Ghost stories are always listened to and well received in private, but pitilessly disavowed in public. For my own part, ignorant as I am of the way in which the human spirit enters the world and the way in which he goes out of it, I dare not deny the truth of many such narratives.
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.
Enthusiasm is always connected with the senses, whatever be the object that excites it. The true strength of virtue is serenity of mind, combined with a deliberate and steadfast determination to execute her laws. That is the healthful condition of the moral life; on the other hand, enthusiasm, even when excited by representations of goodness, is a brilliant but feverish glow which leaves only exhaustion and languor behind.
The sum total of all possible knowledge of God is not possible for a human being, not even through a true revelation. But it is one of the worthiest inquiries to see how far our reason can go in the knowledge of God.
Perhaps a revolution can overthrow autocratic despotism and profiteering or power-grabbing oppression, but it can never truly reform a manner of thinking; instead, new prejudices, just like the old ones they replace, will serve as a leash for the great unthinking mass.
Philosophical knowledge is the knowledge gained by reason from concepts ; mathematical knowledge is the knowledge gained by reason from the construction of concepts.
Reason in a creature is a faculty of widening the rules and purposes of the use of all its powers far beyond natural instinct; it acknowledges no limits to its projects. Reason itself does not work instinctively, but requires trial, practice, and instruction in order gradually to progress from one level of insight to another.
The sceptics, a kind of nomads, despising all settled culture of the land, broke up from time to time all civil society. Fortunately their number was small, and they could not prevent the old settlers from returning to cultivate the ground afresh, though without any fixed plan or agreement.