In mathematical logic, what do you think about so-called "vacuously true" statements?

I have read once a good motivation for the acceptance of vacuous statements in logic. A system of logic that does not permit such statements suffers from lack of generality and is therefore inappropriate as a tool of science. For instance, it is commonly accepted in Newtonian mechanics that a body in a state of rest or uniform linear motion will stay so unless acted upon by an outside force. This statement is true (roughly) on the principle that no instance where it is not true could be observed. In other words, all bodies experience at least the force of friction or gravitational attraction from other bodies. If one were to use Aristotle's vesion of logic, one would not be allowed to accept this principle of Newtonian mechanics, because of the burdensome requirement to demonstrate an instance of which this principle is true.