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man metaphysician has it—they are inseparable from the individual being—an attack upon them is felt as one upon the person itself; whilst facts are objective” and belonging to everybody—they remain the same facts at all times and under all circumstances; they can be proved; they have to be proved; and, when proved, are finally settled.—PRINCE CONSORT. Died 1861.
THE STUDY OF MATHEMATICS. WHEN we pass from the properties of space and number, to those of force and matter, we shall perhaps find a larger class of persons who will hold our fundamental principles to be derived from experiment. That experiment has had a share in the establishment of such principles, the history of science very clearly shows. But if this share be loosely and obscurely conceived, such an opinion may still lead to very unphilosophical views, and very illogical habits. By what experiments is it found that the pressure of the fulcrum is equal to the sum of the weights ? Who supposes that Archimedes thought it necessary to verify this result by actual trial ? or, if he had done so, by what more evident principle could he have tested the equality of the weights ? I shall not here dwell upon the share which experience really has in the formation of our mechanical principles, having already attempted to explain elsewhere the manner in which external phenomena call up and interpret the intellectual conceptions on which science depends.
An imperfect exhibition of the fundamental conception of Hydrostatics may render the elementary reasoning of that science illogical, as we have seen; some mathematicians have been driven, by the apparent insufficiency of such reasoning, to throw themselves entirely upon experiment for the foundations of hydrostatical science. “Fluids," say they, “are found by experiment to press equally in all directions.” There would be no difficulty in pointing out experiments which are sufficient to illustrate the preposition; and to remove any difficulty which the first announcement of it might occasion ; but I do not think that all the experiments of this kind which ever were made, could be held sufficient to establish a proposition so general and so vigorous, if we saw no antecedent reason for it. And in fact, it cannot be doubted that good mathematicians, in tracing the consequences of this general property of fluids, do reason from their perception of its connection with the nature of fluidity, and do not find themselves obliged to refer to the contingent and limited conditions of an experimental proof.
The disposition to ascribe such an empiricial origin to truths which have in fact a deeper root in our minds, is injurious in its influence upon our speculations on other subjects. For it tends to make us suppose that the foundations of other sciences and bodies of demonstration are to be sought in plausible maxims, collected from experience by the same kind of loose and casual observation, and assented to with the same slight attention to the facts on which they profess to rest. It tends moreover to lead us to imagine, that when our common experience suggest to us no maxims possessing this kind of apparent evidence and generality, we may despair of ever arriving at a connected system of truth and certainty; and it teaches us to believe that any appeal to experience, however vaguely made, is to be held inevitable and final, and is to put an end to all speculation on the subject; instead of suggesting to us how difficult the interpretation of our experience is, and how much caution and thought are required in order to infer anything from it. It is easy to see how fatal to our success and welfare in other provinces of speculation impressions of this kind must be.
- WHEWELL. Thoughts on the Study of Mathematics. Died 1866.
TIME hath, my lord, a wallet at his back,
Love, friendship, charity, are subjects all
SHAKSPEARE. From 1564 to 1616.
may the outward shows be least themselves.
Which make such wanton gambols with the wind,
PORTIA. How all the other passions fleet to air, As doubtful thoughts and rash-embraced despair, And shuddering fear, and green-eyed jealousy ! O love, be moderate, allay thy ecstasy, In measure rain thy joy, scant this excess; I feel too much thy blessing : make it less, For fear I surfeit.
O how much more doth beauty beauteous seem,
By that sweet ornament which truth doth give ! The rose looks fair, but fairer we it deem
For that sweet odour which doth in it live. The canker-blooms have full as deep a dye,
As the perfumed tincture of the roses ;