Semantic Under-determinacy and Communication

D. Belleri

• Publisher: Palgrave Macmillan
• Year: 2014
• ISBN:
  9781137398444
• Topic: Philosophy
• Subtopic: History & Theory of Philosophy

Combining a fresh, previously unexplored view of the subject with a detailed overview of the past and ongoing philosophical discussion on the matter, this book investigates the phenomenon of semantic under-determinacy by seeking an answer to the questions of how it can be explained, and how communication is possible despite it.

Part I
On Semantic Under-Determinacy

1

Arguing for Semantic Under-Determinacy

The idea that sentence meaning is semantically under-determined has been introduced by its proponents in order to counter a general approach to the semantics of natural language, that traces back to Frege, Russell, Carnap and the Formal Semantics initiated by Montague and Davidson. The picture promulgated by these authors is one where words are endowed with a stable meaning, and the meaning of a sentence is determined compositionally by the meanings of its constituents and by the way they are syntactically arranged. Sentence meaning is conceived in terms of truth-conditions, so the theory commits to the idea that, given a sentence S, it is possible to derive its truth-condition, for example in the form of a T-sentence (‘S is true if and only if p’) by applying the rules of compositionality to the meanings of the components of the sentence.

Semantic under-determinacy (and the attendant idea of pervasive context-sensitivity) is a threat to the idea of meaning as truth-conditional, because it shows that often meaning (even provided contextual resolution of indexicality and ambiguity) fails to express a truth-condition. Moreover, it threatens compositionality to the extent that, if so-called ‘unarticulated constituents’ (that is, propositional components that are not the semantic value of any articulated sentence part) need to be introduced, then the content of an utterance is not determined only by the meanings of the components of the sentence and their syntactic arrangement, but also by other, non-linguistically provided elements.

There are two main varieties of arguments that have been purported to shed light on semantic under-determinacy: Arguments from Incompleteness and Arguments from Context-Shifts. I will present these arguments respectively in sections 1.1 and 1.2. My intent is to clarify the way in which they show that there is something like semantic under-determinacy, by at the same time resisting the idea that they generate an inevitable slippery slope (as some authors have contended). My aim is that of showing that semantic under-determinacy is a genuine phenomenon by at the same time containing the seemingly universal application of these arguments, which generates confusion and needlessly muddies waters. In section 1.3, I will also briefly consider and discuss the methodological import of a third type of argument, which I will refer to as the Argument from Unclear Applications.

1.1 Arguments from Incompleteness

Some arguments purport directly to attract attention on semantic under-determinacy by triggering intuitions as to the ‘incompleteness’ of the sentences in question. The strategy consists in drawing a conclusion on semantic under-determinacy based on some ‘intuitions’ or ‘feelings’, or anyway pre-theoretical impressions. These arguments exhibit the structure of an inference to the best explanation. They usually present a certain sentence, S, as expressing a certain semantic content p. They subsequently show how p is not evaluable, or at least that we as normal speakers feel at a loss with respect to judging whether it is true or false; this is taken to be explained by the idea that p is not a proposition, and hence that S does not express a proposition, or truth-condition.

Up to this point, the upshot of the argument is that of exposing semantic under-determinacy. By adding to it the extra premise to the effect that an evaluable content is obtained only through the addition of further constituents directly in the proposition, it is possible to make a case for the context-sensitivity of these contents. These contents are supplemented with elements drawn from context that are not the value of any articulated component of the sentence, neither at the superficial or at the deep, covert level: these are so-called unarticulated constituents (Perry, 1986; Crimmins and Perry, 1989; Crimmins, 1992). Arguments from Incompleteness most naturally occur together with considerations as to how content must be ‘fleshed out’ in various ways, often with the use of unarticulated constituents. Here are some examples of sentences whose semantic content has been considered semantically under-determined, and in need of completion through so-called unarticulated constituents.

‘It’s raining’

John and George plan to play tennis on Saturday, but on that day it happens to be raining where they live, in Palo Alto. George utters ‘It’s raining’, so John goes back to sleep. In the sentence ‘It’s raining’, the predicate ‘to rain’ provides a dyadic relation rain(t, l), while the tensed auxiliary ‘is’ provides a time, t. The resulting semantic content is that it is raining at t, where no specific location is supplied. This content is, as it stands, unevaluable, for it could be raining anywhere and a place is needed in order to determine to what exactly the predicate ‘to rain’ is correctly applied. So the content that it’s raining is semantically under-determined. There is, however, a place that is salient in the context of the utterance, namely Palo Alto. That utterance of ‘It’s raining’ is true precisely because it is raining in Palo Alto. So, Palo Alto is in some sense part of the proposition or truth-condition expressed by the utterance, even though it is not the value of any component of the sentence: it is an unarticulated constituent of it. So, it turns out that the semantic content of ‘It’s raining’ is sensitive to and dependent on some aspect of the context – namely, a salient place (the example is inspired by Perry, 1986, p. 138. See also Perry, 1998, pp. 6–7; Korta and Perry, 2011, Ch. 9).

