This post comprises one question and no answers.  You have been warned.

I was reading "How minds can be computational systems", by William Rapaport, and something caught my attention.  He wrote,

Computationalism is - or ought to be - the thesis that cognition is computable ... Note, first, that I have said that computationalism is the thesis that cognition is computable, not that it is computation (as Pylyshyn 1985 p. xiii characterizes it). ... To say that cognition is computable is to say that there is an algorithm - more likely, a collection of interrelated algorithms - that computes it.  So, what does it mean to say that something 'computes cognition'? ... cognition is computable if and only if there is an algorithm ... that computes this function (or functions).

Rapaport was talking about cognition, not consciousness.  The contention between these hypothesis is, however, only interesting if you are talking about consciousness; if you're talking about "cognition", it's just a choice between two different ways to define cognition.

When it comes to consciousness, I consider myself a computationalist.  But I hadn't realized before that my explanation of consciousness as computational "works" by jumping back and forth between those two incompatible positions.  Each one provides part of what I need; but each, on its own, seems impossible to me; and they are probably mutually exclusive.