Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: ledge? either has never occurred to him, or he sets it aside as irrelevant to his special investigation. He may be said to be in the attitude of the youthful Theaetetus, in the dialogue of Plato to which I have already referred, who, when asked by Socrates, What is Knowledge ? answers that "Knowledge consists of all the things we can learn from Theodorus, geometry for instance." Mill, on the other hand, and the same thing is true of all philosophers, has become aware that the true meaning of Socrates' question is, What is implied in the act of knowledge? What constitutes knowledge? In seeking to answer this question, Mill is led, like the Greek Protagoras, as represented by Plato, to say that " Knowledge , is sensible perception." We may say, then, that mathematics seeks to answer the question, What do we know about the number and magnitude of things? while philosophy tries to answer the question, What is the nature of mathematical knowledge ? Let us call the first problem scientific and the second philosophic. It would then seem that science directs its attention to the objects of knowledge, philosophy to the nature of knowledge itself. (2) This seems to give us a clear distinction between science and philosophy. But on closer investigation we find that'the absolute opposition of knowledge and the object of knowledge is one that cannot be maintained. If Mill is right, we must distinguish between the objects with which mathematics deals, and those objects which lie beyond the range of possible experience, or rather, those objects which perhaps lie beyond that range. For it is held that a time might come when the whole fabric of our present mathematical knowledge would be completely upset. We cannot tell, on Mill's theory, what a day or an hour might bring forth. Suddenly our ex...