Metalinguistic Negation: Horn and Geurts Compared

Introduction

Convention tells us that negation is the semantic reversal of an assertion, but as shown by Horn, Geurts, and others, this definition becomes problematic in the face of examples like The king of France is not bald because there is no king of France. How does one define negation to account for pragmatic denials as well as semantic reversals? There has been much debate revolving around this issue, and Horn and Geurts sit at its center. This paper reviews their research and supplies suggestions for future research.

Negation is simply defined as the semantic reversal of an assertion, as illustrated below:

1a. My parents know I'm gay.
1b. My parents don't know I'm gay.

The conventional interpretation of (1b) yields a traditional, internal negation reading. However, a problem with the definition of negation arises in statements like (1c), where it is not the assertion being reversed but the assertion's assertability:

1c. My parents don't know I'm gay, because I'm straight.

Metalinguistic Negation and Background for the Debate

Supporters of three-valued logics — in which statements are either true, false, or truth-valueless — explain cases like (1c) as a semantic ambiguity. However, there is really nothing ambiguous about such examples. Monists are searching for one truth-functional, semantically general theory of negation that applies in all cases. Neither of these views satisfied Horn (362), who was looking for a unified theory of negation. He observed that there are clearly two distinct uses of sentential negation — which rejects the monist perspective — and that the kind of negation exemplified by (1c) is not a truth-functional or semantic operator on propositions. Rather, it is a rejection of the presuppositions, implications, style, register, morphology, and/or phonetic realization of an utterance. Horn terms this metalinguistic negation.

The ambiguity favored by three-valued logicians arose because they needed to allow two interpretations of the negative operator — or give it dual scope possibilities — in order to explain how true negative statements like (1c) can exist when their affirmative complements like (1a) are truth-valueless. However, this theory necessarily multiplies the lexical senses of negative operators, defying the principle that the simplest answer is the best (Occam's Razor). Moreover, these cases of negation are not obviously examples of semantic ambiguity, and the paraphrase in (1d) does not clearly disambiguate as it should according to three-valued logic:

1d. It is not the case that my parents know that I'm gay.

Furthermore, it is difficult to prove that the internal negation in (1b), with its presupposition-laden understanding, is semantically distinct from the external negation in (1c), which cancels the presupposition "I am gay." It is particularly telling that even languages with multiple negative operators do not distinguish between internal and external negation (qtd. in Horn 366). Numerous languages — French and Swahili among others — use different forms of negation for various syntactic, semantic, and synchronic situations, but never for the one distinction that three-valued logicians and ambiguists would predict. The three-valued logicians' response is that the underlying form of external negation reads, "It is not {true/the fact} that …" But this condition is neither necessary nor sufficient for the non-presuppositional reading of (1b).

Ambiguists like Karttunen and Peters (qtd. in Horn 368), who do not rely on the truth conditions of presuppositions in their analysis of negation, call on examples (2a)–(2c) to illustrate that while both (2a) and (2b) conventionally implicate (2c), the right intonation contour and sentential continuation in (2d) produce a contradiction negation that rejects the initial implicature:

2a. Chris managed to solve the problem.
2b. Chris didn't manage to solve the problem.
2c. The problem was difficult to solve.
2d. Chris didn't manage to solve the problem; he found it quite easy. (Horn, p. 368)

Karttunen and Peters point out that this contradiction negation never elicits negative polarity items like any or yet. Consider (2e)–(2g):

2e. Chris managed to solve some problems.
2f. Chris didn't manage to solve any problems.
2g. Chris didn't manage to solve {some / *any} problems — they were easy for him. (Horn, p. 368)

The placement of any in (2g) would be nonsensical. Similarly, consider (3a)–(3c):

3a. Mom already remembered that I'm supposed to be grounded.
3b. Mom didn't remember that I'm supposed to be grounded yet.
3c. Mom didn't {already / …} remember that I'm supposed to be grounded {… / *yet}, because I'm not supposed to be grounded.

In this example, already in the place of yet removes the implicature associated with remember.

Works Cited

Geurts, Bart. "The Mechanisms of Denial." Language. 74.2 (1998): 274–307.

Horn, Laurence. A Natural History of Negation. 2nd ed. Stanford, CA: Center for the Study of Language and Information, 2001. 362–423.