All our scientific and philosophic ideals are altars to unknown gods.

In science the new is an advance; but in morals, as contradicting our inner ideals and historic idols, it is ever a retrogression.

My ideal man is Benjamin Franklin—the figure in American history most worthy of emulation ... Franklin is my ideal of a whole man. ... Where are the life-size—or even pint-size—Benjamin Franklins of today?

Objective evidence and certitude are doubtless very fine ideals to play with, but where on this moonlit and dream-visited planet are they found?

The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church, which had been maintained through the Middle Ages, had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science 'more geometrico.'

The ideal of the supreme being is nothing but a regulative principle of reason which directs us to look upon all connection in the world as if it originated from an all-sufficient necessary cause.

The instinct to command others, in its primitive essence, is a carnivorous, altogether bestial and savage instinct. Under the influence of the mental development of man, it takes on a somewhat more ideal form and becomes somewhat ennobled, presenting itself as the instrument of reason and the devoted servant of that abstraction, or political fiction, which is called the public good. But in its essence it remains just as baneful, and it becomes even more so when, with the application of science, it extends its scope and intensifies the power of its action. If there is a devil in history, it is this power principle.

The truth us that other systems of geometry are possible, yet after all, these other systems are not spaces but other methods of space measurements. There is one space only, though we may conceive of many different manifolds, which are contrivances or ideal constructions invented for the purpose of determining space.