I think so. Complex numbers and infinitesimals are IIRC the only possible alternatives to the reals, but complex numbers only apply to certain limited quantum contexts (roughly speaking, complex numbers apply when information is perfectly preserved, while real numbers apply in contexts where there’s information leakage into the environment), while infinitesimals can be approximated perfectly by real numbers. So in everyday contexts (which is presumably where “common sense” applies), plausibility is captured by real numbers.
If it is not necessary to use reals, can you still say that probability theory as extended logic follows from common sense?
I think so. Complex numbers and infinitesimals are IIRC the only possible alternatives to the reals, but complex numbers only apply to certain limited quantum contexts (roughly speaking, complex numbers apply when information is perfectly preserved, while real numbers apply in contexts where there’s information leakage into the environment), while infinitesimals can be approximated perfectly by real numbers. So in everyday contexts (which is presumably where “common sense” applies), plausibility is captured by real numbers.