INFERENTIAL PRACTICES

Any inferentialist account of concept-constitution for the logical concepts faces two general tasks:

• Developing the very idea that the logical concepts are to be seen as inferentially

constituted. An important aspect of this issue, on which I will focus, consists in the way in which we choose to answer the following question: within the framework of the inferentialist account, what sort of thing, exactly, can be constitutive of a logical concept?

• Spelling out the facts given which a rational subject may be ascribed possession

of a logical concept.

In this section and in Section 3 I will discuss the first task. While Section 2 is devoted to methodological considerations, Section 4 will tackle the second task.

In addressing the first task, one has two options. That is, one can say that the sort of things that can be concept-constituting for a logical concept C are:

• Basic rules of inference: That is, instructions to proceed in a certain way from

option might argue, for example, that Modus Ponens is C-constituting for the concept of the conditional;

• Our inferential practices: It is, for example, (some feature of) our practice of

inferring a sentence q from sentences of the form p and p→q that constitutes

the concept ‘conditional’.

In this section I want to defend the latter option from the following objections. Objection 1 – The idea that inferential practices (that is: the way in which we actually deploy a logical concept in reasoning) are the sort of things that can be concept-constituting has the consequence of making it impossible to judge such practices as correct or incorrect. This consequence is both counter-intuitive and undesirable, therefore the idea is flawed.

Objection 2 – The idea that inferential practices are the sort of things that can be concept-constituting, plus the idea that a rule of inference is but an abstraction from these practices, has the consequence of making it impossible to judge rules of inference themselves as correct or incorrect. This consequence, once again, is both counter-intuitive and undesirable, therefore the idea is flawed.

Objection 3 – Even if the idea that inferential practices are the sort of things that can be concept-constituting were immune from the two objections above, a proponent of the idea would then face the problem of explaining what the relation between a concept-constituting inferential practice (for example, the practice of

inferring q from p and p→q) and the relevant basic inferential rule (for example, Modus

Ponens) consists in. Indeed, she would even face the problem of clarifying what

‘relevant’ means in the sentence above. Until she gives an account of what this relation is, she is not in a position to claim that the idea under discussion is a plausible one.

1.1 The First Objection

We need to reconstruct the objection a bit more in detail before we consider some possible replies.

As noted in Chapter I, talk of inferential practices can either be rendered as talk of idealized practices or as talk of actual practices. In the first case, what we really mean to say when we claim that inferential practices can be concept-constituting is that certain normatively constrained practices can be concept-constituting – where the natural option is to take the source of the normative constraint as given by the rules or sets of rules of inference to which such practices conform. The relevant rules of inference will then tell us how we should use a logical concept. If this is the case, however, then there is no distinction between this option and the view that claims that the rules themselves are the kind of things that can be concept-constituting for logical concepts. Therefore, what we had better mean is that our actual inferential practices are the sort of things that can be concept-constituting. It is, simply put, the way in which we actually reason from a given set of premises to a certain conclusion, i.e. the inferential steps that we actually perform in reasoning thus, that is to count as being concept-constituting.

Now, it seems plausible to suppose that, in principle, any reasoning process can be questioned for correctness – that, intuitively, there is no circumstance in which I should not able to ask the question: is this way of reasoning correct? Whether I am able to answer this question is, of course, a complicated matter – but one might have the strong intuition that it is always conceivable to at least ask the question.

Take a basic inferential practice, for example the practice of inferring q from p and p→q. Among the questions that I can conceive of asking about its correctness is

the question of whether the conclusion of the inference really follows from its

premises. Under the assumption that the practice is constitutive of the concept of the conditional, a possible formulation of this question is: is this the correct way in which the concept ‘conditional’ should be deployed? In other words, is our use of ‘→’ correct

conditional, it doesn’t make sense to enquire about the correctness of the relevant use of the conditional. The inference constitutes the concept: the relation between the premises and the conclusion of the inference is then determined by the way in which we deploy ‘→’. If this is so, there is no point in asking whether the conclusion really

follows / whether our usage of the conditional is correct. That such usage is what it is, is presupposed by any judgment about the correctness of (other, intuitively less basic) reasoning practices. Therefore there is at least a class of inferences for which it is not conceivable to ask a question about correctness, against our intuitions42_.

