CHAPTER VIII.. General Observations and Results.

GENERAL OBSERVATIONS AND RESULTS.

§ 46. The Systematic Order.

The order of succession in which I have stated the various forms of the Principle of Sufficient Reason in this treatise, is not systematic; it has been chosen for the sake of greater clearness, in order first to present what is better known and least presupposes the rest. In this I have followed Aristotle's rule: καὶ μαθήσεως οὐκ ἀπὸ τοῦ πρώτου, καὶ τῆς τοῦ πράγματος ἀρχῆς ἐνίοτε ἀρκτέον, ἀλλ' ὅθεν ῥᾷστ' ἂν μάθοι (et doctrina non a primo, ac rei principio aliquando inchoanda est, sed unde quis facilius discat). But the systematic order in which the different classes of reasons ought to follow one another is the following. First of all should come The Principle of Sufficient Reason of Being; and in this again first its application to Time, as being the simple schema containing only what is essential in all the other forms of the Principle of Sufficient Reason, nay, as being the prototype of all finitude. The Reason of Being in Space having next been stated, the Law of Causality would then follow; after which would come the Law of Motives, and last of all the Principle of Sufficient Reason of Knowing; for the other classes of reasons refer to immediate representations, whereas this last class refers to representations derived from other representations.

Aristot. "Metaph." iv. 1. "Sometimes too, learning must start, not from what is really first and with the actual beginning of the thing concerned, but from where it is easiest to learn." [Tr.'s add.]

The truth expressed above, that Time is the simple schema which merely contains the essential part of all the forms of the Principle of Sufficient Reason, explains the absolutely perfect clearness and precision of Arithmetic, a point in which no other science can compete with it. For all sciences, being throughout combinations of reasons and consequences, are based upon the Principle of Sufficient Reason. Now, the series of numbers is the simple and only series of reasons and consequences of Being in Time; on account of this perfect simplicity--nothing being omitted, no indefinite relations left--this series leaves nothing to be desired as regards accuracy, apodeictic certainty and clearness. All the other sciences yield precedence in this respect to Arithmetic; even Geometry: because so many relations arise out of the three dimensions of Space, that a comprehensive synopsis of them becomes too difficult, not only for pure, but even for empirical intuition; complicated geometrical problems are therefore only solved by calculation; that is, Geometry is quick to resolve itself into Arithmetic. It is not necessary to point out the existence of sundry elements of obscurity in the other sciences.

§ 47. Relation in Time between Reason and Consequence.

According to the laws of causality and of motivation, a reason must precede its consequence in Time. That this is absolutely essential, I have shown in my chief work, to which I here refer my readers in order to avoid repeating myself. Therefore, if we only bear in mind that it is not one thing which is the cause of another thing, but one state which is the cause of another state, we shall not allow ourselves to be misled by examples like that given by Kant, that the stove, which is the cause of the warmth of the room, is simultaneous with its effect. The state of the stove: that is, its being warmer than its surrounding medium, must precede the communication of its surplus caloric to that medium; now, as each layer of air on becoming warm makes way for a cooler layer rushing in, the first state, the cause, and consequently also the second, the effect, are renewed until at last the temperature of stove and room become equalized. Here therefore we have no permanent cause (the stove) and permanent effect (the warmth of the room) as simultaneous things, but a chain of changes; that is, a constant renewing of two states, one of which is the effect of the other. From this example, however, it is obvious that even Kant's conception of Causality was far from clear.

See "Die Welt a. W. u. V.," vol. ii. ch. iv. p. 41, 42 of the 2nd edition, and p. 44 of the 3rd.

Kant, "Krit. d. r. Vern.," 1st edition, p. 202; 5th edition, p. 248 (English translation by M. Müller, p. 177.)

On the other hand, the Principle of Sufficient Reason of Knowing conveys with it no relation in Time, but merely a relation for our Reason: here therefore, before and after have no meaning.

In the Principle of Sufficient Reason of Being, so far as it is valid in Geometry, there is likewise no relation in Time, but only a relation in Space, of which we might say that all things were co-existent, if here the words co-existence and succession had any meaning. In Arithmetic, on the contrary, the Reason of Being is nothing else but precisely the relation of Time itself.

§ 48. Reciprocity of Reasons.

Hypothetical judgments may be founded upon the Principle of Sufficient Reason in each of its significations, as indeed every hypothetical judgment is ultimately based upon that principle, and here the laws of hypothetical conclusions always hold good: that is to say, it is right to infer the existence of the consequence from the existence of the reason, and the non-existence of the reason from the non-existence of the consequence; but it is wrong to infer the non-existence of the consequence from the non-existence of the reason, and the existence of the reason from the existence of the consequence. Now it is singular that in Geometry we are nevertheless nearly always able to infer the existence of the reason from the existence of the consequence, and the non-existence of the consequence from the non-existence of the reason. This proceeds, as I have shown in § 37, from the fact that, as each line determines the position of the rest, it is quite indifferent which we begin at: that is, which we consider as the reason, and which as the consequence. We may easily convince ourselves of this by going through the whole of the geometrical theorems. It is only where we have to do not only with figures, i.e., with the positions of lines, but with planes independently of figures, that we find it in most cases impossible to infer the existence of the reason from the existence of the consequence, or, in other words, to convert the propositions by making the condition the conditioned. The following theorem gives an instance of this: Triangles whose lengths and bases are equal, include equal areas. This cannot be converted as follows: Triangles whose areas are equal, have likewise equal bases and lengths; for the lengths may stand in inverse proportion to the bases.

