Hegel is the merest parrot-jargon—a note which one expositor keeps repeating after another, without any of them understanding a single syllable of what they are uttering.
Before leaving this first head, I have just a remark or two to make on the law of contradiction, and the distinction of necessary and contingent truths. "Mr Ferrier (quoth Mr Cairns) is radically mistaken in setting up the law of contradiction as the test of truth; it is only the test of consistency." I never set up the law of contradiction as the test of truth; but only as the test of one class of truths—the necessary class. Yet from Mr Cairns' statement, people would infer that according to my system the truths of contingency also are to be tested by the same law. That was a small manœuvre. Mr Cairns does not seem to understand the way in which this test is applied, and as the notions of some who may honour this pamphlet with a perusal, are perhaps not much clearer than his, I shall take this opportunity of explaining the point by means of a very simple illustration. Suppose that we wish to test as necessary the truth of the proposition, "two straight lines cannot enclose a space," the way in which we set about it is this: we lay down the counter-statement, "two straight lines can enclose a space"—we then perceive that this contradicts the conception which we must form of two straight lines, if we are to form any conception of them at all—in other words, we see that it is equivalent to the proposition, "two straight lines are not two straight lines," but this again is equivalent to the assertion that "a thing is not what it is," but this contradicts the testing law—the law to which all necessary truth must conform—namely, that "a thing is what it is!" Therefore the proposition "two straight lines can enclose a space" being in this way convicted of absurdity, its opposite is established as a necessary truth. Such is an illustration of the manner in which the law of contradiction has to be applied. It has usually been regarded merely as an example of necessary truth. These remarks may serve to explain not only how it is an instance, but (what is of far more importance) how it is the criterion of necessary truth.
Mr Cairns' notion of the distinction between necessary and
