There is an important distinction in logic between what is contradictory and what is contrary. Of two contradictory propositions one must be true, the other must be false; but of two contrary propositions one must be false, but both may be false. Of contradictory propositions one is always a pure negation, one declares the non-existence of what the other affirms the existence; but of contrary propositions each has a positive content, and both may be false. A true proposition may be based on a false opinion, and it is very important to have a clear idea of what we intend by false opinion. We do not mean by false opinion such plainly false {77} propositions as that two and two are five or that there may be no corners in a square--such propositions are false, because they contradict propositions that are self-evident. If anyone should seriously affirm them, we should not, I think, say that such a one had a false opinion, but that he failed, perhaps through some illusion, to understand the meaning of the terms he was using. An example of what would now, I suppose, be unquestionably regarded by everyone as error is that whole body of opinion that found expression in the theory and practice of witchcraft. This was once almost universally accepted, and though probably at no period nor in any country was there not some one who doubted or disbelieved, still the reasons of such doubt or disbelief would probably be very different from those reasons which lead us to reject it to-day. For witchcraft was grounded on a general belief that spiritual agencies, beneficent and malign, were the cause of material well-being or evil. This conception has now given place to the mechanistic or naturalistic theory on which our modern physical science is based. We interpret all physical occurrences as caused by material agency. But this belief, quite as much as the belief in spiritual agencies, is opinion, not knowledge, and it may be false. It is conceivable that future generations will reject our scientific notions, self-evident though they seem to us, as completely as we reject the notions of the dark ages. It is even conceivable that the whole of our modern science may come to appear to mankind as not even an approximation to knowledge. Error, like illusion, may be universal. No one whose opinion counts as a rational belief now holds that sickness may be caused by the malign influence of the evil eye, and that this influence may be neutralised by making the sign of the cross; some, but very few, believe that a {78} sick man may be healed by the prayers and anointing of righteous men; many believe that material disease, however malignant, may be expelled from the body by faith; while the majority of rational men, whatever independent religious views they hold, regard sickness and disease as material in the ordinary sense, and expect them to yield to drugs and treatment. Now, of these various opinions some must be false, while all may be false.