Actually, C/A/P are more like variables you can multiply together. Even more accurately, they define a three-dimensional space with the CAP theorem (especially in Gilbert and Lynch's formal proof) only saying that you cannot be at the point that represents the maximum of all three. There are definitely tradeoffs or "mode switches" that can be made between C and A, and some even believe that you can give up some P to get more C/A. Personally I believe that the probability of partition is always non-zero in even the best designed and fully provisioned networks, even including those that are econonomically infeasible, and that those who choose to treat a small probability as zero to capture a performance advantage or position themselves as "more consistent" than competitors are being a bit dishonest, but those tradeoffs are being made.
> they define a three-dimensional space with the CAP theorem (especially in Gilbert and Lynch's formal proof) . . .
That's weird because I've read the proof and they speak only of boolean instances of C, A, and P in the proof. They give no examples of systems where any of the three variables have values other than zero or one.
