§ 32. Transcendental Truth.
The forms of intuitive, empirical knowledge which lie within the Understanding and pure Sensibility may, as conditions of all possible experience, be the grounds of a judgment, which is in that case synthetical à priori. As nevertheless this kind of judgment has material truth, its truth is transcendental; because the judgment is based not only on experience, but on the conditions of all possible experience lying within us. For it is determined precisely by that which determines experience itself: namely, either by the forms of Space and of Time perceived by us à priori, or by the causal law, known to us à priori. Propositions such as: two straight lines do not include a space; nothing happens without a cause; matter can neither come into being nor perish; 3 × 7 = 21, are examples of this kind of judgment. The whole of pure Mathematics, and no less my tables of the Prædicabilia à priori,[131] as well as most of Kant's theorems in his "Metaphysische Anfangsgründe der Naturwissenschaft," may, properly speaking, be adduced in corroboration of this kind of truth.
§ 33. Metalogical Truth.
Lastly, a judgment may be founded on the formal conditions of all thinking, which are contained in the Reason; and in this case its truth is of a kind which seems to me best defined as metalogical truth. This expression has nothing at all to do with the "Metalogicus" written by Johannes Sarisberriensis in the twelfth century, for he declares in his prologue, "quia Logicæ suscepi patrocinium, Metalogicus inscriptus est liber," and never makes use of the word again. There are only four metalogically true judgments of this sort, which were discovered long ago by induction, and called the laws of all thinking; although entire uniformity of opinion as to their expression and even as to their number has not yet been arrived at, whereas all agree perfectly as to what they are on the whole meant to indicate. They are the following:—
1. A subject is equal to the sum total of its predicates, or a = a.
2. No predicate can be attributed and denied to a subject at the same time, or a = -a = o.
3. One of two opposite, contradictory predicates must belong to every subject.
4. Truth is the reference of a judgment to something outside of it, as its sufficient reason.
It is by means of a kind of reflection which I am inclined to call Reason's self-examination, that we know that these judgments express the conditions of all thinking, and therefore have these conditions for their reason. For, by the fruitlessness of its endeavours to think in opposition to these laws, our Reason acknowledges them to be the conditions of all possible thinking: we then find out, that it is just as impossible to think in opposition to them, as it is to move the members of our body in a contrary direction to their joints. If it were possible for the subject to know itself, these laws would be known to us immediately, and we should not need to try experiments with them on objects, i.e. representations. In this respect it is just the same with the reasons of judgments which have transcendental truth; for they do not either come into our consciousness immediately, but only in concreto, by means of objects, i.e. of representations. In endeavouring, for instance, to conceive a change without a preceding cause, or a passing into or out of being of Matter, we become aware that it is impossible; moreover we recognise this impossibility to be an objective one, although its root lies in our intellect: for we could not otherwise bring it to consciousness in a subjective way. There is, on the whole, a strong likeness and connection between transcendental and metalogical truths, which shows that they spring from a common root. In this chapter we see the Principle of Sufficient Reason chiefly as metalogical truth, whereas in the last it appeared as transcendental truth and in the next one it will again be seen as transcendental truth under another form. In the present treatise I am taking special pains, precisely on this account, to establish the Principle of Sufficient Reason as a judgment having a fourfold reason; by which I do not mean four different reasons leading contingently to the same judgment, but one reason presenting itself under a fourfold aspect: and this is what I call its Fourfold Root. The other three metalogical truths so strongly resemble one another, that in considering them one is almost necessarily induced to search for their common expression, as I have done in the Ninth Chapter of the Second Volume of my chief work. On the other hand, they differ considerably from the Principle of Sufficient Reason. If we were to seek an analogue for the three other metalogical truths among transcendental truths, the one I should choose would be this: Substance, I mean Matter, is permanent.