In conclusion, my general suggestion is to try out a "categorical
> interpretation of computing" rather than aiming at a "computational
> interpretation of categories".
My philosophical concern is mathematical ontology, specifically
quantification and inheritance.
Inheritance is both a relation and an activity. It comes in a
non-numerably infinite variety of forms, from the monadic to the n-adic
to identity to myriad structure-preserving relations weaker than identity.
Interpreting the identity morphism 1x:y --> z as the natural deduction
inference rule 1x licensing inference from |- x=y to |- x=z gives 1x an
activity to play without quantifying over 1x. It explains a form of
inheritance represented in category theory that is weaker than
full-blown identity. On this view, category theory is the theory of the
myriad inheritance relations weaker than identity.
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