Chapter 12 Chapter 8 Overview and Conclusions

SECTION 46 SYSTEM ORDER The sequence of the different forms of the principle of sufficient reason, which is dealt with in this treatise, is not systematic; it is arranged only for the sake of greater clarity, so that the form which is easy to know and which is the least dependent on others is put forward first.In this we follow the principle of Aristotle: "Sometimes learning begins not from the real beginning of what actually happened first and concerning things, but from the place where it is easy to learn." ①However, different kinds of The sequence of systems to be followed by grounds to each other is as follows: first there should be the principle of sufficient reason of being, which in turn applies first to time, as a simple schema containing only the essential content of all other forms of the law of sufficient reason, and as the principle of all finite paradigm of the world.The grounds of existence in space are next to be dealt with, after which the law of causality follows; after that the law of motives, and finally the law of sufficient ground of cognition; Related to representations of other representations.

-------- ① Aristotle: Chapter 1 of Volume 4. The truth stated above, that time is but a simple schema containing the essential part of all forms of the principle of sufficient reason, illustrates the absolute perfection of clarity and precision of arithmetic, which no other science can equal in this respect.Since science is the connection of grounds and inferences, it must be based on the principle of sufficient reason.The series of numbers is the succinct and only series of grounds and inferences existing in time; Impeccable in terms of certainty, absolute certainty and clarity.It is in this respect that all other sciences are inferior to arithmetic; even geometry: since so many relations arise in the three dimensions of space, it is difficult, not only for pure intuition, but even for empirical intuition, to generalize them synthetically. Relations, too, are too difficult; therefore complex geometrical problems can only be solved by calculation; thus geometry quickly resolves itself into arithmetical problems.As for the existence of many uncertain factors in other sciences, I will not point them out here.

§ 47 Temporal relation between grounds and inferences From the perspective of the law of causality and the law of motivation, grounds must precede inferences in time.This absolutely essential conclusion has already been explained in my representative work, and in order to avoid repetition, the reader is referred to my representative work①.Therefore, if we only remember that one thing is not the cause of another thing, but that one state is the cause of another state, we shall not be led astray by the example given by Kant2: the stove is the cause of the warming of a room , coexisting with the result.The state of the furnace, i.e. its higher temperature than the surrounding heat conductors, must have preceded the transfer of its surplus heat to the heat conductors; Another layer of relatively cool air, then the first state is the cause, and the subsequent second state is the effect, and the cause and effect are constantly renewed until finally the temperature of the furnace and the room are equal.We do not, therefore, find here an eternal cause (the furnace) and an eternal effect (the warming of the room) for something to happen simultaneously, but only a chain of change, a constant alternation of two states, one of which is the result of another state.From this example, however, it becomes clear how confused even Kant's concept of causation is.

-------- ①Second edition, page 41 of Chapter 4 of Volume II, page 44 of the first edition. ② Kant:, first edition, p. 202; fifth edition, p. 248. On the other hand, the principle of sufficient reason for knowing has nothing to do with time, but only with reason: "before" and "after" therefore have no meaning here. In the principle of sufficient reason of being, so far as it is valid for geometry, it is also not concerned with time, but only with space, and if the words coexistence and succession have any meaning, then the space of which we are talking refers to the coexistence of all things.In arithmetic, on the contrary, the laws of existence are only definite temporal relations.

Relevance under Section 48 The hypothetical judgment is based on every correct sense of the principle of sufficient reason, because every hypothetical judgment is ultimately based on the principle of reason, and here the law of inference is assumed to be always valid, that is to say: it follows from the existence of grounds that The existence of inferences can also be deduced from the non-existence of inferences to the non-existence of grounds; but it is wrong to infer the non-existence of inferences from the non-existence of grounds, and the existence of grounds from the existence of inferences.In geometry, however, it is unique that we can almost always deduce the existence of grounds from the existence of inferences, and the non-existence of inferences from the non-existence of grounds.As I said in section 37, it arises from the fact that since each line determines the position of the others, it does not matter where we start, which line is taken as the cause, It doesn't matter which line is taken as the result.We are easily convinced of this by looking at all the theorems of geometry as a whole.Where we have to deal not only with shapes, i.e., with the positions of lines, but also with planes independent of shapes, we find it impossible in most cases to deduce the existence of grounds from the existence of inferences, or in other words, without It is possible to transform these propositions by making this condition the defined condition.The following theorem provides such an illustration: Two triangles with equal heights and bases have equal areas.This theorem cannot be transformed as follows: if two triangles have equal areas, their heights and bases will also be equal; for height and base are inversely proportional.