In § 20 it has already been shown, that the law of causality does not admit of reciprocity, since the effect never can be the cause of its cause; therefore the conception of reciprocity is, in its right sense, inadmissible. Reciprocity, according to the Principle of Sufficient Reason of knowing, would only be possible between equivalent conceptions, since the spheres of these alone cover each other mutually. Apart from these, it only gives rise to a vicious circle.

§ 49. Necessity.

The Principle of Sufficient Reason in all its forms is the sole principle and the sole support of all necessity. For necessity has no other true and distinct meaning than that of the infallibility of the consequence when the reason is posited. Accordingly every necessity is conditioned: absolute, i.e., unconditioned, necessity therefore is a contradicto in adjecto. For to be necessary can never mean anything but to result from a given reason. By defining it as "what cannot not be," on the other hand, we give a mere verbal definition, and screen ourselves behind an extremely abstract conception to avoid giving a definition of the thing. But it is not difficult to drive us from this refuge by inquiring how the non-existence of anything can be possible or even conceivable, since all existence is only given empirically. It then comes out, that it is only possible so far as some reason or other is posited or present, from which it follows. To be necessary and to follow from a given reason, are thus convertible conceptions, and may always, as such, be substituted one for the other. The conception of an "ABSOLUTELY necessary Being" which finds so much favour with pseudo-philosophers, contains therefore a contradiction: it annuls by the predicate "absolute" (i.e., "unconditioned by anything else") the only determination which makes the "necessary" conceivable. Here again we have an instance of the improper use of abstract conceptions to play off a metaphysical artifice such as those I have already pointed out in the conceptions "immaterial substance," "cause in general," "absolute reason," &c. &c. I can never insist too much upon all abstract conceptions being checked by perception.

Compare "Die Welt a. W. u. V.," vol. i. p. 551 et seq. of the 2nd edition (i. p. 582 et seq. of 3rd edition) as to "immaterial substance," and § 52 of the present work as to "reason in general." (Editor's note.)

There exists accordingly a fourfold necessity, in conformity with the four forms of the Principle of Sufficient Reason:--

1^o. Logical necessity, according to the principle of sufficient reason of knowing, in virtue of which, when once we have admitted the premisses, we must absolutely admit the conclusion.

2^o. Physical necessity, according to the law of causality, in virtue of which, as soon as the cause presents itself, the effect must infallibly follow.

3^o. Mathematical necessity, according to the principle of sufficient reason of being, in virtue of which, every relation which is stated in a true geometrical theorem, is as that theorem affirms it to be, and every correct calculation remains irrefutable.

4^o. Moral necessity, in virtue of which, every human being, every animal even, is compelled, as soon as a motive presents itself, to do that which alone is in accordance with the inborn and immutable character of the individual. This action now follows its cause therefore as infallibly as every other effect, though it is less easy here to predict what that effect will be than in other cases, because of the difficulty we have in fathoming and completely knowing the individual empirical character and its allotted sphere of knowledge, which is indeed a very different thing from ascertaining the chemical properties of a neutral salt and predicting its reaction. I must repeat this again and again on account of the dunces and blockheads who, in defiance of the unanimous authority of so many great thinkers, still persist in audaciously maintaining the contrary, for the benefit of their old woman's philosophy. I am not a professor of philosophy, forsooth, that I need bow to the folly of others.

§ 50. Series of Reasons and Consequences.

According to the law of causality, the condition is itself always conditioned, and, moreover, conditioned in the same way; therefore, there arises a series in infinitum a parte ante. It is just the same with the Reason of Being in Space: each relative space is a figure; it has its limits, by which it is connected with another relative space, and which themselves condition the figure of this other, and so on throughout all dimensions in infinitum. But when we examine a single figure in itself, the series of reasons of being has an end, because we start from a given relation, just as the series of causes comes to an end if we stop at pleasure at any particular cause. In Time, the series of reasons of being has infinite extension both a parte ante, and a parte post, since each moment is conditioned by a preceding one, and necessarily gives rise to the following. Time has therefore neither beginning nor end. On the other hand, the series of reasons of knowledge--that is, a series of judgments, each of which gives logical truth to the other--always ends somewhere, i.e., either in an empirical, a transcendental, or a metalogical truth. If the reason of the major to which we have been led is an empirical truth, and we still continue asking why, it is no longer a reason of knowledge that is asked for, but a cause--in other words, the series of reasons of knowing passes over into the series of reasons of becoming. But if we do the contrary, that is, if we allow the series of reasons of becoming to pass over into the series of reasons of knowing, in order to bring it to an end, this is never brought about by the nature of the thing, but always by a special purpose: it is therefore a trick, and this is the sophism known by the name of the Ontological Proof. For when a cause, at which it seems desirable to stop short in order to make it the first cause, has been reached by means of the Cosmological Proof, we find out that the law of causality is not so easily brought to a standstill, and still persists in asking why: so it is simply set aside and the principle of sufficient reason of knowing, which from a distance resembles it, is substituted in its stead; and thus a reason of knowledge is given in the place of the cause which had been asked for--a reason of knowledge derived from the conception itself which has to be demonstrated, the reality of which is therefore still problematical: and this reason, as after all it is one, now has to figure as a cause. Of course the conception itself has been previously arranged for this purpose, and reality slightly covered with a few husks just for decency's sake has been placed within it, so as to give the delightful surprise of finding it there--as has been shown in