Queries and Assertions in Minimally Discursive Practices Jared A. Millson 1 Abstract. Robert Brandom's normative-pragmatic theory is intended to represent the minimal set of practical abilities whose exhibition qualifies creatures as speaking a language. His model of a minimally discursive practice (MDP) is one in which participants, devoid of logical vocabulary, are only capable of making assertions and drawing inferences. This paper argues that Brandom's purely assertional practices are not MDPs and that speech acts of asking questions (queries) must be included in any practice that counts as an MDP. The upshot of the argument is support for the claim that the normative pragmatic analysis of assertions requires a corresponding analysis of queries and vice versa. 1 INTRODUCTION Here are two questions that ought to be of interest to anyone concerned with theorizing about dialog, communication, or language: 1. What is the minimal set of practical abilities whose exhibition qualifies creatures as speaking a language? 2. What theoretical vocabulary is appropriate for specifying the practical abilities necessary and sufficient for linguistic communication? Both questions are central topics in Robert Brandom's Making it Explicit [5]. He is perhaps most well-known for his innovative answer to the second. Brandom eschews the traditional Gricean approach to pragmatics that understands language-use in terms of the mental states speakers express and aim to bring about in others when they utter linguistic expressions. Instead, he thinks of linguistic communication as a social practice in which participants treat one another's performances as having certain normative statuses, namely, commitment and entitlement. Brandom thus opts for a normative vocabulary, rather than intentional vocabulary, in order to specify what agents are doing when they speak with one another. But Brandom's answer to the first question lies at the heart of the book's title concept: making it explicit. He claims to articulate the structure of a normative social practice whose practical repertoire, though primitive, is sufficient for agents to develop the further abilities necessary for introducing the logical vocabulary that permits them to say what they are doing in that practice, i.e. to make it explicit. For Brandom, this minimally discursive practice (MDP) is one in which agents treat one another as making assertions and drawing inferences.2 He calls it the "game of giving and asking for reasons". 1 Agnes Scott College, USA, email: jmillson@agnesscott.edu 2 Brandom does not use this expression in Making It Explicit, but he does use it to characterize the project pursued in that work in [12, 223]. [6] uses the term autonomous discursive practice (ADP) to refer to "a language-game one could play though one played no other" [6, 3]. He claims that "every One reason why Brandom's answer to the first question has received less attention than his answer to the second is that it is in keeping with a traditional view in the philosophy of language. According to this view, the meanings, mental states, and speech acts associated with declarative sentences are to be given theoretical priority over those associated with other forms of sentences (e.g. interrogatives, imperatives, etc.), which are thereby taken to be derivative, even unnecessary. Nuel Belnap [2] derides adherents of this traditional approach for committing the 'declarative fallacy.' He urges us to reject it and implores us to "recognize that from the beginning there are not only declarative sentences, but, at least, both interrogatives and imperatives." Studying declaratives, their associated meanings (propositions) and speech acts (assertions), is not enough to yield an adequate theoretical account of language and linguistic communication. Brandom's picture of MDPs is squarely in the declarativist tradition. This, I believe, is a problem. It is a problem not just for the prospects of implementing his normative pragmatic theory as a model of actual discourse and agent communication, but also for his account of MDPs. At base, his declarativist picture of "the game of giving and asking for reasons" is not up to the role that MDPs are supposed to play in his theory. The reason for this inadequacy is that purely assertional practices are not self-sufficient discursive practices. The ability to make and to take others as making assertions depends upon agents' ability to perform and recognize the performance of certain non-assertional speech acts, in particular, the asking of questions or querying. In other words, the same relation of reciprocal pragmatic dependence that Brandom insists holds between assertions and inferences also holds between assertions and queries. The normative pragmatic analysis of assertions requires a corresponding analysis of queries and vice versa. In this paper I will offer some support for this claim. First, I shall argue that Brandom's "game of giving and asking for reasons" is not an MDP. Second, I will show how a normative practice that includes only assertions and queries does qualify as an MDP. Finally, I will offer a formal treatment of the norms governing this practice in hopes of showing that the practical abilities needed to assert and to query are mutually dependent. 