generation, such results as will place our time, in this respect, on a level with the greatest age of Greece.[18] FOOTNOTES: [11] This subject is due in the main to Mr. C.S. Peirce. [12] I ought to have added Frege, but his writings were unknown to me when this article was written. [Note added in 1917.] [13] Professor of Mathematics in the University of Berlin. He died in 1897. [14] [Note added in 1917.] Although some infinite numbers are greater than some others, it cannot be proved that of any two infinite numbers one must be the greater. [15] Cantor was not guilty of a fallacy on this point. His proof that there is no greatest number is valid. The solution of the puzzle is complicated and depends upon the theory of types, which is explained in _Principia Mathematica_, Vol. I (Camb. Univ. Press, 1910). [Note added in 1917.] [16] This must not be regarded as a historically correct account of what Zeno actually had in mind. It is a new argument for his conclusion, not the argument which influenced him. On this point, see e.g. C.D. Broad, "Note on Achilles and the Tortoise," _Mind_, N.S., Vol. XXII, pp. 318-19. Much valuable work on the interpretation of Zeno has been done since this article was written. [Note added in 1917.] [17] Since the above was written, he has ceased to be used as a textbook. But I fear many of the books now used are so bad that the change is no great improvement. [Note added in 1917.] [18] The greatest age of Greece was brought to an end by the Peloponnesian War. [Note added in 1917.] VI ON SCIENTIFIC METHOD IN PHILOSOPHY When we try to ascertain the motives which have led men to the investigation of philosophical questions, we find that, broadly speaking, they can be divided into two groups, often antagonistic, and leading to very divergent systems. These two groups of motives are, on the one hand, those derived from religion and ethics, and, on the other hand, those derived from science. Plato, Spinoza, and Hegel may be taken as typical of the philosophers whose interests are mainly religious and ethical, while Leibniz, Locke, and Hume may be taken as representatives of the scientific wing. In Aristotle, Descartes, Berkeley, and Kant we find both groups of motives strongly present. Herbert Spencer, in whose honour we are assembled to-day, would naturally be classed among scientific philosophers: it was mainly from science that he drew his data, his formulation of problems, and his conception of method. But his strong religious sense is obvious in much of his writing, and his ethical pre-occupations are what make him value the conception of evolution--that conception in which, as a whole generation has believed, science and morals are to be united in fruitful and indissoluble marriage.