I agree with Al and all the others on this list who have said that
Newton's second law is a statement about F causing the acceleration of a
body. As Al refers to Newton's first law, I will quote it from the
latest translation of the Principia: Law 1 Every body perseveres in
its state of being at rest or of moving uniformly straight
forward, except insofar as it is compelled to change its state by forces
impressed.
It is clear to me that "compelled" means to cause, and that "impressed"
means from the environment. The acceleration is a property of the body
but the forces producing it must come from other bodies in its
environment.