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proof of a transcendental proposition. If I am required to pass, a

priori, beyond the conception of an object, I find that it is

utterly impossible without the guidance of something which is not

contained in the conception. In mathematics, it is a priori

intuition that guides my synthesis; and, in this case, all our

conclusions may be drawn immediately from pure intuition. In

transcendental cognition, so long as we are dealing only with

conceptions of the understanding, we are guided by possible

experience. That is to say, a proof in the sphere of transcendental

cognition does not show that the given conception (that of an event,

for example) leads directly to another conception (that of a cause)-

for this would be a saltus which nothing can justify; but it shows

that experience itself, and consequently the object of experience,

is impossible without the connection indicated by these conceptions.

It follows that such a proof must demonstrate the possibility of

arriving, synthetically and a priori, at a certain knowledge of

things, which was not contained in our conceptions of these things.

Unless we pay particular attention to this requirement, our proofs,

instead of pursuing the straight path indicated by reason, follow

the tortuous road of mere subjective association. The illusory

conviction, which rests upon subjective causes of association, and

which is considered as resulting from the perception of a real and

objective natural affinity, is always open to doubt and suspicion. For

this reason, all the attempts which have been made to prove the

principle of sufficient reason, have, according to the universal

admission of philosophers, been quite unsuccessful; and, before the

appearance of transcendental criticism, it was considered better, as

this principle could not be abandoned, to appeal boldly to the

common sense of mankind (a proceeding which always proves that the

problem, which reason ought to solve, is one in which philosophers

find great difficulties), rather than attempt to discover new

dogmatical proofs.

But, if the proposition to be proved is a proposition of pure

reason, and if I aim at passing beyond my empirical conceptions by the

aid of mere ideas, it is necessary that the proof should first show

that such a step in synthesis is possible (which it is not), before it

proceeds to prove the truth of the proposition itself. The so-called

proof of the simple nature of the soul from the unity of apperception,

is a very plausible one. But it contains no answer to the objection,

that, as the notion of absolute simplicity is not a conception which

is directly applicable to a perception, but is an idea which must be

inferred- if at all- from observation, it is by no means evident how

the mere fact of consciousness, which is contained in all thought,

although in so far a simple representation, can conduct me to the

consciousness and cognition of a thing which is purely a thinking

substance. When I represent to my mind the power of my body as in

motion, my body in this thought is so far absolute unity, and my

representation of it is a simple one; and hence I can indicate this

representation by the motion of a point, because I have made

abstraction of the size or volume of the body. But I cannot hence

infer that, given merely the moving power of a body, the body may be

cogitated as simple substance, merely because the representation in my

mind takes no account of its content in space, and is consequently

simple. The simple, in abstraction, is very different from the

objectively simple; and hence the Ego, which is simple in the first

sense, may, in the second sense, as indicating the soul itself, be a

very complex conception, with a very various content. Thus it is

evident that in all such arguments there lurks a paralogism. We

guess (for without some such surmise our suspicion would not be

excited in reference to a proof of this character) at the presence

of the paralogism, by keeping ever before us a criterion of the

possibility of those synthetical propositions which aim at proving

more than experience can teach us. This criterion is obtained from the

observation that such proofs do not lead us directly from the

subject of the proposition to be proved to the required predicate, but

find it necessary to presuppose the possibility of extending our

cognition a priori by means of ideas. We must, accordingly, always use

the greatest caution; we require, before attempting any proof, to

consider how it is possible to extend the sphere of cognition by the

operations of pure reason, and from what source we are to derive

knowledge, which is not obtained from the analysis of conceptions, nor

relates, by anticipation, to possible experience. We shall thus

spare ourselves much severe and fruitless labour, by not expecting

from reason what is beyond its power, or rather by subjecting it to

discipline, and teaching it to moderate its vehement desires for the

extension of the sphere of cognition.

The first rule for our guidance is, therefore, not to attempt a

transcendental proof, before we have considered from what source we

are to derive the principles upon which the proof is to be based,

and what right we have to expect that our conclusions from these

principles will be veracious. If they are principles of the

understanding, it is vain to expect that we should attain by their

means to ideas of pure reason; for these principles are valid only

in regard to objects of possible experience. If they are principles of

pure reason, our labour is alike in vain. For the principles of

reason, if employed as objective, are without exception dialectical

and possess no validity or truth, except as regulative principles of

the systematic employment of reason in experience. But when such

delusive proof are presented to us, it is our duty to meet them with

the non liquet of a matured judgement; and, although we are unable

to expose the particular sophism upon which the proof is based, we

have a right to demand a deduction of the principles employed in it;

and, if these principles have their origin in pure reason alone,

such a deduction is absolutely impossible. And thus it is

unnecessary that we should trouble ourselves with the exposure and

confutation of every sophistical illusion; we may, at once, bring

all dialectic, which is inexhaustible in the production of

fallacies, before the bar of critical reason, which tests the

principles upon which all dialectical procedure is based. The second

peculiarity of transcendental proof is that a transcendental

proposition cannot rest upon more than a single proof. If I am drawing

conclusions, not from conceptions, but from intuition corresponding to

a conception, be it pure intuition, as in mathematics, or empirical,

as in natural science, the intuition which forms the basis of my

inferences presents me with materials for many synthetical

propositions, which I can connect in various modes, while, as it is

allowable to proceed from different points in the intention, I can

arrive by different paths at the same proposition.

