Section 1 - Concerning the principle of contradiction

Summary

WARNING: Since I am particularly concerned to be brief in this treatise, I think it better here not to copy out afresh the definitions and axioms which are firmly established in ordinary knowledge and which are consonant with right reason. Nor do I think it a good idea to follow the example, by imitating their practice, of those who, slavishly bound by I know not what method, only deem themselves to have proceeded in a rational fashion if they have scrutinised from beginning to end whatever they find on the bookshelves of philosophers. I have thought it good to warn the reader of this in advance, lest he take for a fault that which I have done deliberately.

Proposition I. There is no UNIQUE, absolutely first, universal principle of all truths.

A first and truly unique principle must necessarily be a simple proposition; if it covertly embraced a number of propositions it would merely present the deceptive semblance of a unique principle. If, therefore, a proposition is truly simple, it must be either affirmative or negative. But I maintain that if it is one or the other, it cannot be universal and subsume under itself all truths whatever. For, if you say that it is affirmative, it cannot be the absolutely first principle of all negative truths; and if you say that it is negative it cannot take command of the positive truths.

Let us suppose, namely, that the proposition is negative. Who is there who does not see that, since the logical derivation of all truths from their principles is either direct or indirect, it is not possible, firstly, to deduce anything from a negative principle by the direct method of inference except negative conclusions? If you then go on to insist that affirmative propositions flow from that negative principle indirectly, then you will acknowledge that this can only happen by means of the following proposition: everything of which the opposite is false, is true.