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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 its
steps in innumerable instances； and to abandon the path on which it
had entered； because this does not lead to the desired result。 We
find； too； that those who are engaged in metaphysical pursuits are far
from being able to agree among themselves； but that； on the
contrary； this science appears to furnish an arena specially adapted
for the display of skill or the exercise of strength in mock…contests…
a field in which no combatant ever yet succeeded in gaining an inch of
ground； in which； at least； no victory was ever yet crowned with
permanent possession。
This leads us to inquire why it is that； in metaphysics； the sure
path of science has not hitherto been found。 Shall we suppose that
it is impossible to discover it？ Why then should nature have visited
our reason with restless aspirations after it； as if it were one of
our weightiest concerns？ Nay； more； how little cause should we have to
place confidence in our reason； if it abandons u