I NFERENTIAL C OMMITMENTS IN C ONTEXT

This chapter intends to complement the discussion of Chapter III by tackling two aspects of our usage of the concept of universal quantification in linguistic and communicative practices. Such aspects can be rendered in terms of a theoretical problem and a linguistic datum. Throughout the chapter, both will be discussed with reference to our natural language usages of the universal quantifier.

The theoretical problem amounts to the question: given that our natural language usages of the universal quantifier take place within communicative contexts, how should we render the role and status of the inferential commitments that we undertake when deploying the concept in context?

The linguistic datum consists in the fact that our contextual usages of the quantifier are often restricted. The discussion of contextual quantifier restrictions will focus, here, on the epistemology of such restrictions.

The chapter then relates to the previous one in the following way.

In Chapter III I defended an account of universal quantification according to which:

• The elimination rule for the universal quantifier should be understood as a

concept-defining rule, in the sense that it displays the logical form of concept- constituting inferential practices;

• The rule should be given a fully schematic reading;

• The generality expressed by the concept of universal quantification is full

inferential generality.

An important claim of the view endorsed in that chapter was that our understanding of the concept in terms of its purely inferential role (i.e., as an

uninterpreted concept) should be thought of as independent of the notion of a domain of quantification.

Here I would like to complete the discussion of Chapter III in two ways. I intend to provide additional arguments against what I have labeled the ‘domain model’, and to defend the claim that we should dispense with the notion of a domain also when dealing with (contextually) interpreted instances of the concept of universal quantification.

In so doing, my aim is to sketch a contextualist framework for our

understanding of interpreted usages of the universal quantifier that begins to clarify the role of concept-constituting inferential commitments in (a sub-set of) our

communicative practices.

The structure of this chapter is the following.

Section 1 sketches the framework in which the subsequent sections should be understood, by:

• Clarifying the terminology that I will use;

• Discussing a more articulate definition of what I have called, in Chapter III, the

domain model for the universal quantifier;

• Distinguishing between a foundational account of universal quantification and

a descriptive account of the semantics for the universal quantifier. Sections 2 to 4 discuss the question of whether the notion of a domain of quantification should play any role in a foundational account of universal

quantification, and in particular in the understanding of how the assertoric sense of universally quantified sentences is determined in context. The discussion is articulated in terms of three arguments, which target the epistemological relevance of the notion. The upshot of the arguments is that an account of the assertoric sense of (contextually)

interpreted universally quantified sentences should dispense with the notion of a domain.

Finally, in Section 5 I make some proposals about the shape that a foundational account of universal quantification should take, and sketch a suggestion for

articulating the relation between our concept-constituting inferential commitments and contextually supplied interpretations of the universal quantifier.

1. THE DOMAIN MODEL AND A FOUNDATIONAL SEMANTICS FOR THE UNIVERSAL

QUANTIFIER

1.1 Terminology and Structure

In the next sections I wish to present three arguments. Their structure and intended targets can be summarized as follows.

• Argument (a) (Section 2)

Assumption: The plausibility of an inferentialist account of the concept of universal quantification based on the notion of a canonical commitment to the consequences of the concept;

Polemical Target: The idea that the notion of a domain of quantification should play any role in how the assertoric sense of (contextually interpreted) quantified sentences is determined according to such an account.

• Argument (b) (Section 3)

Assumption: The plausibility of an inferentialist account of the concept of universal quantification based on the notion of a canonical warrant;

Polemical Target: Once again, the idea that the notion of a domain of quantification should play any role in how the assertoric sense of (interpreted) quantified sentences is determined.

• Argument (c) (Section 4)

Assumption: The plausibility of a contextualist account of how the assertoric sense of a universally quantified sentence is determined;

Polemical Target: The idea that the notion of a domain of quantification should play any role in such an account.

Both the terminology used in presenting the targets of arguments (a) to (c) and the restricted scope of the first two require that we put a few things in perspective before we start discussing the arguments themselves. In particular, they require that we spell out the assumptions on which the arguments rely, and the framework in which the relevance of their targets should be understood.