I have shown in Section 20 that causality does not permit correlation, since an effect can never be the cause of its cause; the concept of correlation is therefore inadmissible in its proper sense.From the point of view of the principle of sufficient reason for cognition, correlation is only possible between concepts of equivalent value, because only the extensions of these concepts contain each other.Beyond that, a vicious circle can only be created. Section 49 Necessity The principle of sufficient reason in its various forms is the sole maxim and ground of all necessity.For necessity has no real and special meaning other than grounded and inferred.Every necessity is thus defined: absolute, that is, unconditional necessity is self-contradictory.For necessity means nothing other than that something follows from a certain cause.On the other hand, by defining it as "it can't be," we are able to give a purely verbal definition, and veil ourselves behind a very abstract concept, in order to avoid defining the thing.But it is not difficult to drive us out of this refuge by simply asking how the non-existence of anything is possible or even conceivable, since any existence can only be given by experience.Thus, the only possibility of existence is to be ascertained or exist on some ground or another, and then it follows.The two concepts of becoming inevitable and arising from a given ground are interchangeable, and they are completely interchangeable.Thus, the notion of "absolutely necessary being," which has been ardently championed by pseudo-philosophers, contains a contradiction: it cancels the "necessary" become the only prescriptiveness imaginable.Here again we have given an example of the misuse of abstract concepts, exposing metaphysical tricks, as I have pointed out in such concepts as 'immaterial substance', 'general cause', 'absolute ground', etc.I would never have insisted so strongly that all abstractions should be tested intuitively.

Thus, in accordance with the four forms of the principle of sufficient reason, there are fourfold necessities:— -------- ① Compare pages 551 and following of Volume 1 of the second edition (pages 582 and following of the third edition) on "immaterial entities" and this book on "general grounds", Section 52.editor. 1.Logical necessity, according to the principle of sufficient reason of cognition, once we admit the premises, we must absolutely admit the conclusion. 2.Physical necessity, according to the law of causality, states that whenever a cause occurs, the effect must follow without question.

3.Mathematical necessity, by the principle of sufficient reason of existence, states that any relation stated in a correct geometric theorem is indeed a relation determined by that theorem, and every correct calculation is irrefutable. 4.Moral necessity, according to which every human being, and even every animal, is compelled, provided a motive arises, to do that which corresponds to the innate and unalterable character of the individual.Now, therefore, actions from this cause are as inevitable as all other consequences, though here than in other cases it is more difficult to predict what the consequences will be, because it is difficult to fathom and thoroughly know the characteristics of the experience of the individual and the attainment of knowledge. It is a completely different matter from figuring out the chemical composition of a neutral salt and predicting how it will react.I must stress this repeatedly, because those fools, for the benefit of their old ladies' philosophy, disregard the unanimity of so many good thinkers, and still presumptuously insist on the contrary.I'm not a professor of philosophy, so I certainly don't need to conform to other people's stupidity.

