To be beneficent when we can is a duty; and besides this, there are many minds so sympathetically constituted that, without any other motive of vanity or self-interest, they find a pleasure in spreading joy around them, and can take delight in the satisfaction of others so far as it is their own work. But I maintain that in such a case an action of this kind, however proper, however amiable it may be, has nevertheless no true moral worth, but is on a level with other inclinations. . . . For the maxim lacks the moral import, namely, that such actions be done from duty, not from inclination.
The instruction of children should aim gradually to combine knowing and doing. Among all sciences mathematics seems to be the only one of a kind to satisfy this aim most completely.
Intuition and concepts constitute... the elements of all our knowledge, so that neither concepts without an intuition in some way corresponding to them, nor intuition without concepts, can yield knowledge.
Natural science physics contains in itself synthetical judgments a priori, as principles. ... Space then is a necessary representation a priori, which serves for the foundation of all external intuitions.
The ultimate destiny of the human race is the greatest moral perfection, provided that it is achieved through human freedom, whereby alone man is capable of the greatest happiness.
Philosophical knowledge is the knowledge gained by reason from concepts ; mathematical knowledge is the knowledge gained by reason from the construction of concepts.
We come no nearer the infinitude of the creative power of God, if we enclose the space of its revelation within a sphere described with the radius of the Milky Way, than if we were to limit it to a ball an inch in diameter. All that is finite, whatever has limits and a definite relation to unity, is equally far removed from the infinite... Eternity is not sufficient to embrace the manifestations of the Supreme Being, if it is not combined with the infinitude of space.