[FOM] Turing machines, algorithms, and category theory

[Paul Hollander]

[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.

Cheers,

Paul Hollander