Front Page Titles (by Subject) Section IV: The Discipline of Pure Reason with Regard to its Proofs - Critique of Pure Reason
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Section IV: The Discipline of Pure Reason with Regard to its Proofs - Friedrich Max Müller, Critique of Pure Reason 
Immanuel Kant’s Critique of Pure Reason. In Commemoration of the Centenary of its First Publication. Translated into English by F. Max Mueller (2nd revised ed.) (New York: Macmillan, 1922).
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The Discipline of Pure Reason with Regard to its Proofs
What distinguishes the proofs of transcendental and synthetical propositions from all other proofs of a synthetical knowledge a priori is this, that reason is not allowed here to apply itself directly to an object through its concepts, but has first to prove the objective validity of those concepts and the possibility of their synthesis a priori. This rule is not suggested by prudence only, but refers to the very nature and the possibility of such proofs. If I am to go beyond the concept of an object a priori, this is impossible without some special guidance coming to me from without that concept. In mathematics it is intuition a priori which thus guides my synthesis, so that all our conclusions may be drawn immediately from pure intuition. In transcendental knowledge the same [p. 783] guidance, so long as we are dealing with concepts of the understanding only, is to be found in possible experience. For here the proof does not show that the given concept (for instance, the concept of that which happens) leads directly to another concept (that of a cause). This would be a saltus which nothing could justify. What our proof really shows is, that experience itself and therefore the object of experience would be impossible without such a (causal) connection. The proof, therefore, had at the same time to indicate the possibility of arriving synthetically and a priori at a certain knowledge of things which was not contained in our concept of them. Unless we attend to this point, our proofs, like streams which have broken their banks, run wildly across the fields wherever the inclination of some hidden association may chance to lead them. The semblance of a conviction, based on subjective causes of association and mistaken for the perception of a natural affinity, cannot balance the misgivings which are justly roused by such bold proceedings. Hence all attempts at proving the principle of sufficient reason have, according to the universal admission of all competent judges, been vain; and before the appearance of transcendental criticism it was thought better, as that principle could never be surrendered, to make a sturdy appeal to the common sense of mankind (an expedient which [p. 784] always shows that the cause of reason is desperate) than to attempt new dogmatical proofs of it.
But, if the proposition that has to be proved is an assertion of pure reason, and if I even intend by means of pure ideas to go beyond my empirical concepts, it would be all the more necessary that the proof should contain the justification of such a step of synthesis (if it were possible) as a necessary condition of its own validity. The so-called proof of the simple nature of our thinking substance (soul), derived from the unity of apperception, seems very plausible; but it is confronted by an inevitable difficulty, because, as the absolute unity is not a concept that can be immediately referred to a perception, but, as an idea, can only be inferred, it is difficult to understand how the mere consciousness which is, or at least may be, contained in all thought, though it may be so far a simple representation, can lead me on to the consciousness and the knowledge of a thing, in which thought alone is contained. For if I represent to myself the power of my body, as in motion, it is then to me an absolute unity, and my representation of it is a simple one. I can, therefore, very well express this representation by the motion of a point; because the volume of the body is here of no consequence, and can, without any diminution of its power, be conceived as small as one likes, and, therefore, even as existing in one point. But I should never conclude from this that, if nothing [p. 785] is given to me but the motive power of a body, that body can be conceived as a simple substance, because its representation is independent of the quantity of its volume, and, therefore, simple. I thus detect a paralogism, because the simple in the abstract is totally different from the simple as an object, and the ego which, conceived in the abstract, contains nothing manifold, can, as an object, when signifying the soul, become a very complex concept, comprehending and implying many things. In order to be prepared for such a paralogism (for unless we suspected it, the proof might excite no suspicion), it is absolutely necessary to be always in possession of a criterion of such synthetical propositions, which are meant to prove more than experience can ever supply. This criterion consists in our demanding that the proof should not be carried directly to the predicate in question, but that, first, the principle of the possibility of expanding our given concept a priori into ideas and realising them, should be established. If we always exercised this caution, and, before attempting any such proof, wisely considered ourselves, how, and with what degree of confidence, we might expect such an expansion through pure reason, and whence we might take, in such cases, knowledge which cannot be evolved from concepts nor anticipated with reference [p. 786] to possible experience, we might spare ourselves many difficult, and yet fruitless endeavours, by not asking of reason what evidently is beyond its power, or rather, by subjecting reason, which when once under the influence of this passion for speculative conquest, is not easily checked, to a thorough discipline of moderation.
