A simple idea.

Physicists disagree about what exists, but they tend to agree that nothing is just the lack of that which exists. Note that this is physical nothing, or physical impossibility. Nothing "contains", as it were, all the physically impossible objects, but there are none, so nothing is "empty", as it were. There is one more interesting point to add, which will play a crucial role later on - sure physicists will agree that nothing is the lack of any physical thing, but since what counts as a physically possible object needn't be congruent across physical theories (it's not), physicists will disagree about the list of stuff that nothing is meant to denote the lack of.

Is it really that difficult to extend this idea to logical impossibility? I think not. Analogously, we extend the idea of physical nothing to logical nothing as the lack of what can exist. Here, nothing "contains", as it were, all the logically impossible objects, but there can't be such things, so nothing is "empty", as it were. Furthermore logicians will tend to agree that nothing possible is the lack of any possible thing, but since what counts as a logically possible object needn't be congruent across logical theories (it isn't), logicians will disagree about the list of stuff that nothing possible is meant to denote the lack of.

Clearly, in some set theoretic ontological model nothing possible can be identified with the empty set. That is we think of the empty set Ø_K(L) as the object associated with all the impossible objects in the L theory, K. We can thus speak of the order of the empty set, here called the rarity, defined as the cardinality of all the K(L) impossible objects.