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 ******st 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.Anew 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 ********.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.