practice contradiction seems to exist between propositions which are either both universals, or both particulars, or are neither universals nor particulars. Thus, for example, take the propositions, "Religion is true," and "Religion is not true." Of course I shall be told that these are "general" propositions which must be reduced to their quantitative equivalents before the relation of Opposition can be rightly determined. But while the force of this claim is quite admissible, it can be made only on the supposition that we can have no other principle by which to measure the relations in question, all of which can be denied. Not that any reproach is to be cast upon the usual laws of Opposition, but that there is no use to strain them for the sake of finding some remote application of them in ordinary experience. Some other rule might do as well.
The incident which called my attention to the need of a more careful exposition of Opposition than is usually given to it is the following. I have quite generally observed that the ordinary student can very readily perceive that if A be true, E must be false, and vice versa, but he does not so readily admit that if A be false, E is indeterminate. The fact induced me to ask the question why this mistake should occur. There seems so often a psychological tendency to commit the error, that one suspects there may be a truth at the bottom of the phenomenon, and on careful investigation I have come to the conclusion that there is such a truth, based upon mental operations not provided for in the recognized formal signs of propositions and their meaning. Thus the true contradictory Of "Religion is true," is not "Some religion is not true," but "Religion is not true," as I think every one would readily admit. The reason for this fact will be stated again. Let it suffice at present to suggest the assumptions made by the accepted laws of Opposition and the need of modifying them for general practice.
Thus, for example, if I assert an A proposition, qualified by its sign "All," and some one denies it, he is supposed in ordinary logical parlance to imply the truth of O, but quite as
