That no idea can be formed of the content of a word is...

That no idea can be formed of the content of a word is therefore no reason for denying it any meaning or for excluding it from use. The appearance to the contrary doubtless arises because we consider the words in isolation and in asking for their meaning look only for an idea. A word for which we lack a corresponding mental picture thus appears to have no content. But one must always keep in mind a complete proposition. Only in a proposition do the words really have a meaning.

The mental pictures that may pass before us need not correspond to the logical components of the judgment. It is enough if the proposition as a whole has a sense; its parts thereby also obtain their content.[^71] Our quantitative judgments about great distances, or about the size of objects, like the Earth, that are vastly larger or smaller than us, do not rest on our ability to form a mental image of anything accurately representative of the magnitudes involved.

But this does not deprive our judgments of warrant or show that they do not concern genuine objects. Indeed, Frege avers, our temptation to think that these judgments must be contentless arises from our temptation to identify the meanings of their constituent terms with the intuitive images or mental pictures that occur to us as we hear or consider them in succession.

When, because of the inherent limitations of our intuitive faculties, we cannot supply a mental image for a particular term, for instance “the size of the Earth,” we may then be tempted to conclude that the term has no meaning.

But we can, after all, make judgments about magnitudes even when they far exceed our intuitive grasp; and although we attach no intuitive content to the idea of there being 0 of any particular type of object, nevertheless our quantitative judgments involving 0 are unimpaired. The possibility of making such judgments meaningfully, Frege suggests, itself suffices to defend the objecthood of numbers against the envisaged objection.

That they can be made at all shows that these judgments concern entities that do not depend on our particular intuitive abilities. Frege’s defense of the objecthood of numbers therefore rests, in this case, on a notion of content according to which judgments may have particular, well-defined contents even if some or all of their key terms cannot be supplied with representative intuitive images.