The first rule, therefore, is to attempt no transcendental proofs before having first considered from whence we should take the principles on which such proofs are to be based, and by what right we may expect our conclusions to be successful. If they are principles of the understanding (for instance of causality), it is useless to attempt to arrive, by means of them, at ideas of pure reason; because they are valid only with regard to objects of experience. If they are principles of pure reason, it is again labour lost, because, though reason possesses such principles, they are all, as objective principles, dialectical and cannot be valid, except perhaps as regulative principles, for the empirical use of reason, in order to make it systematically coherent. If such so-called proofs exist already, we ought to meet their deceptive pleadings with the non liquet of a mature judgment; and although we may be unable to expose their sophisms, we have a perfect right [p. 787] to demand a deduction of the principles employed, which, if these principles are to have their origin in reason alone, will never be forthcoming. You may thus dispense with the analysis and refutation of every one of these sophisms, and dispose in a lump of the endless fallacies of Dialectic, by appealing to the tribunal of critical reason, which insists on laws.
The second peculiarity of transcendental proofs is this, that for every transcendental proposition one proof only can be found. If I have to draw conclusions, not from concepts, but from the intuition which corresponds to a concept, whether it be pure intuition, as in mathematics, or empirical, as in physical science, the intuition on which my conclusions are to rest supplies me with manifold material for synthetical propositions, which I may connect in more than one way, so that, by starting from different points, I can arrive at the same conclusion by different paths.
Every transcendental proposition, on the contrary, starts from one concept only, and predicates the synthetical condition of the possibility of the object, according to that concept. There can therefore be but one proof, because beside that concept there is nothing else whereby that object could be determined. The proof therefore [p. 788] can contain nothing more but the determination of an object in general according to that concept, which is itself one only. In the transcendental Analytic, for instance, we had deduced the principle, that everything which happens has a cause, from the single condition of the objective possibility of the concept of an event in general, namely, that the determination of any event in time, and therefore the event itself also, as belonging to experience, would be impossible, unless it were subject to such a dynamical rule. This is therefore the only possible proof; for the event which we represent to ourselves has objective validity, that is, truth, on this condition only, that an object is determined as belonging to that concept by means of the law of causality. It is true that other arguments in support of this proposition have been attempted, for instance, one derived from contingency; but if that argument is examined more carefully, we can discover no characteristic sign of contingency, except the happening, that is, existence preceded by the non-existence of the object, which leads us back to the same argument as before. If the proposition has to be proved that everything which thinks is simple, no attention is paid to what is manifold in thought, and the concept of the ego only is kept in view, which is simple, and to which all thinking is referred. The same applies to the transcendental proof of the existence of God, which rests entirely on the reciprocability of the two concepts of a most real [p. 789] and a necessary Being, and cannot be found anywhere else.
By this caution the criticism of the assertions of reason is much simplified. Wherever reason operates with concepts only, only one proof is possible, if any. If therefore we see the dogmatist advance with his ten proofs, we may be sure that he has none. For if he had one which (as it ought to be in all matters of pure reason) had apodictic power, what need would he have of others? His object can only be the same as that of the parliamentary lawyer who has one argument for one person, and another for another. He wants to take advantage of the weakness of the judges, who, without enquiring more deeply, and in order to get away as soon as possible, lay hold of the first argument that catches their attention, and decide accordingly.
