I propose this simple, counter-COMP truth:
Without something to enumerate, numbers are meaningless.
Two plus two does not ‘equal’ anything without a fairly extensive list of a priori meta-artihmetic conditions. As far as I can tell, for two plus two to equal something, there must be:
Cause and effect
An experience of counting
A rigid reference body of equivalences
Functional phase spaces which are in some sense independent of the reference body
A semiotic phase locking function which relates specific functions to the supreme ultimate reference body
Something which experiences the function as meaningful
A capacity for participation in experience
A capacity to direct and control experience, i.e. to cause some function to be enacted as a consequence of another
Reliable memory to switch between functions
Storage for isolating currently enacted functions from accumulations of sets of tacit functional results.
Lots of things.
In short, in order to have computation, you need… a computer.
The items on this list all supervene on sense. The capacity to detect and project signal. Computation is a way of using signals to refer to other signals - figuratively. They are figures. Quantification is a way of bundling things with other things, but virtually, not literally. There is no actual bundling unless there is some thing doing the computing that some thing cares about.
Does a thing have to be a material object? Our imagination suggests that it does not, although the capacity to imagine is associated with living cells. We have no experience however with things which are neither physical objects, subjective experiences, or subjective experiences of physical instruments interacting with physical objects. There is no experience of math existing ab initio.
This correlates with our cosmological investigations as well. Contrary to what we should expect from an inevitable multiverse of every possible combination of universes, our universe exhibits a distinct lack of unexplained chaos. It is one thing to expect that we would naturally find ourselves in one of the many universes which supports our existence, but it is another thing to extend that to the point that we find ourselves also in one of the universes which makes sense wherever we look, all of the time. If anything, the exhaustively granular orderliness of the cosmos defies the imagination, with each particle of sand requiring a team of trillions of lucky monkeys to have typed out the right string of ontological meta-characters, while at the same time synchronizing effortlessly with global, local, and regional harmonies of order. If all of this happens without sense, without anything making sense, then it seems infinitely unlikely that beings such as ourselves who require sense to navigate our own lives should exist, and exist in such a natural and seamless way to the rest of the unconscious universal mechanism.