Philosophical knowledge is the knowledge gained by reason from concepts ; mathematical knowledge is the knowledge gained by reason from the construction of concepts.
Enlightenment is the liberation of man from his self-caused state of minority... Supere aude! Dare to use your own understanding!is thus the motto of the Enlightenment.
If, like Hume, I had all manner of adornment in my power, I would still have reservations about using them. It is true that some readers will be scared off by dryness. But isn't it necessary to scare off some if in their case the matter would end up in bad hands?
[S]uppose the mind of [a] friend of humanity were clouded over with his own grief, extinguishing all sympathetic participation in the fate of others; he still has the resources to be beneficent to those suffering distress, but the distress of others does not touch him because he is sufficiently busy with his own; and now, where no inclination any longer stimulates him to it, he tears himself out of his deadly insensibility and does the action without any inclination, solely from duty.
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.
One cannot avoid a certain feeling of disgust, when one observes the actions of man displayed on the great stage of the world. Wisdom is manifested by individuals here and there; but the web of human history as a whole appears to be woven from folly and childish vanity, often, too, from puerile wickedness and love of destruction: with the result that at the end one is puzzled to know what idea to form of our species which prides itself so much on its advantages.
All appearances have a determinate magnitude (the relation of which to another assignable). The infinite does not appear as such, likewise not the simple. For the appearances are included between two boundaries (points) and are thus themselves determinate magnitudes.
It is the Land of Truth (enchanted name!), surrounded by a wide and stormy ocean, the true home of illusion, where many a fog bank and ice, that soon melts away, tempt us to believe in new lands, while constantly deceiving the adventurous mariner with vain hopes, and involving him in adventures which he can never leave, yet never bring to an end.
Act in such a way that you treat humanity, whether in your own person or in the person of any other, never merely as a means to an end, but always at the same time as an end.