The third peculiar rule of pure reason, if it is once subjected to a proper discipline with regard to transcendental proofs, is this, that such proofs must never be apagogical or circumstantial, but always ostensive or direct. The direct or ostensive proof combines, with regard to every kind of knowledge, a conviction of its truth with an insight into its sources; the apagogical proof, on the contrary, though it may produce certainty, cannot help us to comprehend the truth in its connection with the grounds of its possibility. It is therefore a mere expedient, [p. 790] and cannot satisfy all the requirements of reason. The apagogical proofs have, however, this advantage with regard to their evidence over direct proofs, that contradiction always carries with it more clearness in the representation than the best combination, and thus approaches more to the intuitional character of a demonstration.
The real reason why apagogical proofs are so much employed in different sciences, seems to be this. If the grounds from which some knowledge is to be derived are too numerous or too deeply hidden, one tries whether they may not be reached through their consequences. Now it is quite true that this modus ponens, that is, this inferring of the truth of some knowledge from the truth of its consequences, is only permitted, if all possible consequences flowing from it are true. In that case they have only one possible ground, which therefore is also the true one. This procedure, however, is impracticable, because to discover all possible consequences of any given proposition exceeds our powers. Nevertheless, this mode of arguing is employed, though under a certain indulgence, whenever something is to be established as a hypothesis only, in which case a conclusion, according to analogy, is admitted, namely, that if as many consequences as one has tested agree with an assumed ground, all others will also agree with it. To change in this way a hypothesis into a demonstrated truth, is clearly impossible. [p. 791] The modus tollens of reasoning, from consequences to their grounds, is not only perfectly strict, but also extremely easy. For if one single false consequence only can be drawn from a proposition, that proposition is wrong. Instead, therefore, of examining, for the sake of an ostensive proof, the whole series of grounds that may lead us to the truth of a cognition by means of a perfect insight into its possibility, we have only to prove that one single consequence, resulting from the opposite, is false, in order to show that the opposite itself is false, and therefore the cognition, which we had to prove, true.
This apagogical method of proof, however, is admissible in those sciences only where it is impossible to foist the subjective elements of our representations into the place of what is objective, namely, the knowledge of that which exists in the object. When this is not impossible, it must often happen that the opposite of any proposition contradicts the subjective conditions of thought only, but not the object itself, or, that both propositions contradict each other under a subjective condition, which is mistaken as objective, so that, as the condition is false, both may be false, without our being justified in inferring the truth of the one from the falseness of the other.
In mathematics such subreptions are impossible; [p. 792] and it is true, therefore, that the apagogical proof has its true place there. In natural science, in which everything is based on empirical intuitions, that kind of subreption can generally be guarded against by a repeated comparison of observations; but even thus, this mode of proof is of little value there. The transcendental endeavours of pure reason, however, are all made within the very sphere of dialectical illusion, where what is subjective presents itself, nay, forces itself upon reason in its premisses as objective. Here, therefore, it can never be allowed, with reference to synthetical propositions, to justify one’s assertions by refuting their opposite. For, either this refutation may be nothing but the mere representation of the conflict of the opposite opinion with the subjective conditions under which our reason could alone comprehend it, and this would be of no avail for rejecting the proposition itself, — (thus we see, for instance, that the unconditioned necessity of the existence of a Being cannot possibly be comprehended by us, which subjectively bars every speculative proof of a necessary Supreme Being but by no means, the possibility of such a Being by itself), — or, on the other hand, it may be that both the affirmative and the negative party have been deceived by the transcendental illusion, and base their arguments on an impossible concept of an object. In that case the rule applies, non entis nulla sunt praedicata, that is, [p. 793] everything that has been asserted with regard to an object, whether affirmatively or negatively, is wrong, and we cannot therefore arrive apagogically at the knowledge of truth by the refutation of its opposite. If, for example, we assume that the world of sense is given by itself in its totality, it is wrong to conclude that it must be either infinite in space, or finite and limited; for either is wrong, because phenomena (as mere representations) which nevertheless are to be things by themselves (as objects) are something impossible, and the infinitude of this imaginary whole, though it might be unconditioned, would (because everything in phenomena is conditioned) contradict that very unconditioned quantity which is presupposed in its concept.
