If people attach something to a word within their minds, then this is a fact of their individual psychologies, not capable of establishing the different fact that the word actually means something within their language.
Thus, while the mentalist conception of meaning led to the atomist view of language ('we find out meanings of individual words and thereby explain language and its workings'), the interactive conception leads instead to the holistic view ('we must capture the workings of language and meanings will come out as spin-offs').
It is this holism that ushers in the indeterminacy of meanings of individual words.
As it is always a sentence (or sometimes perhaps even a supersentential whole) that must be employed for a valid move within a language game and that is hence independently meaningful in this sense, individual meanings can only be the artificially individuated contributions which the individual words bring to the sentence's achieving the moves within the relevant games.
And it is important to see that the indeterminacy of individual meanings is not an indeterminacy of semantics: semantics is a matter of the ability of our linguistic tools to serve as various kinds of vehicles of various language games, and though such an ability is vague in the sense that it is usually not a yes-no 6 matter, it is not indeterminate (indeed it is not even clear what it would mean to call it so).
On the other hand, furnishing individual words with values which would compositionally add up to the determinate abilities of the significant wholes can surely be done in more than one way – hence meaning assignment in this sense is indeterminate almost trivially.
From this viewpoint, to situate beliefs within an individual, and to talk, as many semanticists do, about the individual’s 'belief box', is analogous to expressing that a tree is five meters high by saying that the tree has the five meters somewhere within its 'height box'.
As Quine showed, the holistic character of language makes it impossible to distribute the relatively clearcut boundary between semanticsL and semanticsW to individual statements and expressions in any unique way; and this makes the boundary between meaningL and meaningW of an individual linguistic item rather illusory.
Evincing Kamp's own example (personal communication), if we analyze the sentences One of the three candidates is over forty and Two of the three candidates are under forty by traditional means, we are unable to account for the important difference between them, namely that the former can, while the latter cannot, be followed by We eliminate him. This vantage point lets us see DRT, and semantic theory in general, as an explicit reconstruction of structural, inferential patterns governing our use of language carried out via explicating the roles of individual expressions within these patterns.
I am convinced that nobody, not even the most diehard mentalists and conceptualists, would claim that semantics is the matter of describing some mental (neural) particulars within the head of an individual speaker - for this would be no theory of English (nor of any other language), but rather the theory of some features of a particuar person.