‘Jill is ready’

The sentence expresses the proposition that Jill is ready, where the component corresponding to the purpose, or activity, for which Jill is ready, is missing. As a result, the content of the sentence is not evaluable: it does not amount to a proposition. So, it is semantically under-determined. It could express a proposition if the element corresponding to Jill’s purpose were added to the content, yet since the latter would not be the semantic value of any component of the sentence, it would be an unarticulated constituent (see Bach, 1994a, pp. 127–8; 1994b).

‘Steel isn’t strong enough’

The content expressed by this sentence is that steel is not strong enough. However, one may wonder ‘for what’ steel is not strong enough. Without this piece of information the semantic content of the sentence is unevaluable. So, the sentence suffers from semantic under-determinacy. Plus, the content of the sentence could become evaluable if it were supplemented with the purpose for which steel fails to be strong enough. The latter not corresponding to any element of the sentence, it would be an unarticulated constituent (Bach, 1994a, p. 128).

‘Jamal is tall’

The semantic content of the sentence is that Jamal is tall. However, by itself this content cannot be evaluated as true or false, because it fails to specify the comparison class relative to which Jamal is to be ascribed the property of being tall. So, the sentence is semantically under-determined. If such a comparison class were supplemented in the content, then the latter would express a full-fledged proposition. So, the content is sensitive to or dependent on the specification of such a class, which however would act as an unarticulated constituent (Bach, 2012, pp. 171–2). Similar observations hold for other gradable expressions such as ‘small’and ‘big’ (Sperber and Wilson, 1986, p. 188).

‘The leaves are green’

The content of this sentence is that the leaves are green. However, it may be pointed out that there are many respects in which a leaf can be green. It can be green because that is its natural colour, because it has been painted green, because a green light shines on it. The semantic content fails to specify in which respect the leaf is green, and is therefore strictly speaking unevaluable. So, it is semantically under-determined. The content could be made evaluable if it were supplemented with a ‘respect’ component, so it is context-sensitive to such an aspect in a way. However, the component would be an unarticulated constituent, in that it would not correspond to any element in the sentence (see Travis, 1997, p. 90; Lahav, 1989, p. 263).¹

Other sentences trigger intuitions of incompleteness on account of exhibiting a different form of defectiveness, which pertains to the sentence as a whole being incapable of nailing down a truth-condition. These sentences do not seem to lack any specific component and yet their semantic content fails to express a truth-condition. The following are some of the most cited examples.

‘Peter’s book is grey’

The semantic content of this sentence is that the book which bears some relation with Peter is grey, however which specific relation should be instantiated in order for an utterance of this sentence to be true is not specified; consequently, it is not possible to judge whether an utterance of it is true or false. So, the sentence suffers from semantic under-determinacy (see Sperber and Wilson, 1986, p. 188).

‘Bill cut the grass’

The semantic content of this sentence is simply that Bill cut the grass. As it stands, this content could be true in a variety of more or less far-fetched situations, for instance one in which Bill mows the grass with a regular lawnmower but also one in which Bill slices each leaf of grass with a knife and a fork. Nothing in the semantic content of the sentence enables the hearer to sort which situation is the one in which the utterance is true, so the sentence turns out as semantically under-determined (see Searle, 1980, p. 221).

Incompleteness, and intuitions thereof, is taken to reveal semantic under-determinacy. Yet so far we have been content with an intuitive grasp of the kind of incompleteness that afflicts the above sentences. As I will explain in the next section, it is important, for the Argument from Incompleteness to succeed and resist objections, that the task of sustaining the case for semantic under-determinacy is not left to our intuitions only, and that the notion of incompleteness be spelled out in clearer, theoretically more rigorous terms.