The objection can be addressed by means of three strategies.

i) One can bite the bullet and acknowledge that indeed there is a special class of inferences, the concept-constituting ones, for which a question of correctness cannot be asked. After all, one thing is to say that it is conceivable to ask this question in all circumstances, and a different thing is to say that we should always in fact be able to ask such a question. If this goes against some shared intuitions, then those intuitions are wrong.

ii) One can argue that even if an inferential practice is concept-constituting, a question about its correctness can still be asked, though only in a somewhat restricted form. More precisely, a question of correctness can still be asked about specific instances of the practice in question. The form that the question might take is: does the particular inference that we are judging conform to the inferential practices in which, within our epistemic and linguistic community, standard usages of a given logical concept consist? For to say that actual inferential practices are concept-constituting, is not to say that all such practices are. In fact, an intuitive constraint on a plausible account of concept-

42 _{The philosophical background for the objection considered here is, of course, given by} the classical debate on rule-following and meaning that followed the publication of

Wittgestein’s Philosophical Investigations and Remarks on the Foundations of Mathematics, and in particular by Kripke’s discussion of a dispositional account of meaning and formulation of the skeptical problem, in [Kripke 2007]. A discussion of some aspects of the debate, which I am keeping in mind in my articulation and treatment of the objection, is the one offered by [Boghossian 1989].

constitution is precisely that it formulates a criterion by appeal to which one may isolate a class of relevant practices. The correctness of a specific inference will then be individuated in terms of its conforming to such practices.

‘Conform’, in the reply above, can mean: ‘is relevantly similar’, ‘has the same logical form as’ or ‘can be reconstructed by means of an appeal to the same rule of inference’, depending on the view that we take on the relation between inferential practices and rules of inference – more on this in the context of the discussion of the third objection. iii) One can accept the intuition that it should always be possible to ask a question of correctness about inferential practices, but reject the idea (which is an implicit assumption of the objection) that an inferential practice’s being concept-constituting implies that it is not questionable for correctness under any definition of correctness to which we may attach a normative sense. This thought may be further articulated in various ways, which I will consider in a moment43_.

The first Two Strategies The first two strategies present some obvious difficulties.

43 _{One might claim that a fourth available strategy consists in arguing that, even if we take} actual inferential practices to be constitutive of the logical concepts, an independent criterion of correctness can still be given – for example as the semantic requirement that the inferences in question be valid inferences. My reply to this claim is the following.

• To say that only the valid (basic) inferences are the ones that can be concept- constituting is to give an account of concept-constitution in terms of idealized

inferential practices, that is: practices that conform to a norm the correctness of which is assessed independently of the features of such practices. Such a norm can only be the rule, or set of rules, of inference of which the practices are instantiations. So the claim really concerns a way of articulating the distinct option that takes rules of inference, rather than practices, to be constitutive of the logical concepts. • Furthermore, it is not clear that adopting a semantic constraint as a criterion of

correctness for our inferential practices is consistent with the basic inferentialist assumption that the logical concepts are constituted by their purely inferential role - I will discuss some aspects of this issue in the next chapter, with specific reference to the concept of universal quantification.

Ad i)

Consider, in particular, the way in which (a version of) the first strategy is pursued in [Peacocke 1988: 158; 179-81], partly following [Wittgenstein 1978 I.8, VI.24].

Although Peacocke speaks of rules of inference rather than of inferential practices, in the context of this discussion the view can be reformulated in terms of inferential practices, I hope, without being unjust to its original formulation.

The idea, which Peacocke inherits from Wittgenstein, is that we have a class of inferences for the correctness of which an epistemic subject (Wittgenstein’s rule- follower) can give no inferential or non-inferential reason. [Peacocke 1988: 76; 1992: Chapter I] develops this idea in terms of an account of what it is for an inference or a set of inferences to be concept-constituting. Our acceptance of the inferences that constitute the logical concepts ultimately relies on a psychological state: we find those inferences primitively compelling. That we find them primitively compelling means that we do not accept them in virtue of any belief or evidence that we might have

concerning their correctness: it simply strikes us as obvious that the conclusion follows from the premise(s). It is, then, in virtue of a psychological fact that we accept them as the correct concept-constituting inferences for a given logical concept.

Now, the difficulties encountered by the reduction of a question of correctness to a question about the obtaining of a psychological fact partly depend, of course, on what one expects of an account of correctness for inferential practices.

If, for example, one endorses the project in [Boghossian 2000; 2003], and thus endorses the view that we should seek to ask (and answer) a question of objective correctness for our basic logical reasoning, then clearly Peacocke’s strategy is not viable. For, simply put, it is conceivable that what epistemic subjects will find

primitively obvious will vary, both as a function of a subject’s cognitive abilities and as a function of the objective circumstances in which a subject reasons.

