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or pain accompanying their acquisition or possession. The student is liable to grow weary of them and soon discovers that continuous mental energy is not granted to human beings. On the other hand, the most sensual pleasure is inseparable from the consciousness of pleasure; no man can be happy who, to borrow Plato’s illustration, is leading the life of an oyster. Hence (by his own confession) the main thesis is not worth determining; the real interest lies in the incidental discussion. We can no more separate pleasure from knowledge in the Philebus than we can separate justice from happiness in the Republic.

IV. An interesting account is given in the Philebus of the rank and order of the sciences or arts, which generally agrees with the scheme of knowledge in the sixth book of the Republic. The chief difference is that the position of the arts is more exactly defined. They are divided into an empirical part and a scientific part; the first is mere guesswork, while the second is determined by rule and measure. Music is given as an example of the more empirical arts; although affirmed to be necessary to human life, it is depreciated. No attempt is made, as in the Republic, to base harmony on scientific principles, but a preference is expressed for simple melodies, and flute music is especially condemned. According to the standard of accuracy adopted here, music is rightly placed lower in the scale than carpentry, because the latter is more capable of being reduced to measure.

The theoretical element of the arts may also become a purely abstract science when separated from matter, and is then said to be pure and unmixed. The distinction Plato makes here seems identical to that between pure and applied mathematics, and may be expressed in the modern formula: science is theoretical art, and art is practical science. Regarding his reason for the superiority of the pure science of number over the mixed or applied, we can only agree with him in part. He says that the numbers the philosopher employs are always the same, whereas numbers used in practice represent different sizes or quantities. He does not see that this power of expressing different quantities by the same symbol is the characteristic—not the defect—of numbers, and is due to their abstract nature; although we admit, of course, what Plato seems to feel in his distinctions between pure and impure knowledge, that the imperfection of matter enters into their applications.

Above the other sciences, as in the Republic, towers dialectic, which is