Modern philosophy makes much of the notion of logical possibility. In particular, this notion lies at the heart of the tendency of modern philosophers to use obviously unrealistic thought experiments. It also underlies the popularity of the possible worlds logic. But is the notion of logical possibility as uncontroversial as it is taken to be?
Philosopher Roderick Long was, in my view, on target when he wrote.
Thus I essentially agree with Fraçois’s answer: “Just because we can imagine the gravitational constant being, not 6.674×10^-11 m^3 kg^-1 s^-2, but rather 6.252×10^-11 m^3 kg^-1 s^-2, does not mean that it can actually be 6.252×10^-11 m^3 kg^-1 s^-2. Just because we can write it down and make calculations based on it doesn’t mean it’s actually possible.”
The source of the problem with logical possibility is that it is necessarily relative to our knowledge about a particular phenomenon. Thus, for instance, until it was discovered that the Earth is moving through space, it had been logically possible that it stays stationary. But after it it has become logically impossible.
It may be countered that in some cases the human mind is just capable of seeing that something must be so, but not in others. For instance, we are just capable of seeing that the Pythagoras theorem is true. But we cannot see that, say, the gravitational constant must have the observed value. However, the question is what can make us sure that we can never see that claims like the latter are necessarily true. There does not seem to be an obvious reason for that.
In other words, there is no good reason to believe that certain facts about the world are merely contingent. Any attempt to prove the contrary must rely on implicit claims to access to some kind of Platonic realm of certainty only in certain supposedly purely mental spheres (e.g. mathematics), which borders on religion.