But every transcendental proposition sets out from a conception, and

posits the synthetical condition of the possibility of an object

according to this conception. There must, therefore, be but one ground

of proof, because it is the conception alone which determines the

object; and thus the proof cannot contain anything more than the

determination of the object according to the conception. In our

Transcendental Analytic, for example, we inferred the principle: Every

event has a cause, from the only condition of the objective

possibility of our conception of an event. This is that an event

cannot be determined in time, and consequently cannot form a part of

experience, unless it stands under this dynamical law. This is the

only possible ground of proof; for our conception of an event

possesses objective validity, that is, is a true conception, only

because the law of causality determines an object to which it can

refer. Other arguments in support of this principle have been

attempted- such as that from the contingent nature of a phenomenon;

but when this argument is considered, we can discover no criterion

of contingency, except the fact of an event- of something happening,

that is to say, the existence which is preceded by the non-existence

of an object, and thus we fall back on the very thing to be proved. If

the proposition: "Every thinking being is simple," is to be proved, we

keep to the conception of the ego, which is simple, and to which all

thought has a relation. The same is the case with the transcendental

proof of the existence of a Deity, which is based solely upon the

harmony and reciprocal fitness of the conceptions of an ens

realissimum and a necessary being, and cannot be attempted in any

other manner.

This caution serves to simplify very much the criticism of all

propositions of reason. When reason employs conceptions alone, only

one proof of its thesis is possible, if any. When, therefore, the

dogmatist advances with ten arguments in favour of a proposition, we

may be sure that not one of them is conclusive. For if he possessed

one which proved the proposition he brings forward to demonstration-

as must always be the case with the propositions of pure reason-

what need is there for any more? His intention can only be similar

to that of the advocate who had different arguments for different

judges; this availing himself of the weakness of those who examine his

arguments, who, without going into any profound investigation, adopt

the view of the case which seems most probable at first sight and

decide according to it.

The third rule for the guidance of pure reason in the conduct of a

proof is that all transcendental proofs must never be apagogic or

indirect, but always ostensive or direct. The direct or ostensive

proof not only establishes the truth of the proposition to be

proved, but exposes the grounds of its truth; the apagogic, on the

other hand, may assure us of the truth of the proposition, but it

cannot enable us to comprehend the grounds of its possibility. The

latter is, accordingly, rather an auxiliary to an argument, than a

strictly philosophical and rational mode of procedure. In one respect,

however, they have an advantage over direct proofs, from the fact that

the mode of arguing by contradiction, which they employ, renders our

understanding of the question more clear, and approximates the proof

to the certainty of an intuitional demonstration.

The true reason why indirect proofs are employed in different

sciences is this. When the grounds upon which we seek to base a

cognition are too various or too profound, we try whether or not we

may not discover the truth of our cognition from its consequences. The

modus ponens of reasoning from the truth of its inferences to the

truth of a proposition would be admissible if all the inferences

that can be drawn from it are known to be true; for in this case there

can be only one possible ground for these inferences, and that is

the true one. But this is a quite impracticable procedure, as it

surpasses all our powers to discover all the possible inferences

that can be drawn from a proposition. But this mode of reasoning is

employed, under favour, when we wish to prove the truth of an

hypothesis; in which case we admit the truth of the conclusion-

which is supported by analogy- that, if all the inferences we have

drawn and examined agree with the proposition assumed, all other

possible inferences will also agree with it. But, in this way, an

hypothesis can never be established as a demonstrated truth. The modus

tollens of reasoning from known inferences to the unknown proposition,

is not only a rigorous, but a very easy mode of proof. For, if it

can be shown that but one inference from a proposition is false,

then the proposition must itself be false. Instead, then, of

examining, in an ostensive argument, the whole series of the grounds

on which the truth of a proposition rests, we need only take the

opposite of this proposition, and if one inference from it be false,

then must the opposite be itself false; and, consequently, the

proposition which we wished to prove must be true.

The apagogic method of proof is admissible only in those sciences

where it is impossible to mistake a subjective representation for an

objective cognition. Where this is possible, it is plain that the

opposite of a given proposition may contradict merely the subjective

conditions of thought, and not the objective cognition; or it may

happen that both propositions contradict each other only under a

subjective condition, which is incorrectly considered to be objective,

and, as the condition is itself false, both propositions may be false,

and it will, consequently, be impossible to conclude the truth of

the one from the falseness of the other.

In mathematics such subreptions are impossible; and it is in this

science, accordingly, that the indirect mode of proof has its true

place. In the science of nature, where all assertion is based upon

empirical intuition, such subreptions may be guarded against by the

repeated comparison of observations; but this mode of proof is of

little value in this sphere of knowledge. But the transcendental

efforts of pure reason are all made in the sphere of the subjective,

which is the real medium of all dialectical illusion; and thus

reason endeavours, in its premisses, to impose upon us subjective

representations for objective cognitions. In the transcendental sphere

of pure reason, then, and in the case of synthetical propositions,

it is inadmissible to support a statement by disproving the

counter-statement. For only two cases are possible; either, the

counter-statement is nothing but the enouncement of the

inconsistency of the opposite opinion with the subjective conditions

of reason, which does not affect the real case (for example, we cannot

comprehend the unconditioned necessity of the existence of a being,

and hence every speculative proof of the existence of such a being