DOLOR TORÁCICO

The aim of this chapter is to outline an account of what the concept of

universal quantification consists in. The account relies on the general idea that (a sub- set of) our actual inferential practices are constitutive of the logical concepts that we use, in the sense that they determine their inferential role and, thus, what should counts as their correct semantics.

The presentation has the following structure.

In Section 1 I formulate three basic constraints that a reconstruction of the concept-constituting usages of the concept of universal quantification has to obey. In Section 2 I present three options for a reconstruction of what the concept consists in.

In Section 3 I discuss these three options in the light of the three constraints and defend my own variant of one of them as the most plausible.

Throughout the chapter, I will focus exclusively on first-order quantification, unless otherwise indicated.

1. UNIVERSAL QUANTIFICATION: THREE CONSTRAINTS

In Chapter II, I defended the plausibility of two ideas, namely:

• The idea that a logical concept is constituted by certain ‘basic’ inferential

practices, which consist in inferences from its canonical grounds and to its canonical consequences;

• The idea that to possess a logical concept is to use it correctly. Correct usage of

a concept C is defined in terms of a subject’s undertaking an inferential commitment to the canonical consequences of C when uttering (propositional contents containing) C.

Both ideas are very general ones, in the sense that subscribing to them leaves open a whole set of questions about our grasp of a logical concept C75_.

Here I would like to restrict the scope of the discussion and focus on the concept of universal quantification. Within this restricted framework, my primary aim is to answer the following two questions:

i) What are the basic constraints on a reconstruction of the concept-constituting usage of universal quantification?

And:

ii) What are the options for the reconstruction? 1.1 Preliminary Discussion

Preliminary Discussion of i)

By the expression ‘basic constraints’ I mean to refer to the intuitive correctness conditions on the way in which one chooses to render the concept-constituting usages of the concept of universal quantification, given the assumption that such usages consist in the canonical inferences that we perform with the concept, that is: in inferences from the canonical grounds and to the canonical conclusions of statements in which the concept figures as the main logical operator.

75 _{For example, neither view commits us to any particular account of how we learn the} logical concepts: by participating in an inferential practice? By understanding how to apply rules of inference that correctly reconstruct concept-constituting practices?

A natural assumption in any attempt to reconstruct our basic inferential practices involving a logical concept C is that the reconstruction should proceed by individuating the rules of inference that correctly abstract the practices in question. That is: a natural way to go is by considering the (sub-set of concept-constituting) inferences that we perform with C, and individuating the rules that display the logical form of these inferences. Under the supposition that concept-constituting usages are the canonical ones, then the aim of the theorist of concepts will be to individuate the rules of inference that correctly display the canonical grounds and the canonical consequences of (statements containing) C.

The project defined by this aim is, then, a reconstructive project: it looks at basic rules of inference as the means via which we reconstruct and express the logical

concepts’ inferential roles, given the way in which we deploy the concepts in our reasoning practices.

In fact, it is natural, in this framework, to regard basic rules of inference as performing a two-fold task.

On the one hand, rules can be the sort of thing via which subjects can learn (how to use) a logical concept.

This is not to say that subjects normally learn the logical concepts in this way. One may argue, for example, that while it is standard practice to become acquainted with the inferential role that the universal quantifier plays in a given logical system by being presented with its introduction and elimination rules, this is not typically the way in which we learn to quantify in the context of a natural language. In one case, we are presented with a precise definition of the concept’s inferential role; in the other case, we presumably learn to infer in a certain way, when using the concept, by being exposed to and participating in the practice of deploying the concept in inferences76_.

76 _{The crucial assumption in this paragraph is, of course, that we have one concept of} universal quantification, which we deploy both in natural languages and in formal reasoning. Chapter II was partly devoted to a discussion of (a general version of) this assumption, on which, then, I will say no more in the present discussion.

However, in virtue of the fact that one can learn the concept by appeal to the rules, the latter should be regarded as providing a definition of what we take the correct

inferential usages of the universal quantifier to be – one, in particular, that is within the epistemic grasp of a cognitive subject.

On the other hand, as already remarked, the rules in question should display the logical form of our concept-constituting inferences. They should thus, intuitively, display the concept’s inferential role in its most general form. But what, exactly, is the generality of a rule supposed to render?

The simple answer is: both a set of linguistic and cognitive data, and its theoretical counterpart.

The data can be rendered in the following way. Our concept-constituting inferential commitments appear to survive the language in which they may be expressed. In particular, they survive the specific interpretations that, within any given language, occurrences of the relevant logical concepts receive.

Consider, in particular, our usages of the universal quantifier in natural languages. These are normally restricted, that is: we normally deploy restricted

instances of the concept. If one endorses a contextualist view about quantification, one will say that the usages in question are restricted by the linguistic context in which we utter propositional contents containing the concept [e.g. Glanzberg 2000, 2006; Stanley & Szabò 2000]. Yet, in the different contexts, we intuitively regard inferences of the same form as being correct or incorrect, irrespective of the way in which context contributes to fix the semantic (or pragmatic) features of our quantified utterances.

The upshot of this observation is, prima facie, that if we take a logical concept to be constituted by its inferential role, then the concept is not reducible to its