taught us to be wary in affirming that in anything we have the perfect truth, and that nature has spoken the last word to us, that last word which may give a new meaning to the whole context. Our knowledge consists of more or less tentative hypotheses. Probability is the guide of our lives. Absolute knowledge is not our assured possession. We must still be wooers of truth.
This account of knowledge must in the meantime be held provisionally. Hypothetical certainties have been referred to. There are various classes of certainties which may be so designated, and the nature and bearing of these must be investigated, especially since their relation to our knowledge of the actual world is often so grievously misunderstood. Prominent among them are the truths of mathematics. The laws of thought afford another illustration. We shall begin with the latter.
According to the law of Identity we must affirm Α to be Α; according to the law of non-contradiction we cannot think Α to be not Α. There is necessity laid upon our thinking; we have reached absolute certainty. Yet the nature of this certainty must be carefully observed. It is not said that we must always think thus. It is not said that this is a law of the mind. As soon as we venture to say what a law is, and what the mind is, we are involved in questions of infinite complexity. Neither is it said that the real world, independent of mind, has this as its fundamental principle. Descartes thought it possible, that a demon might be misleading him in what seemed most certain, and though our fears may not take this shape, we need at least to be chary in handling the relation of the subjective to the objective. What is meant by these ‘laws’ is, that when, at this present moment, Α and not-Α are before me, I am unable consciously to interchange them.
Have the laws thus explained any limit to their application? Aristotle regarded them as holding in their original form absolute sway over all thought, and in a sense this is true. An idea cannot take its negative to itself. In deductions from a hypothesis, that only which logically accords with it, can be
