That leader at length arose. The philosophy which he taught was essentially new. It differed from that of the celebrated ancient teachers, not merely in method, but also in object. Its object was the good of mankind, in the sense in which the mass of mankind always have understood and always will understand the word good. "Meditor," said Bacon, "instaurationem philosophiae ejusmodi quae nihil inanis aut abstracti habeat, quaeque vitae humanae conditiones in melius provehat." [Redargutio Philosophiarum.]
The difference between the philosophy of Bacon and that of his predecessors cannot, we think, be better illustrated than by comparing his views on some important subjects with those of Plato. We select Plato, because we conceive that he did more than any other person towards giving to the minds of speculative men that bent which they retained till they received from Bacon a new impulse in a diametrically opposite direction.
It is curious to observe how differently these great men estimated the value of every kind of knowledge. Take Arithmetic for example. Plato, after speaking slightly of the convenience of being able to reckon and compute in the ordinary transactions of life, passes to what he considers as a far more important advantage. The study of the properties of numbers, he tells us, habituates the mind to the contemplation of pure truth, and raises us above the material universe. He would have his disciples apply themselves to this study, not that they may be able to buy or sell, not that they may qualify themselves to be shopkeepers or travelling merchants, but that they may learn to withdraw their minds from the ever-shifting spectacle of this visible and tangible world, and to fix them on the immutable essences of things. [Plato's Republic, Book vii.]
Bacon, on the other hand, valued this branch of knowledge, only on account of its uses with reference to that visible and tangible world which Plato so much despised. He speaks with scorn of the mystical arithmetic of the later Platonists, and laments the propensity of mankind to employ, on mere matters of curiosity, powers the whole exertion of which is required for purposes of solid advantage. He advises arithmeticians to leave these trifles, and to employ themselves in framing convenient expressions, which may be of use in physical researches. [De Augmentis, Lib. iii. Cap. 6.]
The same reasons which led Plato to recommend the study of arithmetic led him to recommend also the study of mathematics.
The vulgar crowd of geometricians, he says, will not understand him. They have practice always in view. They do not know that the real use of the science is to lead men to the knowledge of abstract, essential, eternal truth. [Plato's Republic, Book vii.]
Indeed, if we are to believe Plutarch, Plato carried this feeling so far that he considered geometry as degraded by being applied to any purpose of vulgar utility. Archytas, it seems, had framed machines of extraordinary power on mathematical principles.
[Plutarch, Sympos. viii. and Life of Marcellus. The machines of Archytas are also mentioned by Aulus Gellius and Diogenes Laertius.] Plato remonstrated with his friend, and declared that this was to degrade a noble intellectual exercise into a low craft, fit only for carpenters and wheelwrights. The office of geometry, he said, was to discipline the mind, not to minister to the base wants of the body. His interference was successful; and from that time, according to Plutarch, the science of mechanics was considered as unworthy of the attention of a philosopher.
Archimedes in a later age imitated and surpassed Archytas. But even Archimedes was not free from the prevailing notion that geometry was degraded by being employed to produce anything useful. It was with difficulty that he was induced to stoop from speculation to practice. He was half ashamed of those inventions which were the wonder of hostile nations, and always spoke of them slightingly as mere amusements, as trifles in which a mathematician might be suffered to relax his mind after intense application to the higher parts of his science.
The opinion of Bacon on this subject was diametrically opposed to that of the ancient philosophers. He valued geometry chiefly, if not solely, on account of those uses, which to Plato appeared so base. And it is remarkable that the longer Bacon lived the stronger this feeling became. When in 1605 he wrote the two books on the Advancement of Learning, he dwelt on the advantages which mankind derived from mixed mathematics; but he at the same time admitted that the beneficial effect produced by mathematical study on the intellect, though a collateral advantage, was "no less worthy than that which was principal and intended." But it is evident that his views underwent a change. When, near twenty years later, he published the De Augmentis, which is the Treatise on the Advancement of Learning, greatly expanded and carefully corrected, he made important alterations in the part which related to mathematics. He condemned with severity the high, pretensions of the mathematicians, "delicias et fastum mathematicorum." Assuming the well-being of the human race to be the end of knowledge, [Usui et commodis hominum consulimus.] he pronounced that mathematical science could claim no higher rank than that of an appendage or auxiliary to other sciences.