The first two arguments will not crucially rely on the idea that our interpreted usages of the universal quantifier take place in a communicative context. Although I will refer to such usages as taking place within assertoric contexts, nothing in the arguments depends on any features of a context that we might consider relevant for the way in which an interpretation of the universal quantifier is provided. The focus is simply on the contribution that the notion of a domain makes to speakers’

understanding of the sense of interpreted instances of the quantifier.

The third argument does bear on the idea that interpretations are contextually supplied, in the sense that understanding and evaluating a propositional content requires the specification of (at least some of the features of) the context of utterance. However, no commitment is either presupposed or implicated by the argument as to which such features we should take to be relevant – in other words, no commitment is undertaken to a specific notion of context.

Three further provisos are necessary for a correct understanding of the arguments.

First, when, in Sections 2 to 4, I speak of a context, I refer to an assertoric context – all that I am concerned with in these sections are communicative contexts in which the speech acts performed by speakers are assertions.

In the case of first and third arguments, this is mainly to simplify the exposition – nothing in the structure of the arguments depends on the fact that the focus is on assertion, and one may reformulate them with respect to speech acts other than assertion122_.

In the case of the second argument, the focus on assertion does play a role – mainly in virtue of the theoretical framework within which the argument is formulated. This is the verificationist account discussed and defended in [Dummett 1991]. The scope of the argument is thus restricted in two ways: in terms of its focus (assertoric practices) and in terms of its theoretical background (a verificationist theory of sense).

I take it that the first restriction, however, is not such as to diminish the relevance of the argument in the framework of the current discussion. Even if the notion of a domain turned out to be problematic only for an understanding of

assertoric usages of the universal quantifier, this would be enough to at least raise the suspicion that an account of sense relying on the notion would be implausible. Assertion is, after all, one of our main speech acts.

The second restriction has to be understood in the framework of the general project of which this thesis explores some aspects – namely, in the light of the general idea that the logical concepts are constituted by their inferential usage, and that

122 _{Things are in fact more complicated. An assumption of the first four sections of this} chapter, and an explicit component of some of the claims that I make in Section 5, is that there is a sense in which canonical commitments are invariant with respect to illocutionary force. That is: their form and quality is stable across variations in speech act type, although they may take different (illocutionary) force.

However, this assumption is, to say the least, not self-evident; it needs to be further articulated and defended, in the form of an account of the exact relation between:

• The inferential commitments undertaken by speakers in assertoric practices; • The Inferential commitments undertaken by speakers in other speech-act practices. I will clarify the challenges that confront an attempt to provide such an account in sub-section 5.2.

speakers’ grasp of the logical concepts should also be individuated with reference to such usage.

There are two natural ways to articulate the idea that a theory of logical concepts should be a theory of inferential usage. One is the pragmatist idea that I endorse, according to which it is the canonical consequences of a logical concept that are epistemically primary in this usage. The other is the verificationist idea according to which it is the canonical warrants associated with sentences in which a logical concept C figures that are, instead, primary.

As the first argument targets the notion of a domain of quantification with respect to the first idea, thus complementing the focus of the second argument, the restricted scope of the second argument does not per se undermine in any crucial way the generality of the claims made in this section.

Second, by the ‘sense of a sentence’ I mean: the proposition expressed by an utterance of the sentence. ‘Sentence’ here is to be understood as interpreted

sentence123_.

Third, when I speak of the notion of a domain I don’t intend to commit myself to any specific model-theoretic rendering of the notion. What I have in mind is an informal notion, according to which the domain over which a quantifier ranges is a totality of objects, which the constants in the language can name and which provide the possible values for the variable bound by the quantifier.

Although the natural way to render formally this intuitive notion is, of course, by appeal to the notion of a set (and, in particular, of a well-founded set), in these sections I will keep the discussion informal. As it is the intuitive idea common to all model-theoretic renderings of the notion that is targeted in the arguments, any issue concerning any specific such rendering would play a misleading role in the discussion, and distract attention from its structure and aims.

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