In linguistics and literary studies, the term indeterminacy refers to the instability of meaning, the uncertainty of reference, and the variations in interpretations of grammatical forms and categories in any natural language.
As David A. Swinney has observed, "Indeterminacy exists at essentially every descriptive level of word, sentence, and discourse analysis" (Understanding Word and Sentence, 1991).
Examples and Observations
"A basic reason for linguistic indeterminacy is the fact that language is not a logical product, but originates from the conventional practice of individuals, which depends on the particular context of the terms used by them."
(Gerhard Hafner, "Subsequent Agreements and Practice." Treaties and Subsequent Practice, ed. by Georg Nolte. Oxford University Press, 2013)
Indeterminacy in Grammar
"Clear-cut grammatical categories, rules, etc. are not always attainable, since the system of grammar is arguably subject to gradience. The same considerations apply to the notions of 'correct' and 'incorrect' usage since there are areas where native speakers disagree as to what is grammatically acceptable. Indeterminacy is, therefore, a feature of grammar and usage.
"Grammarians also speak of indeterminacy in cases where two grammatical analyses of a particular structure are plausible."
(Bas Aarts, Sylvia Chalker, and Edmund Weiner, The Oxford Dictionary of English Grammar, 2nd ed. Oxford University Press, 2014)
Determinacy and Indeterminacy
"An assumption usually made in syntactic theory and description is that particular elements combine with one another in very specific and determinate ways…
"This supposed property, that it is possible to give a definite and precise specification of the elements connected to one another and how they are connected, will be referred to as determinacy. The doctrine of determinacy belongs to a broader conception of language, mind, and meaning, which holds that language is a separate mental 'module,' that syntax is autonomous, and that semantics is well-delimited and fully compositional. This broader conception is not however well-founded. Over the last few decades, research in cognitive linguistics has demonstrated that grammar is not autonomous from semantics, that semantics is neither well-delimited nor fully compositional, and that language draws on more general cognitive systems and mental capacities from which it cannot be neatly separated…
"I suggest that the usual situation is not one of determinacy, but rather indeterminacy (Langacker 1998a). Precise, determinate connections between specific elements represent a special and perhaps unusual case. It is more common for there to be some vagueness or indeterminacy in regard to either the elements participating in grammatical relationships or the specific nature of their connection. Otherwise stated, grammar is basically metonymic, in that the information explicitly coded linguistically does not itself establish the precise connections apprehended by the speaker and hearer in using an expression."
(Ronald W. Langacker, Investigations in Cognitive Grammar. Mouton de Gruyter, 2009)
Indeterminacy and Ambiguity
"Indeterminacy refers to… the capacity… of certain elements to be notionally related to other elements in more than one way… Ambiguity, on the other hand, refers to the failure of an increment to make a distinction which is crucial to the discharge of the speaker's present obligations…
"But if ambiguity is rare, indeterminacy is an all-pervading feature of speech, and one which users are quite accustomed to living with. We might even argue that it is an indispensable feature of verbal communication, allowing for an economy without which language would be impossibly unwieldy. Let us examine two illustrations of this. The first comes from the conversation that was attributed to the friend and the old lady immediately after the latter had asked for a lift:
Where does your daughter live?
She lives near the Rose and Crown.
Here, the reply is obviously indeterminate, as there are any number of public houses of that name, and often more than one in the same town. It creates no problems for the friend, however, because many other factors than the label, including, no doubt, her knowledge of the locality, are taken into account in identifying the place referred to. Had it been a problem, she could have asked: 'Which Rose and Crown?' The everyday use of personal names, some of which may be shared by several acquaintances of both participants, but which are nevertheless usually sufficient to identify the intended individual, provide a similar way indeterminacy is ignored in practice. It is worth noting in passing that, were it not for users' tolerance of indeterminacy, every pub and every person would have to be uniquely named!"
(David Brazil, A Grammar of Speech. Oxford University Press, 1995)
Indeterminacy and Optionality
"What appears to be indeterminacy may actually reflect optionality in the grammar, i.e., a representation that allows multiple surface realizations of a single construction, such as the choice of relatives in There's the boy (that/whom/0) Mary likes. In L2A, a learner who accepts John *seeked Fred at Time 1, then John sought Fred at Time 2, might be inconsistent not because of indeterminacy in the grammar, but because the grammar permits both forms optionally. (Observe that optionality in this instance would reflect a grammar that diverges from the English target grammar.)"
(David Birdsong, "Second Language Acquisition and Ultimate Attainment." Handbook of Applied Linguistics, ed. by Alan Davies and Catherine Elder. Blackwell, 2004)