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.
Philosophical knowledge is the knowledge gained by reason from concepts ; mathematical knowledge is the knowledge gained by reason from the construction of concepts.
Nature has willed that man should, by himself, produce everything that goes beyond the mechanical ordering of his animal existence, and that he should partake of no other happiness or perfection than that which he himself, independently of instinct, has created by his own reason.
Every man is to be respected as an absolute end in himself; and it is a crime against the dignity that belongs to him as a human being, to use him as a mere means for some external purpose.
It is by his activities and not by enjoyment that man feels he is alive. In idleness we not only feel that life is fleeting, but we also feel lifeless.
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.
Human reason has the peculiar fate in one species of its cognitions that it is burdened with questions which it cannot dismiss, since they are given to it as problems by the nature of reason itself, but which it also cannot answer, since they transcend every capacity of human reason.
The schematicism by which our understanding deals with the phenomenal world ... is a skill so deeply hidden in the human soul that we shall hardly guess the secret trick that Nature here employs.
Manners or etiquette ('accessibility, affability, politeness, refinement, propriety, courtesy, and ingratiating and captivating behavior') call for no large measure of moral determination and cannot, therefore, be reckoned as virtues. Even though manners are no virtues, they are a means of developing virtue.... The more we refine the crude elements in our nature, the more we improve our humanity and the more capable it grows of feeling the driving force of virtuous principles.
In man (as the only rational creature on earth) those natural capacities which are directed to the use of his reason are to be fully developed only in the race, not in the individual.
Enlightenment is man's leaving his self-caused immaturity. Immaturity is the incapacity to use one's intelligence without the guidance of another. Such immaturity is self-caused if it is not caused by lack of intelligence, but by lack of determination and courage to use one's intelligence without being guided by another. Sapere Aude! Have the courage to use your own intelligence! is therefore the motto of the enlightenment.