The Uses Of Mathesis -- By: Thomas Hill
BSac 32:127 (July 1875) p. 498
The Uses Of Mathesis
The word “uses,” in the title of this Article, is intended only in its broader significations. We shall not touch, unless incidentally, upon the obvious applications of the mathematics to the practical arts of life, the arts of measurement and manufacture; but shall speak of their value in the cultivation of the intellectual, moral, and spiritual faculties; of their service in leading the student to a higher appreciation of the whole sphere of human joys, a clearer understanding of all objects of human thought, a better performance of all human duties.
The word “mathematics,” on the other hand, we shall use in the older and narrower sense; not meaning, as Peirce has defined them, the science which draws necessary conclusions; but, for the present, restricting the word to signify the sciences of space, of number, and of time. This is not from any dissatisfaction with the wider definition, which is also true; but simply because we have no other word by which to class together geometry, algebra, and arithmetic; and it is these
BSac 32:127 (July 1875) p. 499
of which we wish particularly to speak. They are three entirely discrete sciences, and were originally classed together because they were the only sciences in which deductive reasoning could be used; the advance of thought has in our century brought various forms of mechanics under the same category, and very properly included them under the same name. Nevertheless there are other points in which the sciences of space, time, and number deserve to be considered apart; and it is to them that the present Article is devoted.
The relation of space and time to the Divine Author of the universe is a matter beyond the reach of the human understanding, and a matter of no special consequence to our present considerations. Whether space and time be merely forms of human thought, having nothing directly answering to them in nature, and in the Creator of nature; or be modes of the divine existence, attributes of God’s eternal substance; or be entities self-existent and independent of the Almighty Being and his power; in either case, the majority of our conclusions will hold good, and we shall, we trust, make manifest to the patient reader, the great value of geometry, algebra, and arithmetic as a foundation for all aesthetic, moral, and religious culture. But the reader who holds different views of the nature of space and time must not be surprised to find us betraying our faith in the common view of the unlearned, neither holding with Spinoza, nor with Carlyle’s Kant, nor with Auguste Comte.
Geometry gives us the science of space in its formal or logical aspect; dealing with magnitudes of one, two, or three...
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