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 similarity between number and colour; but this does not consist in the fact that both are sensibly perceptible in external things, but in the fact that both are objective” (p. 34).

“I distinguish the objective,” he continues, “from the palpable, the spatial, the actual. The earth’s axis, the centre of mass of the solar system, are objective, but I should not call them actual, like the earth itself” (p. 35). He concludes that number is neither spatial and physical, nor subjective, but non-sensible and objective. This conclusion is important, since it applies to all the subject-matter of mathematics and logic. Most philosophers have thought that the physical and the mental between them exhausted the world of being. Some have argued that the objects of mathematics were obviously not subjective, and therefore must be physical and empirical; others have argued that they were obviously not physical, and therefore must be subjective and mental. Both sides were right in what they denied, and wrong in what they asserted; Frege has the merit of accepting both denials, and finding a third assertion by recognising the world of logic, which is neither mental nor physical.

The fact is, as Frege points out, that no number, not even 1, is applicable to physical things, but only to general terms or descriptions, such as “man,” “satellite of the earth,” “satellite of Venus.” The general term “man” is applicable to a certain number of objects: there are in the world so and so many men. The unity which philosophers rightly feel to be necessary for the assertion of a number is the unity of the general term, and it is the general term which is the proper subject of number. And this applies equally when there is one object or none which falls under the general term. “Satellite of the earth” is a term only applicable to one object, namely,