1.1.1 Incompleteness as genericity

The arguments just reviewed aim at establishing semantic under-determinacy through intuitions of incompleteness. With sentences like ‘It’s raining’, ‘Jill is ready’ and so on, there is a ‘felt’ need to supplement them (Taylor, 2001, p. 53) – and that is what grounds our judgement of incompleteness. Incompleteness can be represented in a Russellian framework, which conceives of propositions as structured n-tuples of objects and properties: in such a framework, the contents of incomplete sentences may be regarded as featuring a ‘gap’, an unsaturated slot which calls for filling. For instance, the content expressed by ‘It’s raining’ may be represented as an n-tuple with structure <R, t, _> containing the property of raining R, the time t, but only a gap in the location slot. Russellian propositions are a useful representational tool, provided that the intuition that the content is incomplete is shared by everyone (or nearly everyone) in the first place. Importantly, this may not be the case. Presented with a sentence like ‘Jill is ready’, one could in fact ‘feel’ that its content is just complete enough. So how is the contrast settled? What we need is a criterion independent of intuitions that helps us spell out precisely in what way these sentences are incomplete.

Incomplete sentences seem to fail to determine a truth-condition. But what does this mean exactly? One may suppose that ‘determining a truth-condition’ implies ‘sorting the possible worlds where the utterance is true’ from ‘the possible worlds where the utterance is false’. If this is so, then the semantic content of incomplete sentences does not seem to fail to do that. The semantic content of ‘Jill is ready’ seems to succeed in sorting the worlds where an utterance of the sentence is true from those where it is false. The former will be all the worlds where Jill is ready to do something (and there is nothing for which she is not ready), while the latter will be all those worlds in which there is nothing she is ready for. So there is at least a sense in which the semantic content of one of the attended sentences does not fail to provide a truth-condition, as Cappelen and Lepore (2005, p. 158) and Borg (2004, pp. 231–2; 2012, p. 108) insist. In order for the incompleteness argument to show something, a stronger sense of ‘determining a truth-condition’ should be adopted.

One could understand ‘determining a truth-condition’ as ‘determining in which particular world, or set of worlds, a specific utterance of the sentence is to be evaluated as true or false’: for instance, whether the speaker’s utterance of ‘Jill is ready’ is to be evaluated as true or false in w₁, where Jill is ready for skiing; or in w₂, where Jill is ready to get married. If this is what determining a truth-condition amounts to, then it is clear that the semantic contents of ‘Jill is ready’ or ‘The leaves are green’ do not succeed in doing this. Merely based on the content of the sentence to the effect that Jill is ready, there is no way of determining in which particular world w₁, w₂, w₃ ... w_n the utterance is to be evaluated, because the semantic content does not feed us with enough information to narrow down the conditions in which Jill is ready to conditions of being ready for a specific thing.

Yet the doubt remains that this may be too strong a requirement for any semantic content. It seems that other sentences would suffer from the same problem, yet we would not list them among cases of obvious semantic under-determinacy. One example is provided by the sentence ‘Lisa is happy’ (cf. Borg, 2004, pp. 232–4 for similar observations). The semantic content of this sentence, by itself, does not enable the hearer to know in which particular world the utterance is to be evaluated. This is because there are countless differently arranged worlds where Lisa is happy: in w₁ she is happy because she has just got married; in w₂ she is happy because she has won the lottery; in w_n she is happy because she has been able to eat lasagne, and so on. The mere content to the effect that Lisa is happy does not determine whether the utterance is to be evaluated at any of w₁, w₂ … w_n, for the simple reason that it supplies no information as to the reason for which Lisa is happy. Due to this failure, we would have to list ‘Lisa is happy’ among cases of semantic under-determinacy even though it does not immediately strike as such an example. Moreover, even longer sentences, which supposedly provide more information as to how the world should look like, may wind up as semantically under-determined because they may fail to determine in which particular world, or set of worlds, they should be evaluated for truth or falsity. To illustrate, consider the sentence ‘Jill is ready because she has won the lottery’: there are a number of possible worlds where this obtains, but matters are arranged slightly differently. In w₁ Jill is happy because she has won the lottery with ticket no. 3000321, while in w₂ she is happy because she has won the lottery with ticket no. 3000322, while in w₃ she is happy because she has won the lottery with ticket no. 3000323 and so on. Given the semantic content of the sentence, namely that Jill is happy because she has won the lottery, there is no way to determine in which particular world, w₁, w₂ and w₃ the utterance should be evaluated. So again, a sentence like ‘Jill is happy because she has won the lottery’ would have to be regarded as semantically under-determined even though it does not seem so at first sight.

This prompts an attempt to reformulate the sense in which a semantically incomplete sentence ‘fails to determine a truth-condition’, such that it is not as weak as ‘sorting out worlds’ but not as strong as ‘determining in which particular world, or set of worlds, the utterance should be evalu...

Table of contents

• Cover
• Title
• Copyright
• Contents
• List of Tables
• Preface and Acknowledgements
• Introduction
• Part I On Semantic Under-Determinacy
• Part II Semantic Under-Determinacy and Communication
• Notes
• Bibliography
• Index