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.
We assume a common sense as the necessary condition of the universal communicability of our knowledge, which is presupposed in every logic and every principle of knowledge that is not one of skepticism.
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.
Ours is an age of criticism, to which everything must be subjected. The sacredness of religion, and the authority of legislation, are by many regarded as grounds for exemption from the examination by this tribunal, But, if they are exempted, and cannot lay claim to sincere respect, which reason accords only to that which has stood the test of a free and public examination.
A science of all these possible kinds of space [the higher dimensional ones] would undoubtedly be the highest enterprise which a finite understanding could undertake in the field of geometry... If it is possible that there could be regions with other dimensions, it is very likely that God has somewhere brought them into being.
Aristotle can be regarded as the father of logic. But his logic is too scholastic, full of subtleties, and fundamentally has not been of much value to the human understanding. It is a dialectic and an organon for the art of disputation.
Philosophical knowledge is the knowledge gained by reason from concepts ; mathematical knowledge is the knowledge gained by reason from the construction of concepts.
Since the narrower or wider community of the peoples of the earth has developed so far that a violation of rights in one place is felt throughout the world, the idea of a cosmopolitan right is not fantastical, high-flown or exaggerated notion. It is a complement to the unwritten code of the civil and international law, necessary for the public rights of mankind in general and thus for the realization of perpetual peace.
The means employed by Nature to bring about the development of all the capacities of men is their antagonism in society, so far as this is, in the end, the cause of a lawful order among men.