And in spite of that these persons would perhaps not be great mathematicians, because mathematics contain a great number of premises, and there is perhaps a kind of intellect that can search with ease a few premises to the bottom, and cannot in the least penetrate those matters in which there are many premises.
There are then two kinds of intellect: the one able to penetrate acutely and deeply into the conclusions of given premises, and this is the precise intellect; the other able to comprehend a great number of premises without confusing them, and this is the mathematical intellect. The one has force and exactness, the other comprehension. Now the one quality can exist without the other; the intellect can be strong and narrow, and can also be comprehensive and weak.
3
Those who are accustomed to judge by feeling do not understand the process of reasoning, for they would understand at first sight, and are not used to seek for principles. And others, on the contrary, who are accustomed to reason from principles, do not at all understand matters of feeling, seeking principles, and being unable to see at a glance.
4
Mathematics, intuition.—True eloquence makes light of eloquence, true morality makes light of morality; that is to say, the morality of the judgment, which has no rules, makes light of the morality of the intellect.
For it is to judgment that perception belongs, as science belongs to intellect. Intuition is the part of judgment, mathematics of intellect.
To make light of philosophy is to be a true philosopher.
5
Those who judge of a work by rule[3] are in regard to others as those who have a watch are in regard to others. One says, "It is two hours ago"; the other says, "It is only three-quarters of an hour." I look at my watch, and say to the one, "You are weary," and to the other, "Time gallops with you"; for it is only an hour and a half ago, and I laugh at those who tell me that time goes slowly with me, and that I judge by imagination. They do not know that I judge by my watch.[4]