2 THE GAME OF GIVING AND ASKING FOR REASONS Deontic scorekeeping (DSK) is Brandom's model for normative social practices. According to DSK, the way participants take or treat each other's performances is represented by two sorts of normative autonomous discursive practice must include core practices of giving and asking for reasons" [6, 111]. attitudes they may adopt. The first attitude is one in which a participant undertakes a certain normative status (e.g. obligation, permission, etc.); the second is one in which she attributes such a status to others. Brandom argues that practices which confer assertional force on utterances must involve practically distinguishing between two kinds of normative status: commitment and entitlement. In order to treat a move as an assertion, a scorekeeper needs to take that move as committing its player to further moves, namely, the undertaking of commitments which follow inferentially from the first. A scorekeeper must also distinguish between those commitments to which a player is entitled and those to which she is not, since "giving reasons for a claim is producing other assertions that license or entitle one to it, that justify it," and "asking for reasons for a claim is asking for its warrant, for what entitles one to that commitment" [5]. Being liable to assessments in terms of entitlement means that players who undertake commitments are (also) committed to undertaking commitments that entitle the player to the ones in question. The liability to justify one's assertions is a "conditional taskresponsibility" [5]. It is a task-responsibility because it requires the responsible agent to do something, namely, to give of reasons for her claims. But one need not give reasons unless one's assertion is challenged. The justificatory responsibility that accompanies assertion is conditional upon such challenges. A player can demonstrate entitlement to a commitment when so challenged either by asserting another claim from which the challenged commitment can be appropriately inferred or by deferring to another who asserted the claim. When a scorekeeper attributes a commitment to a player, she also attributes entitlement to that commitment by default, unless there is some reason for thinking otherwise, in which case, she can challenge the commitment. There is thus a "default and challenge structure" to entitlement. So long as a player has not committed herself to something incompatible with a her assertion that p and has no outstanding challenges to it, that is, challenges to which she has not responded by vindicating entitlement to p, all other players can inherit entitlement to p and are therefore authorized to reassert it. 3 CHALLENGING ANOTHER FOR REASONS Although they are only briefly mentioned by Brandom, it is clear that challenges play a crucial role in the deontic scorekeeping model of MDPs. In order for commitment-undertaking performances to count as assertions, they must saddle their performer with a responsibility to vindicate entitlement, a responsibility conditional upon being challenged. If it were not possible to have one's commitments challenged, then the condition for undertaking the task of justification would never, in principle, arise, and thus it would make no sense to say that players were undertaking such a responsibility. The possibility of having one's commitments challenged is necessary for commitments to have the significance of justificatory responsibility, and hence for their undertaking to count as asserting. Challenges are, of course, themselves performances in the social practice under consideration. But what characterizes them as such? First, a challenge must provide the condition requiring the challenged asserter to undertake the task of demonstrating entitlement to the asserted claim. It must detach the asserter's conditional justificatory responsibility. Second, a challenge must have the effect of canceling or suspending the default entitlement of the targeted assertion, pending its vindication. And finally, a challenge must itself be a move susceptible to normative assessment, i.e. an act that can be performed correctly or incorrectly. This means that it must be possible to challenge challenges. Indeed, doing so would be one way an asserter could restore default entitlement to her assertion.3 This third feature of challenging requires a re-specification of the first two. If challenges are themselves acts that can be performed appropriately or inappropriately, and if (as seems obvious) an inappropriate challenge cannot void an assertion's default entitlement or require the asserter to discharge her justificatory responsibility, then it must be an appropriate challenge that possesses the first two features. Thus, it is only entitled challenges that have the effect of removing the targeted assertion's default status and enjoining the asserter to vindicate her claim. Given the central importance of challenging in Brandom's account of assertion and the distinctive features it possess, it is all the more surprising that he relegates challenges to the status of 'auxiliary' speech acts whose presence in the game of giving and asking for reasons is entirely optional. The reason for this relegation, however, is that Brandom believes "the simplest way to implement such a feature of the model of asserting is to require that the performances that have the significance of challenging entitlements to assertional commitments themselves be assertions" [5]. More specifically, he thinks that a scorekeeper can challenge a player's assertional commitment by undertaking a commitment incompatible with it. Mobilizing incompatible assertions to do the work of challenging may be the most parsimonious way of getting challenges into Brandom's toy practice, but it also upholds the declarative fallacy, since the only speech acts that agent need be able to perform are assertions. 