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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

must be opposed on subjective grounds; while the possibility of this

being in itself cannot with justice be denied); or; both propositions;

being dialectical in their nature; are based upon an impossible

conception。 In this latter case the rule applies: non entis nulla sunt

predicata; that is to say; what we affirm and what we deny; respecting

such an object; are equally untrue; and the apagogic mode of

arriving at the truth is in this case impossible。 If; for example;

we presuppose that the world of sense is given in itself in its

totality; it is false; either that it is infinite; or that it is

finite and limited in space。 Both are false; because the hypothesis is

false。 For the notion of phenomena (as mere representations) which are

given in themselves (as objects) is self…contradictory; and the

infinitude of this imaginary whole would; indeed; be unconditioned;

but would be inconsistent (as everything in the phenomenal world is

conditioned) with the unconditioned determination and finitude of

quantities which is presupposed in our conception。

  The apagogic mode of proof is the true source of those illusions

which have always had so strong an attraction for the admirers of

dogmatical philosophy。 It may be compared to a champion who

maintains the honour and claims of the party he has adopted by

offering battle to all who doubt the validity of these claims and

the purity of that honour; while nothing can be proved in this way;

except the respective strength of the combatants; and the advantage;

in this respect; is always on the side of the attacking party。

Spectators; observing that each party is alternately conqueror and

conquered; are led to regard the subject of dispute as beyond the

power of man to decide upon。 But such an opinion cannot be

justified; and it is sufficient to apply to these reasoners the

remark:



                  Non defensoribus istis

        Tempus eget。



  Each must try to establish his assertions by a transcendental

deduction of the grounds of proof employed in his argument; and thus

enable us to see in what way the claims of reason may be supported。 If

an opponent bases his assertions upon subjective grounds; he may be

refuted with ease; not; however to the advantage of the dogmatist; who

likewise depends upon subjective sources of cognition and is in like

manner driven into a corner by his opponent。 But; if parties employ

the direct method of procedure; they wil

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