The apagogical mode of proof is also the blind by which the admirers of our dogmatical philosophy have always been deceived. It may be compared to a prizefighter who is willing to prove the honour and the incontestable rights of his adopted party by offering battle to all and every one who should dare to doubt them. Such brawling, however, settles nothing, but only shows the respective strength of the two parties, and even this on the part of those only who take the offensive. The spectators, seeing that each party is alternately conqueror and conquered, [p. 794] are often led to regard the very object of the dispute with a certain amount of scepticism. In this, however, they are wrong, and it is sufficient to remind them of non defensoribus istis tempus eget. It is absolutely necessary that every one should plead his cause directly by means of a legitimate proof based on a transcendental deduction of the grounds of proof. Thus only can we see what he may have to say himself in favour of his own claims of reason. If his opponent relies on subjective grounds only, it is easy, no doubt, to refute him; but this does not benefit the dogmatist, who generally depends quite as much on the subjective grounds of his judgment, and can be quite as easily driven into a corner by his opponent. If, on the contrary, both parties employ only the direct mode of proof, they will either themselves perceive the difficulty, nay, the impossibility of finding any title for their assertions, and appeal in the end to prescription only, or, our criticism will easily discover the dogmatical illusion, and compel pure reason to surrender its exaggerated pretensions in the sphere of speculative thought, and to retreat within the limits of its own domain, — that of practical principles.
The Canon of Pure Reason [p. 795]
It is humiliating, no doubt, for human reason that it can achieve nothing by itself, nay, that it stands in need of a discipline to check its vagaries, and to guard against the illusions arising from them. But, on the other hand, it elevates reason and gives it self-confidence, that it can and must exercise that discipline itself, and allows no censorship to any one else. The bounds, moreover, which it is obliged to set to its own speculative use check at the same time the sophistical pretensions of all its opponents, and thus secure everything that remains of its formed exaggerated pretensions against every possible attack. The greatest and perhaps the only advantage of all philosophy of pure reason seems therefore to be negative only; because it serves, not as an organon for the extension, but as a discipline for the limitation of its domain, and instead of discovering truth, it only claims the modest merit of preventing error.
Nevertheless, there must be somewhere a source of positive cognitions which belong to the domain of pure reason, and which perhaps, owing to some misunderstanding only, may lead to error, while they form in [p. 796] reality the true goal of all the efforts of reason. How else could we account for that inextinguishable desire to gain a footing by any means somewhere beyond the limits of experience? Reason has a presentiment of objects which possess a great interest for it. It enters upon the path of pure speculation in order to approach them, but they fly before it. May we not suppose that on the only path which is still open to it, namely, that of its practical employments, reason may hope to meet with better success?
I understand by a canon a system of principles a priori for the proper employment of certain faculties of knowledge in general. Thus general logic, in its analytical portion, is a canon for the understanding and reason in general, but only so far as the form is concerned, for it takes no account of any contents. Thus we saw that the transcendental analytic is the canon of the pure understanding, and that it alone is capable of true synthetical knowledge a priori. When no correct use of a faculty of knowledge is possible, there is no canon, and as all synthetical knowledge of pure reason in its speculative employment is, according to all that has been hitherto said, totally impossible, there exists no canon of the speculative employment of reason (for that employment is entirely dialectical), but all transcendental logic is, in this respect, disciplinary only. Consequently, if there exists [p. 797] any correct use of pure reason at all, and, therefore, a canon relating to it, that canon will refer not to the speculative, but to the practical use of reason, which we shall now proceed to investigate.