However, even if we don’t explicitly formulate the issue of correctness as an issue of objective correctness, the reductive strategy endorsed by Peacocke appears to be subject to immediate difficulties. The first concerns the error theory that a

proponent of this strategy may adopt. Since it is plausible that, in principle, two rational subjects may disagree on which basic inferences involving a concept C they find primitively obvious, we need a criterion for determining which one is right – for in the absence of such a criterion we won’t be able to tell which of the two (sets of) inferences are constitutive of C. We need, in other words, to be able to appeal to some kind of idealization of the psychological state that distinguishes the C-constituting inferences from the non-constitutive ones. But even given a criterion of this sort, how will we be able to tell whether a subject is indeed in the required psychological state? The problem, it seems, is that psychological states are not the sort of thing that is easily manifestable – how do we access, and share, the phenomenological impact of a concept-constituting inference? The problem is, of course, a very general one – but the specific difficulty here consists in the fact that concept-constitution itself is affected by it. Furthermore, in the context of Peacocke’s account, it is aggravated by the fact that the account relies on a Fregean conception of concepts as public entities: they are supposed to be distinct from the subjective mental representations that individual speakers link with (the expressions associated with) them [Peacocke 1992: 2- 5].

Things don’t look better if we move from consideration of a particular epistemic subject to consideration of the inferential practices adopted by a wider epistemic community to which presumably the subject belongs. For suppose that we say that a manifested criterion for assessing competing, as it were, impressions of primitive obviousness is to be found in the conformity of the inferential dispositions to which they give rise to the community’s usage of the relevant logical concept. Still: this won’t allow us to assess what has gone wrong (indeed: what can go wrong) with a deviant impression of primitive obviousness. Suppose I don’t find a set X of basic inferences involving a logical concept C primitively obvious, and find instead another set Y primitively obvious. Even if standard usages suggest that it is X that is C-

constituting, once we choose to individuate the correct C-constituting inferences on the basis of a psychological state, it seems that there is no option left but to say that that X is simply not C-constitutingfor me. Intuitively, however, we want to leave open at least the possibility that I am making a mistake – that I should, indeed, accept X, in

virtue of the fact that, within my epistemic community, X determines how C should be deployed.

Ad ii)

The problem with the second strategy is that it does not address the objection. For the objection concerns the possibility of asking a question of correctness about a way of deploying a given logical concept (a way of reasoning with it), not about a specific instance of this usage / way of reasoning. In other words, the objection can be formulated as the claim that taking actual inferential practices to be concept- constituting does not allow us to conceive of the question:

• To which standards should a concept-constituting way of deploying the

concept conform?

as an appropriate question to ask. The proponent of the second strategy will, it seems, be unable to counter the objection when it is understood in its intended generality.

The Third Strategy

What about the third strategy? Well, we need to articulate it further before we can discuss it. There are in fact various options for articulating it, which correspond to different questions that we may ask about a concept-constituting inferential practice. These are the following:

• First Option: We can ask whether the practice endangers the stability of other

accepted inferential practices, that is: whether it has the consequence of making other concept-constituting inferences inconsistent;

• Second Option: We can ask whether the practice is useful or interesting at all,

• Third Option: We can ask whether the practice complies with our views about

independent facts (for example metaphysical or epistemological facts) that we believe should constrain our reasoning.

The options above find their natural application in specific domains. My aim here is to offer some arguments in support of the intuitive plausibility of each (that is: in support of the idea that the question it raises is a plausible reformulation of the correctness question), with respect to its natural domain of application. My own strategy, which I will discuss in Sections 3 and 4, will incorporate aspects from each of these options, although in a wider framework than the one in which they are

introduced here.

The first option is viable if what we are considering is the introduction, via a logical rule, of new concept-constituting inferences in an existing logical language. It boils down to the requirement that the newly introduced inferences be conservative with respect to the inferences that we may already perform in the language. Strictly speaking, the requirement of conservativeness applies to rules of inference rather than specific inferences or sets of inferences, and thus we should reformulate the option as follows. A newly introduced concept-constituting set of inferences may be evaluated as correct or incorrect from the point of view of an existing inferential practice on the basis of this criterion: that the rules of inference that we use to codify the new practice are conservative with respect to already existing rules for concept-constituting

inferences, i.e. that they don’t allow for new derivations of sentences not containing the newly introduced connective, which were previously unobtainable in the

language44_.

44 _{When I say that a rule ‘codifies’ or ‘abstracts from’ an inferential practice, I mean: it} displays the logical form of the inferences in which such practice consists. The issue of how we should understand this aspect of the relation between a rule of inference and the inferential practice from which it abstracts is tackled in Chapter III, with specific reference to the concept