They are neither incompatible nor incommensurable. They are different levels of description. The levels of complexity are so different that it is not useful (nor, with our current level of knowledge, possible) to reduce the agent-level to the physical level; but the agent-level is theoretically and necessarily reducible to the physical level, even if we don’t currently know in detail how to do it. And a person’s beliefs and actions at the agent-level directly affect the physical level.
As I mentioned, there are reasons for thinking they’re incompatible. Something’s (someone’s) being a rational agent implies s/he has goals and that in light of those goals ought in given circumstances to do certain things. Physical science makes no place for goals or purposes or right or wrong in nature—there is no physical apparatus which can detect the rightness of an action. Your thought may be that rationality can be made sense of without recourse to goals/purposes or right and wrong. I don’t think this can be done. At best you’d be left with an ersatz which fails to capture what we mean by ‘rational’.
They are neither incompatible nor incommensurable. They are different levels of description. The levels of complexity are so different that it is not useful (nor, with our current level of knowledge, possible) to reduce the agent-level to the physical level; but the agent-level is theoretically and necessarily reducible to the physical level, even if we don’t currently know in detail how to do it. And a person’s beliefs and actions at the agent-level directly affect the physical level.
As I mentioned, there are reasons for thinking they’re incompatible. Something’s (someone’s) being a rational agent implies s/he has goals and that in light of those goals ought in given circumstances to do certain things. Physical science makes no place for goals or purposes or right or wrong in nature—there is no physical apparatus which can detect the rightness of an action. Your thought may be that rationality can be made sense of without recourse to goals/purposes or right and wrong. I don’t think this can be done. At best you’d be left with an ersatz which fails to capture what we mean by ‘rational’.