By a lie a man throws away and, as it were, annihilates his dignity as a man. A man who himself does not believe what he tells another ... has even less worth than if he were a mere thing. ... makes himself a mere deceptive appearance of man, not man himself.
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.
The arts of speech are rhetoric and poetry. Rhetoric is the art of transacting a serious business of the understanding as if it were a free play of the imagination; poetry that of conducting a free play of the imagination as if it were a serious business of the understanding.
Freedom is independence of the compulsory will of another, and in so far as it tends to exist with the freedom of all according to a universal law, it is the one sole original inborn right belonging to every man in virtue of his humanity.
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.
Philosophical knowledge is the knowledge gained by reason from concepts ; mathematical knowledge is the knowledge gained by reason from the construction of concepts.