Section 50 Grounds and Inferences Series According to the law of causality, the condition itself is always limited, and it is also the condition itself that is limited, so that, seen from the "before" aspect, an infinite sequence arises.This is exactly the same as the law of existence in space: each relative space is a figure, which has its own limitations, and is connected with another relative space by this. Such relative space is the condition of another relative space figure , which can be pushed to infinity in all directions.But when we consider a single figure itself, the series of grounds for existence is limited, since we start with a given relation, and if we stop at any particular cause at will, then the One reason series ends.In time, the series of grounds of existence can be extended infinitely both forward and backward, because each moment is determined by the previous moment and necessarily produces the next moment.Therefore, time has no beginning and no end.On the other hand, the series of grounds of knowledge—a series of judgments, each of which gives logical truth to the other—always ends somewhere, that is, at either an empirical, a priori, or a metalogical truth. .If the basis of the major premise we have reached is an empirical truth, and we still have to continue to ask "why", then what is pursued is no longer a cognitive basis, but a cause-in other words, the series of cognitive grounds has given way to to form according to the series.But if, on the contrary, we allow the series of grounds of formation to give way to the series of grounds of knowledge, in order to facilitate it to have an end, then this is not due to the nature of things, but always due to a special purpose: it is therefore a trick, and this This is known as the sophistry of ontological proofs.For when it has been proved through cosmology that a cause has been found and made the first cause, it seems necessary to stop there, we find that the problem is not so simple, that cause and effect will not stop, it will continue. "Why" is asked, so it can only be set aside, and the principle of sufficient reason of knowledge, which is somewhat imaginative of it, is used in its place; what was sought after is the reason, and now it is given the reason of knowledge-the concept itself It remains to be demonstrated, and the existence of a ground of knowledge derived from this concept remains a question, and this ground, after all, is a ground, and now has to be a cause.Of course, this concept itself has been prepared for this in advance. Out of the need of face, the seemingly not very valuable existence is placed in it at this time, so that you can be surprised when you find it—just as I explained in section 7.On the other hand, if the series of judgments depends entirely on the rules of a priori or super-logical truth, and we continue to ask "why", then we will not find the answer at all, because the question is meaningless, that is, we do not know what is being asked. What kind of basis is it.

Because the principle of sufficient reason is the law of all explanations, explaining a thing means reducing a given existence or connection to a certain form of the principle of sufficient reason, and the existence or connection corresponding to this form must also be such an existence or connection. connect.Hence the principle of sufficient reason itself, that is, the connection shown by any of its forms, can no longer be explained; for there is no principle by which all explanations can be accounted for: just as the eye sees anything other than itself. things, but cannot see themselves.There are, of course, series of motives, since the determination to find out becomes a determination to employ a complete series of means; In it, and from the very beginning, there is a power to activate the concrete will.The fact that motives perform such tasks is an account of our recognition of the empirical character given here, but this fact does not answer the question why this particular motive acts on this particular character; guilt, and can never be an object.Thus a series of motives like this can find its end in some such ultimate motive, and, according to the nature of this ultimate moment, become a series of causes, or a series of grounds of knowledge, i.e., when the ultimate moment is a real object, into The former; becomes the latter when the ultimate link is a pure concept.

