Determined Reference as a CI Component in the Meaning of Definites
Multiple definite articles: Several languages with a distinction between several definite
articles have been described in the literature with some known examples being Sioux
(Lakhota; Boas and Deloria, 1941; Rood and Taylor, 1996, van Vallin 2012) and Northern
Frisian (Fering; Ebert 1971). Standard German has a reflex of this in the case of contracted
vs. non-contracted prepositions – beim (`at-the.weak´) vs. bei dem (`at the.strong´) (Schwarz,
2009). Schwarz interprets both definite articles as expressing maximality. The strong article
additionally expresses anaphoricity, which is absent for the weak article. This is shown by
grammaticality judgements whereby only the strong definite article is licenced in the
presence of a salient antecedent.
We would like to present an additional observation regarding the difference between strong
and weak definites, namely that the existence presupposition triggered by the definite article
can only be cancelled in weak definites, never in strong definites.
(1) Ich konnte nicht beim/ #bei dem König von Frankreich dinieren, weil F. keine Monarchie
ist. `I couldn't dine at-the.weak/ at the.strong king of France, because France isn't a monarchy.´
We would like to account for this difference by discerning two dimensions in the meaning of
definites: maximality and determined reference, one of which is presuppositional whereby the
latter is a conventional implicature.
These two meaning dimensions rely on the two main schools of interpretation to definite
descriptions: uniqueness and familiarity based approaches (Lyons, 1999). Common to the
uniqueness based approaches is the use of the ι-operator, originally created to depict
uniqueness (Russell, 1905) and later revised to maximality by Sharvy (1980). The prevailing
use of the ι-operator in the semantic literature follows the referential tradition in assuming
uniqueness, and therefore existence as well, to be presuppositions triggered by the definite
description (Strawson, 1950). The familiarity based approach, stemming from Maetzner
(1864) and more explicitly Christophersen (1939), regards definite descriptions as expressing
discourse related epistemological assumptions. This view became influential in DRT (Kamp,
1981), for example, in which definite descriptions are interpreted anaphorically.
We will propose a combined approach to the interpretation of definite descriptions that draws
a distinction between maximality and determined reference. Maximality appears as a presupposition, following the uniqueness based approach. On the other hand, determined
reference is based on a hierarchy of discourse related epistemic propositions, comprised of (i)
referentiality, (ii) hearer-oldness and (iii) discourse-oldness (anaphoricity).
First we shall explain this hierarchy. Then we shall argue that determined reference is a
conventional implicature (CI), rather than a presupposition. Finally, we shall demonstrate
how our interpretation of definites accounts for the pattern observed in (1).
The degrees of determined reference are defined as follows, where x is the referent denoted
by the definite description:
(i)
Referentiality: Know (I, ∃! 𝑥𝑃𝑥)
(ii)
Hearer-oldness: BELIEVE (I, (KNOW (you, ∃! 𝑥𝑃𝑥)))
(iii) Discourse-oldness: BELIEVE(I, (KNOW (you, ∃! 𝑥𝑃𝑥 & Max ({x ∈ [[P]] } ∈
UD)))
These epistemic propositions form a hierarchy, whereby discourse-oldness entails heareroldness and both entail referentiality. This is illustrated with the examples in (1), where the
definite descriptions differ in their degree of determined reference.
(1)
a. A student arrived. The student was helpless. [CIs: (i), (ii), (iii)]
b. The sun is rising. [CIs: (i), (ii); not (iii))]
c. Give me the hammer on the table. [CI: (i); not: (ii) and (iii)]
d. The richest women in Peru is probably not a linguist. [none of the inferences]
CI status of determined reference We will argue that the degrees of determined reference
have the status of CIs. CIs as defined by Grice (1975) are often difficult to discern from
presuppositions. We shall rely on the following two properties discussed in Levinson (1983)
and Potts (2006) to support our analysis of determined reference as CI: (A) Presuppositions
can project, but do not have to: If the presupposition trigger is embedded in the scope of other
logical operators, the presupposition can be cancelled. Conversely, CIs must project and they
can never be flouted. (B) Presupposition failure with an unembedded presupposition trigger
leads to the loss of truth value in the assertion. Conversely, even (infelicitous) flouting of a CI
does not affect the truth value of the assertion.
We shall apply this distinction to sentence in (1) repeated here:
(1) Ich konnte nicht beim/ #bei dem König von Frankreich dinieren, weil F. keine Monarchie
ist. `I couldn't dine at-the.weak/ at the.strong king of France, because France isn't a monarchy.´
(1) with the weak definite article shows cancelling of the existence presupposition with the
definite article (the presupposition trigger) being embedded in the scope of negation and the
modal can. This results in a felicitous assertion with an attributive interpretation of the
definite description.
(2) #Ich habe beim König von Frankreich diniert, obwohl Frankreich keine Monarchie ist.
(2) shows that with the definite article being unembedded, the cancellation of the
presupposition results in an infelicitous assertion. Moreover, the first assertion loses its truth
value.
(1) with the strong definite article invokes the CIs i-iii, which cannot be felicitously flouted
despite being embedded under other logical operators. Since the CIs of determined reference
entail the existence presupposition, the latter cannot be cancelled.
Additional evidence that determined reference is a CI is that when a strong definite article is
used and the implicature is infelicitously flouted, the truth value of the first sentence (whether
or not I dined with the French king) remains defined and unaffected. This truth value does not
depend on the truth value of the CI, which can be independently valued. This stands in
contrast to the loss of any truth value in (2).
Conclusion We presented a refined analysis of the meaning components of definite
descriptions: In addition to the standard maximality interpretation, various types of definites
can be distinguished by CIs related to the discourse status of the referent. Data from
languages with two definite articles support our analysis. Our ι+CI analysis is fully
compatible current compositional treatments of definites and shows a further fruitful
application of two-dimensional semantics.