“How, then, are numbers to be given to us, if we cannot have any ideas or intuitions of them?” (§62). This is a version of what we have called “the integration challenge” (cf. §1.5).6 Since numbers cannot be perceived or tracked by means of instruments, how do we manage to refer to them, let alone gain knowledge of them? Frege’s response to this challenge takes us right to the heart of his philosophy: Only in the context of a sentence do words have meaning. We must, therefore, define the sense of a sentence in which a number-word occurs.
