…the substantially possible refers to the information of a person who knows everything now existing, whether particular fact or law, together with all their consequences. [—] The terms, substantial necessity and substantial possibility […] refer to supposed information of the present in the present, including among the objects known all existing laws as well as special facts.
…possibility may be understood in many senses; but they may all be embraced under the definition that that is possible which, in a certain state of information, is not known to be false. By varying the supposed state of information all the varieties of possibility are obtained. Thus, essential possibility is that which supposes nothing to be known except logical rules. Substantive possibility, on the other hand, supposes a state of omniscience.
In respect to the ideal world we are virtually omniscient; that is to say, there is nothing but lack of time, of perseverance, and of activity of mind to prevent our making the requisite experiments to ascertain positively whether a given combination occurs or not. Thus, every proposition about the ideal world can be ascertained to be either true or false. A description of thing which occurs in that world is possible, in the substantive logical sense. Very many writers assert that everything is logically possible which involves no contradiction. Let us call that sort of logical possibility, essential, or formal, logical possibility. It is not the only logical possibility; for in this sense, two propositions contradictory of one another may both be severally possible, although their combination is not possible. But in the substantive sense, the contradictory of a possible proposition is impossible, because we are virtually omniscient in regard to the ideal world. For example, there is no contradiction in supposing that only four, or any other number, of independent atoms exist. But it is made clear to us by ideal experimentation, that five atoms are to be found in the ideal world. Whether all five are to be found in the sensible world or not, to say that there are only four in the ideal world is a proposition absolutely to be rejected, notwithstanding its involving no contradiction.