§51 Every science chooses as its lead out of the forms of the principle of sufficient reason the form which is most suitable to it. Since the question "why" always requires a sufficient ground, and since it connects its concepts by the principle of sufficient ground, which divides science from the concept of mere heaps, we call this " Why" is the mother of all science (v. 4).Moreover, we find that in every science a form of the principle of sufficient reason predominates and guides the subject.Therefore, in pure mathematics, the law of existence is its main lead (although the explanation of these proofs can only be derived from the law of cognition); in applied mathematics, the law of causality is displayed together with the law of existence, but in physics, chemistry, geology In , the law of causality completely dominates.The principle of sufficient ground for knowledge applies broadly to the whole of sciences, as in the whole of sciences it is through the knowledge of the individual in general; and in botany, zoology, mineralogy, and other taxonomic sciences it is the chief thread of its absolute dominance. .The laws of motivation (motives) are the chief guides of history, politics, practical psychology, etc., when we consider all motives and maxims, whatever they may be, as material for explaining behaviour—and when we proceed from their value and origin And when it becomes the object of research, the law of motivation becomes the guideline of ethics.In my magnum opus I have made an exhaustive division of the sciences according to this principle. -------- ① Volume II, Second Edition, page 126 (page 139, third paragraph). Section 52 Two main conclusions In this essay I have endeavored to show that the principle of sufficient reason is a common formulation of four quite different relations, each of which is based on a particular law given a priori (principle of sufficient reason is the law of innate synthesis).According to the law of unity, we have to assume that the four laws discovered by the law of resolution, since they are all expressed in one predicate, must therefore arise from the same original characteristic of our cognitive faculties and As their common root, we shall therefore have to regard this root as the sheer dependence, relativity, indeterminacy, and finiteness of the objects of our consciousness—consciousness itself limited to sensibility, understanding, reason, Subject and object—or call it the innermost origin of the finiteness of the world, which Plato repeatedly denigrates as constantly arising and passing away, but in fact never exists. ".And the Christians, by instinct, rightly call it a transitory thing, according to this form (time) of the principle of reason.I have defined this form as the simplest paradigm and prototype of all finite things.The general meaning of the principle of sufficient reason can be summed up as follows: everything that exists wherever and whenever it exists exists because of the existence of other things.However, the principle of sufficient reason in its various forms is a priori, that is, its root is in our intellect, and therefore it must not apply to all beings (the universe), including the intellect in which it manifests itself.For such a world, which manifests itself by means of a priori forms, can only be appearance; what applies to appearances as a consequence of these forms cannot, therefore, apply to the world itself, the thing-in-itself in which it presents itself.Therefore, we cannot say: "The world and its all things exist only because of the existence of other things." This proposition is a typical cosmological proof. If this treatise leads to the conclusions just expressed, it seems to me that any speculative philosopher who wishes to base his conclusions on the principle of sufficient reason, or who does speak of a reason, must specify which one he means. Class basis.One might think that if there is some doubt about a ground, it can be taken for granted that it should be done, and that all confusion will be cleared up.It is not too often, however, that we find the terms ground and cause confused in indiscriminate use: it is just to hear people speak of ground and ground, condition and Conditioned on and principles and by principles, perhaps because there is a hidden consciousness, these concepts are being used in an unapproved manner.Thus even Kant speaks of the thing itself as the ground of appearance, and as the ground of the possibility of all appearances, the cause of the intelligibility of appearances, an as yet unrecognized ground of the possibility of the whole series of sensations, as The transcendental object of the ground of all appearances, and why our senses must, in all conditions, be the ground of the determining condition, etc.All these statements seem to me to be quite at odds with Kant's following words, which are more weighty, far-reaching, and eternal, when he says: "The contingency of things is itself only phenomena, and leads only to the experience of definite phenomena. return." -------- ① Kant: pages 561, 562, 564 of the first edition, page 590 of the fifth edition (pages 483-486 of M. Miller's English translation). ② Same as above, page 540 of the first edition, page 641 of the fifth edition (page 465 of the English translation). ③ Kant: page 563 of the first edition, page 591 of the fifth edition (page 485 of M. Miller's English translation). ④The contingency of experience means in Kant's view that it shows that it is almost completely dependent on other things. The objection to Kant on page 552. Since the concepts of reason and inference, principle and principle, etc., have been used in a less definite and even very transcendental sense since Kant, and are still used in this way, everyone will know that the philosophical works that have been published in the last few years Know Kant. What follows is my refutation of the indiscriminate use of the word "reason" and of the whole law of sufficient reason connected with it; in conclusion.The four laws of our cognitive faculties, whose common expression is the principle of sufficient reason, show that they themselves are It is determined by the same original nature and inherent characteristics in our cognitive ability, which itself manifests itself as sensibility, understanding and rationality.Thus, even if we conceived the possibility of a fifth kind of object, in this case we would also have to assume that the principle of sufficient reason would also appear in a different form for such objects.Nevertheless, we have no right to speak of an absolute ground. A general ground, like a triangle in general, exists only as a concept established by inferential reflection, as a representation derived from other representations. , is just a generalized way of thinking.Just as a triangle is either acute, right, or obtuse, and at the same time equilateral, isosceles, or scalene, so each ground belongs to one of the four possible grounds I have indicated.Moreover, since we have only these four distinct classes of objects, every ground can belong to only one of these four, and there can be no other objects besides which reason itself can at any rate be among them; for As soon as we use a ground, we presuppose these four objects, as well as our capacity for representation (i.e., the whole world), and we certainly confine ourselves within these limits, never going beyond them.However, if someone else takes this in a different light and thinks that the general ground is nothing more than an idea, which derives from these four grounds and expresses what they have in common, then we have to revisit the reality. On the debate between theory and non-realism, and I will take the latter's position.