He holds the principles of mathematics to be analytical; and if his were correct, they would certainly be apodeictic also: but we could not infer from this that reason has the faculty of forming apodeictic judgements in philosophy also- that is to say, those which are synthetical judgements, like the judgement of causality. But if we adopt a universal empiricism, then mathematics will be included.
Now if this science is in contradiction with a reason that admits only empirical principles, as it inevitably is in the antinomy in which mathematics prove the infinite divisibility of space, which empiricism cannot admit; then the greatest possible evidence of demonstration is in manifest contradiction with the alleged conclusions from experience, and we are driven to ask, like Cheselden's blind patient, "Which deceives me, sight or touch?" (for empiricism is based on a necessity felt, rationalism on a necessity seen). And thus universal empiricism reveals itself as absolute scepticism. It is erroneous to attribute this in such an unqualified sense to Hume, 7 since he left at least one certain touchstone (which can only be found in a priori principles), although experience consists not only of feelings, but also of judgements.
{PREFACE ^paragraph 35}
However, as in this philosophical and critical age such empiricism can scarcely be serious, and it is probably put forward only as an intellectual exercise and for the purpose of putting in a clearer light, by contrast, the necessity of rational a priori principles, we can only be grateful to those who employ themselves in this otherwise uninstructive labour.
Of the Idea of a Critique of Practical Reason.
The theoretical use of reason was concerned with objects of the cognitive faculty only, and a critical examination of it with reference to this use applied properly only to the pure faculty of cognition; because this raised the suspicion, which was afterwards confirmed, that it might easily pass beyond its limits, and be lost among unattainable objects, or even contradictory notions. It is quite different with the practical use of reason. In this, reason is concerned with the grounds of determination of the will, which is a faculty either to produce objects corresponding to ideas, or to determine ourselves to the effecting of such objects (whether the physical power is sufficient or not); that is, to determine our causality. For here, reason can at least attain so far as to determine the will, and has always objective reality in so far as it is the volition only that is in question. The first question here then is whether pure reason of itself alone suffices to determine the will, or whether it can be a ground of determination only as dependent on empirical conditions. Now, here there comes in a notion of causality justified by the critique of the pure reason, although not capable of being presented empirically, viz., that of freedom; and if we can now discover means of proving that this property does in fact belong to the human will (and so to the will of all rational beings), then it will not only be shown that pure reason can be practical, but that it alone, and not reason empirically limited, is indubitably practical; consequently, we shall have to make a critical examination, not of pure practical reason, but only of practical reason generally. For when once pure reason is shown to exist, it needs no critical examination. For reason itself contains the standard for the critical examination of every use of it. The critique, then, of practical reason generally is bound to prevent the empirically conditioned reason from claiming exclusively to furnish the ground of determination of the will. If it is proved that there is a [practical] reason, its employment is alone immanent; the empirically conditioned use, which claims supremacy, is on the contrary transcendent and expresses itself in demands and precepts which go quite beyond its sphere. This is just the opposite of what might be said of pure reason in its speculative employment.
However, as it is still pure reason, the knowledge of which is here the foundation of its practical employment, the general outline of the classification of a critique of practical reason must be arranged in accordance with that of the speculative. We must, then, have the Elements and the Methodology of it; and in the former an Analytic as the rule of truth, and a Dialectic as the exposition and dissolution of the illusion in the judgements of practical reason. But the order in the subdivision of the Analytic will be the reverse of that in the critique of the pure speculative reason. For, in the present case, we shall commence with the principles and proceed to the concepts, and only then, if possible, to the senses; whereas in the case of the speculative reason we began with the senses and had to end with the principles. The reason of this lies again in this: that now we have to do with a will, and have to consider reason, not in its relation to objects, but to this will and its causality. We must, then, begin with the principles of a causality not empirically conditioned, after which the attempt can be made to establish our notions of the determining grounds of such a will, of their application to objects, and finally to the subject and its sense faculty. We necessarily begin with the law of causality from freedom, that is, with a pure practical principle, and this determines the objects to which alone it can be applied.
BOOK I. The Analytic of Pure Practical Reason
CHAPTER I. Of the Principles of Pure Practical Reason
{BOOK_1|CHAPTER_1 ^paragraph 5}
I. DEFINITION
Practical principles are propositions which contain a general determination of the will, having under it several practical rules. They are subjective, or maxims, when the condition is regarded by the subject as valid only for his own will, but are objective, or practical laws, when the condition is recognized as objective, that is, valid for the will of every rational being.
{BOOK_1|CHAPTER_1 ^paragraph 10}
Supposing that pure reason contains in itself a practical motive, that is, one adequate to determine the will, then there are practical laws; otherwise all practical principles will be mere maxims. In case the will of a rational being is pathologically affected, there may occur a conflict of the maxims with the practical laws recognized by itself. For example, one may make it his maxim to let no injury pass unrevenged, and yet he may see that this is not a practical law, but only his own maxim; that, on the contrary, regarded as being in one and the same maxim a rule for the will of every rational being, it must contradict itself. In natural philosophy the principles of what happens, (e.g., the principle of equality of action and reaction in the communication of motion) are at the same time laws of nature; for the use of reason there is theoretical and determined by the nature of the object. In practical philosophy, i.e., that which has to do only with the grounds of determination of the will, the principles which a man makes for himself are not laws by which one is inevitably bound; because reason in practical matters has to do with the subject, namely, with the faculty of desire, the special character of which may occasion variety in the rule. The practical rule is always a product of reason, because it prescribes action as a means to the effect. But in the case of a being with whom reason does not of itself determine the will, this rule is an imperative, i.e., a rule characterized by "shall," which expresses the objective necessitation of the action and signifies that, if reason completely determined the will, the action would inevitably take place according to this rule. Imperatives, therefore, are objectively valid, and are quite distinct from maxims, which are subjective principles. The former either determine the conditions of the causality of the rational being as an efficient cause, i.e., merely in reference to the effect and the means of attaining it; or they determine the will only, whether it is adequate to the effect or not. The former would be hypothetical imperatives, and contain mere precepts of skill; the latter, on the contrary, would be categorical, and would alone be practical laws. Thus maxims are principles, but not imperatives. Imperatives themselves, however, when they are conditional (i.e., do not determine the will simply as will, but only in respect to a desired effect, that is, when they are hypothetical imperatives), are practical precepts but not laws. Laws must be sufficient to determine the will as will, even before I ask whether I have power sufficient for a desired effect, or the means necessary to produce it; hence they are categorical:
Names that designate the followers of a sect have always been accompanied with much injustice; just as if one said, "N is an Idealist." For although he not only admits, but even insists, that our ideas of external things have actual objects of external things corresponding to them, yet he holds that the form of the intuition does not depend on them but on the human mind.
