The most common definitions of computation I have seen are in terms of "what Turing Machines, Lambda Calculus, etc. do," which is unsatisfying. The definition of computable functions does not seem to be a definition of what computation itself, as a process, is.
I have not been able to find anything like the sort of deep conceptual analysis that exists for similar questions like: "what are numbers," "what are propositions," etc. E.g., if numbers are an "abstract object," would that make computation an "abstract process"? Or is computation just the step-wise enumeration of 'relations' or entailment (which there is a solid literature for)? I know there isn't a definitive answer, I'm just looking for some sort of exploration of the topic so I'm not working in the dark.
We can say 2 + 2 = 4 and 6 - 2 = 4, but these are not computed the same way.
There is a lot in the physics literature and the philosophy of physics literature on "what is a computer," physically speaking. Obviously, the physical instantiation of adding two groups of two things together is different from throwing out two of six things. This would suggest that, vis-á-vis computation, 2 + 2 ≠ 6-2, which is very different from how we think of identity in numbers. That is, the outputs are equivalent, but not the processes by which we get the output.
This seems relevant to issues in the philosophy of information vis-á-vis the "scandal of deduction," that deterministic computation does not produce new information, and the problem of non-constructive rigid designators. It also seems relevant to the philosophy of physics re: pancomputationalism (all the rage in popular science it seems), but I can't find anything really in depth.