Is it Always Possible to Articulate your Desires Using Precise Language?

So far, we have only considered specific examples in which it appears as though it is permissible to care about the vague. However, one might have a much more general worry about the Indifference principle.

Firstly, it seems to entail that I can only care intrinsically about a very limited set of propositions. For, according to some philosophers, only the propositions of fundamental physics, mathematics, and logic are truly completely precise. Secondly, it follows that it was only until quite recently, with the discovery of modern physical concepts, that we were able to have thoughts about these precise propositions at all. That is to say, up until the birth of modern physics, pretty much everybody had irrational desires because the only desires they could have formed would have been formed using vague concepts.

This objection, if it has any force, rests on some presuppositions that are fairly specific to a linguistic conception of vagueness. The objector assumes, for example, that in order to have a vague belief or desire, one must first mentally do something with vague concepts, such as articulate a vague sentence in the language of thought. However, this picture is emphatically denied on the account of vagueness I have been sketching so far.

The idea that we can obtain a useful categorization of precise and vague proposi­tions by looking at the kinds of sentences or concepts that express them is also a bad starting point. Indeed, on the view I have been endorsing, it is plausibly not true that the sentences of fundamental physics express precise propositions.

The upshot of this is that the objector, in talking about our concepts, is assum­ing a radically different picture of vagueness. The lines between vague and precise propositions, on my view, simply do not correspond to the lines drawn by sentences (or concepts) that are used in a certain way; they are drawn by the role that those propositions have in thought. Indeed, according to my view pretty much the only sentences that pick out precise propositions are the sentences of mathematics and logic, and thus very few contingent precise propositions are picked out this way; arguably, then, most precise propositions are not expressible on this view.

Thus, to respond to the objection, while I agree that sentences of a public (or private) language rarely express precise propositions, it does not follow that we do not bear any interesting relations to precise propositions in the sense articulated by my preferred theory of propositional attitudes. The notion of a precise proposition can be implicitly introduced by the role it plays in a theory of rational propositional attitudes, a theory in which knowledge of physics is not a requirement of rationality.^[146]