Sublime

Pythagoras, as everyone knows, said that “all things are numbers.” This statement, interpreted in a modern way, is logically nonsense, but what he meant was not exactly nonsense. He discovered the importance of numbers in music, and the connection which he established between music and arithmetic survives in the mathematical terms “ harmonic mean”

The first comprehensive statement of the liberal philosophy is to be found in Locke, the most influential though by no means the most profound of modern philosophers.

“I do not know what is meant by ‘objective truth,’ but I shall consider a statement ‘true’ if all, or virtually all, of those who have investigated it are agreed in upholding it.” In this sense, it is “true” that snow is white, that Caesar was assassinated, that water is composed of hydrogen and oxygen, and so on. We are then faced with a question

MOST modern men take it for granted that empirical knowledge is dependent upon, or derived from, perception. There is, however, in Plato and among philosophers of certain other schools, a very different doctrine, to the effect that there is nothing worthy to be called “knowledge” to be derived from the senses, and that the only real knowledge has t

The only logic admitted by the Greeks was deductive, and all deduction had to start, like Euclid, from general principles regarded as self-evident. Timon denied the possibility of finding such principles. Everything, therefore, will have to be proved by means of something else, and all argument will be either circular or an endless chain hanging fr

Bacon was the first of the long line of scientifically minded philosophers who have emphasized the importance of induction as opposed to deduction. Like most of his successors, he tried to find some better kind of induction than what is called “induction by simple enumeration.” Induction by simple enumeration may be illustrated by a parable. There

Occam is best known for a maxim which is not to be found in his works, but has acquired the name of “Occam’s razor.” This maxim says: “Entities are not to be multiplied without necessity.” Although he did not say this, he said something which has much the same effect, namely: “It is vain to do with more what can be done with fewer.” That is to say,