Arithmetic

Then this is knowledge of the kind for which we are seeking, having a double use, military and philosophical; for the man of war must learn the art of number or he will not know how to array his troops, and the philosopher also, because he has to rise out of the sea of change and lay hold of true being, and therefore he must be an arithmetician.

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Then this is a kind of knowledge which legislation may fitly prescribe; and we must endeavour to persuade those who are to be the principal men of our State to go and learn arithmetic, not as amateurs, but they must carry on the study until they see the nature of numbers with the mind only; nor again, like merchants or retail-traders, with a view to buying or selling, but for the sake of their military use, and of the soul herself; and because this will be the easiest way for her to pass from becoming to truth and being.

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I mean, as I was saying, that arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tangible objects into the argument. You know how steadily the masters of the art repel and ridicule any one who attempts to divide absolute unity when he is calculating, and if you divide, they multiply, taking care that one shall continue one and not become lost in fractions.

The reckoning of numbers is not to be despised. For in many places of the Holy Scriptures it shines forth how great a mystery they hold. For it was not in vain said in the praises of God: “Thou hast ordered all things in measure, and number, and weight.” The number six, which is perfect in its parts, declares the perfection of the world by a certain signification of its number. Similarly the forty days on which Moses and Elias and the Lord himself fasted are not understood without knowledge of numbers. So also there are other numbers in the Sacred Scriptures, whose figures none but those who know this science can solve. It has been given to us also in some part to live under the discipline of numbers, when we reckon the hours by it, when we dispute of the course of the months, when we recognize the space of the returning year. For through number we are instructed lest we be confounded. Take away number from all things, and all perish. Take reckoning from the world, and blind ignorance embraces all, nor can one be distinguished from the other animals who do not know the reason of calculation.