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within the province of pure reason advances with that undeviating

certainty which characterizes the progress of science; we shall be

at no loss to determine。 If we find those who are engaged in

metaphysical pursuits; unable to come to an understanding as to the

method which they ought to follow; if we find them; after the most

elaborate preparations; invariably brought to a stand before the

goal is reached; and compelled to retrace their steps and strike

into fresh paths; we may then feel quite sure that they are far from

having attained to the certainty of scientific progress and may rather

be said to be merely groping about in the dark。 In these circumstances

we shall render an important service to reason if we succeed in simply

indicating the path along which it must travel; in order to arrive

at any results… even if it should be found necessary to abandon many

of those aims which; without reflection; have been proposed for its

attainment。

  That logic has advanced in this sure course; even from the

earliest times; is apparent from the fact that; since Aristotle; it

has been unable to advance a step and; thus; to all appearance has

reached its completion。 For; if some of the moderns have thought to

enlarge its domain by introducing psychological discussions on the

mental faculties; such as imagination and wit; metaphysical;

discussions on the origin of knowledge and the different kinds of

certitude; according to the difference of the objects (idealism;

scepticism; and so on); or anthropological discussions on

prejudices; their causes and remedies: this attempt; on the part of

these authors; only shows their ignorance of the peculiar nature of

logical science。 We do not enlarge but disfigure the sciences when

we lose sight of their respective limits and allow them to run into

one another。 Now logic is enclosed within limits which admit of

perfectly clear definition; it is a science which has for its object

nothing but the exposition and proof of the formal laws of all

thought; whether it be a priori or empirical; whatever be its origin

or its object; and whatever the difficulties… natural or accidental…

which it encounters in the human mind。

  The early success of logic must be attributed exclusively to the

narrowness of its field; in which abstraction may; or rather must;

be made of all the objects of cognition with their characteristic

distinctions; and in which the understanding has only to deal with

itself and with its own forms。 It is; obviously; a much more difficult

task for reason to strike into the sure path of science; where it

has to deal not simply with itself; but with objects external to

itself。 Hence; logic is properly only a propaedeutic… forms; as it

were; the vestibule of the sciences; and while it is necessary to

enable us to form a correct judgement with regard to the various

branches of knowledge; still the acquisition of real; substantive

knowledge is to be sought only in the sciences properly so called;

that is; in the objective sciences。

  Now these sciences; if they can be termed rational at all; must

contain elements of a priori cognition; and this cognition may stand

in a twofold relation to its object。 Either it may have to determine

the conception of the object… which must be supplied extraneously;

or it may have to establish its reality。 The former is theoretical;

the latter practical; rational cognition。 In both; the pure or a

priori element must be treated first; and must be carefully

distinguished from that which is supplied from other sources。 Any

other method can only lead to irremediable confusion。

  Mathematics and physics are the two theoretical sciences which

have to determine their objects a priori。 The former is purely a

priori; the latter is partially so; but is also dependent on other

sources of cognition。

  In the earliest times of which history affords us any record;

mathematics had already entered on the sure course of science; among

that wonderful nation; the Greeks。 Still it is not to be supposed that

it was as easy for this science to strike into; or rather to construct

for itself; that royal road; as it was for logic; in which reason

has only to deal with itself。 On the contrary; I believe that it

must have remained long… chiefly among the Egyptians… in the stage

of blind groping after its true aims and destination; and that it

was revolutionized by the happy idea of one man; who struck out and

determined for all time the path which this science must follow; and

which admits of an indefinite advancement。 The history of this

intellectual revolution… much more important in its results than the

discovery of the passage round the celebrated Cape of Good Hope… and

of its author; has not been preserved。 But Diogenes Laertius; in

naming the supposed discoverer of some of the simplest elements of

geometrical demonstration… elements which; according to the ordinary

opinion; do not even require to be proved… makes it apparent that

the change introduced by the first indication of this new path; must

have seemed of the utmost importance to the mathematicians of that

age; and it has thus been secured against the chance of oblivion。 A

new light must have flashed on the mind of the first man (Thales; or

whatever may have been his name) who demonstrated the properties of

the isosceles triangle。 For he found that it was not sufficient to

meditate on the figure; as it lay before his eyes; or the conception

of it; as it existed in his mind; and thus endeavour to get at the

knowledge of its properties; but that it was necessary to produce

these properties; as it were; by a positive a priori construction; and

that; in order to arrive with certainty at a priori cognition; he must

not attribute to the object any other properties than those which

necessarily followed from that which he had himself; in accordance

with his conception; placed in the object。

  A much longer period elapsed before physics entered on the highway

of science。 For it is only about a century and a half since the wise

Bacon gave a new direction to physical studies; or rather… as others

were already on the right track… imparted fresh vigour to the

pursuit of this new direction。 Here; too; as in the case of

mathematics; we find evidence of a rapid intellectual revolution。 In

the remarks which follow I shall confine myself to the empirical

side of natural science。

  When Galilei experimented with balls of a definite weight on the

inclined plane; when Torricelli caused the air to sustain a weight

which he had calculated beforehand to be equal to that of a definite

column of water; or when Stahl; at a later period; converted metals

into lime; and reconverted lime into metal; by the addition and

subtraction of certain elements;* a light broke upon all natural

philosophers。 They learned that reason only perceives that which it

produces after its own design; that it must not be content to

follow; as it were; in the leading…strings of nature; but must proceed

in advance with principles of judgement according to unvarying laws;

and compel nature to reply its questions。 For accidental observations;

made according to no preconceived plan; cannot be united under a

necessary law。 But it is this that reason seeks for and requires。 It

is only the principles of reason which can give to concordant

phenomena the validity of laws; and it is only when experiment is

directed by these rational principles that it can have any real

utility。 Reason must approach nature with the view; indeed; of

receiving information from it; not; however; in the character of a

pupil; who listens to all that his master chooses to tell him; but

in that of a judge; who compels the witnesses to reply to those

questions which he himself thinks fit to propose。 To this single

idea must the revolution be ascribed; by which; after groping in the

dark for so many centuries; natural science was at length conducted

into the path of certain progress。



  *I do not here follow with exactness the history of the experimental

method; of which; indeed; the first steps are involved in some

obscurity。



  We come now to metaphysics; a purely speculative science; which

occupies a completely isolated position and is entirely independent of

the teachings of experience。 It deals with mere conceptions… not; like

mathematics; with conceptions applied to intuition… and in it;

reason is the pupil of itself alone。 It is the oldest of the sciences;

and would still survive; even if all the rest were swallowed up in the

abyss of an all…destroying barbarism。 But it has not yet had the

good fortune to attain to the sure scientific method。 This will be

apparent; if we apply the tests which we proposed at the outset。 We

find that reason perpetually comes to a stand; when it attempts to

gain a priori the perception even of those laws which the most

common experience confirms。 We find it compelled to retrace i

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