Early Greek speculation culminates in the ideas of Plato, or rather in the single idea of good. His followers, and perhaps he himself, having arrived at this elevation, instead of going forwards went backwards from philosophy to psychology, from ideas to numbers. But what we perceive to be the real meaning of them, an explanation of the nature and origin of knowledge, will always continue to be one of the first problems of philosophy. Plato also left behind him a most potent instrument, the forms of logic—arms ready for use, but not yet taken out of their armoury. They were the late birth of the early Greek philosophy, and were the only part of it which has had an uninterrupted hold on the mind of Europe. Philosophies come and go; but the detection of fallacies, the framing of definitions, the invention of methods still continue to be the main elements of the reasoning process. [Sidenote: _begins with simple ideas: Descartes._] Modern philosophy, like ancient, begins with very simple conceptions. It is almost wholly a reflection on self. It might be described as a quickening into life of old words and notions latent in the semi-barbarous Latin, and putting a new meaning into them. Unlike ancient philosophy, it has been unaffected by impressions derived from outward nature: it arose within the limits of the mind itself. From the time of Descartes to Hume and Kant it has had little or nothing to do with facts of science. On the other hand, the ancient and mediaeval logic retained a continuous influence over it, and a form like that of mathematics was easily impressed upon it; the principle of ancient philosophy which is most apparent in it is scepticism; we must doubt nearly every traditional or received notion, that we may hold fast one or two. The being of God in a personal or impersonal form was a mental necessity to the first thinkers of modern times: from this alone all other ideas could be deduced. There had been an obscure presentiment of ‘cogito, ergo sum’ more than 2000 years previously. The Eleatic notion that being and thought were the same was revived in a new form by Descartes. But now it gave birth to consciousness and self-reflection: it awakened the ‘ego’ in human nature. The mind naked and abstract has no other certainty but the conviction of its own existence. ‘I think, therefore I am;’ and this thought is God thinking in me, who has also communicated to the reason of man his own attributes of thought and extension—these are truly imparted to him because God is true (cp. Rep. ii. 382 ff.). It has been often remarked that Descartes, having begun by dismissing all presuppositions, introduces several: he passes almost at once from scepticism to dogmatism. It is more important for the illustration of Plato to observe that he, like Plato, insists that God is true and incapable of deception (Rep. ii. 382)—that he proceeds from general ideas, that many elements of mathematics may be found in him. A certain influence of mathematics