The Commens Dictionary
Quote from ‘Letters to Georg Cantor’
By a true proposition (if there be any such thing) I mean a proposition which at some time, past or future, emerges into thought, and has the following three characters:
1st, no direct effort of yours, mine, or anybody’s, can reverse it permanently, or even permanently prevent its asserting itself;
2nd, no reasoning or discussion can permanently prevent its asserting itself;
3rd, any prediction based on the proposition, as to what ought to present itself in experience under certain conditions, will be fulfilled when those conditions are satisfied.
By a reality, I mean anything represented in a true proposition.
By a positive reality or truth, I mean one to which all three of the above criteria can be applied, - of course imperfectly, since we can never carry them out to the end.
By an ideal reality or truth, I mean one to which the first two criteria can be applied imperfectly, but the third not at all, since the proposition does not imply that any particular state of things will ever appear in experience. Such is a truth of pure mathematics.
By an ultimate reality or truth, I mean one to which the first criterion can be in some measure applied, but which can never be overthrown or rendered clearer by any reasoning, and upon which alone no predictions can be based. Thus, if you are kicked by a horse, the fact of the pain is beyond all discussion and far less can it be shaken or established by any experimentation.