"Philosophy, as I understand the word, is a positive theoretical science, and a science in an early stage of development. As such it has no more to do with belief than any other science. Indeed, I am bound to confess that it is at present in so unsettled a condition, that if the ordinary theorems of molecular physics and of archaeology are but the ghosts of beliefs, then to my mind, the doctrines of the philosophers are little better than the ghosts of ghosts. I know this is an extremely heretical opinion."

“Few persons care to study logic, because everybody conceives himself to be proficient enough in the art of reasoning already. But I observe that this satisfaction is limited to one's own ratiocination and does not extend to that of other men. We come to the full possession of our power of drawing inferences the last of all our faculties, for it is not so much a natural gift as a long and difficult art.”

“Every man is fully satisfied that there is such a thing as truth, or he would not ask any question.”

“Understand me well. My appeal is to observation — observation that each of you must make for himself.”

“As the mathematics are now understood, each branch — or, if you please, each problem, — is but the study of the relations of a collection of connected objects, without parts, without any distinctive characters, except their names or designating letters. These objects are commonly called points; but to remove all notion of space relations, it may be better to name them monads. The relations between these points are mere complications of two different kinds of elementary relations, which may be termed immediate connection and immediate non-connection. All the monads except as serve as intermediaries for the connections have distinctive designations.”

“The one intelligible theory of the universe is that of objective idealism, that matter is effete mind, inveterate habits becoming physical laws. But before this can be accepted it must show itself capable of explaining the tridimensionality of space, the laws of motion, and the general characteristics of the universe, with mathematical clearness and precision ; for no less should be demanded of every Philosophy.”

“Since space is continuous, it follows that there must be an immediate community of feeling between parts of mind infinitesimally close together. Without this, I believe it would have been impossible for any co-ordination to be established in the action of the nerve-matter of one brain.”