4 JUSTIFICATORY STALEMATE I will now demonstrate that discursive practices, conceived in accordance with the scorekeeping model, cannot consist solely of (the making of) assertions. The source of the difficulty for Brandom's position is a problem that I am calling justificatory stalemate, which arises when no participant in an assertional practice is, in principle, subject to a demand for reasons. Justificatory stalemate can be characterized by the following inconsistent set of claims. 1. Challenges can only be issued by incompatible assertions. 2. Assertional incompatibility is symmetrical. 3. Challenges can be challenged. 4. Legitimate challenges rescind the default entitlement of challenged assertions. 5. Legitimate challenges provide the condition requiring the challenged asserter to undertake the task of demonstrating entitlement to the asserted claim. Claim 1 follows from a commitment to declarativism and the subsequent insistence that non-assertional practices are pragmatically dependent upon assertional ones and not vice versa. This position restricts the range of speech acts necessary and sufficient for discursive practice to those that have the pragmatic force of assertions. Thus, challenges must have assertional force. Claim 2 is straightforward: commitment to p is incompatible with commitment to q iff commitment to q is incompatible with commitment to p. Claims 3–5 were explained above. Finally, notice that since assertions offered up in the game of giving and asking for reasons are attributed (by others) with default entitlement, and since challenges just are assertions, they too will have default entitlement. 3 This list of conditions appears in [14]. The conjunction of claims 1–4 is inconsistent with 5. An entitled challenge removes the challenged assertion's default status, i.e. 4. But when this structural feature of discourse is combined with 2 and 3, it follows that the default legitimacy of any incoming challenge is always put into question by the challenged assertion itself. In other words, incompatible assertions with default entitlement are prima facie legitimate challenges of one another. But as such, each suspends the default entitlement of the other, and thus neither is a legitimate challenge of the other. Here is a brief example that illustrates the problem. Imagine a language game consisting of three agents: Jim, Susan, and Emma. The normative-pragmatic repertoire of these players consists solely of the ability to attribute and undertake assertional commitments. To add some history to the practice, we can stipulate that each of them has a pre-existing set of commitments and entitlements recorded both for themselves and for the other two. But we shall not assume that any demand for reasons has been made or fulfilled. What we want to determine is whether a scorekeeper can take or treat one player's assertion as a challenge of another's such that the latter's conditional responsibility to provide reasons is detached. Suppose that Jim asserts P. Susan looks to challenge Jim's assertion by asserting Q, which she endorses and takes to be incompatible with P. In order for Susan's claim to count as a challenge of Jim's, Emma (the remaining participant) must take Q to be incompatible with P. If, however, Emma attributes default entitlement to both P and Q, as is required by the default-challenge structure of entitlement, then, given the symmetry of incompatibility, Jim's original assertion is just as much a legitimate challenge of Susan's claim as vice versa. Thus, paradoxically, if both P and Q are default entitled, then neither is so entitled, or, alternatively, if both P and Q are (legitimate) challenges, then neither are (legitimate) challenges. Since, according to claim 1 there are no alternative speech act types to play the role of challenges, there is no way to challenge someone's claim without depriving one's own challenge of default entitlement and thereby its status as a legitimate challenge. No one in the practice is ever, in principle, subject to a legitimate demand to provide reasons; the practice is locked in justificatory stalemate. Hence, claim 5 cannot be true if claims 1–4 are true. 5 AVERTING STALEMATE There are several ways for the inferentialist to object to the problem of justificatory stalemate. The most obvious response would be to insist that one of the players must volunteer a demonstration of entitlement to his or her challenge. Successful justification of one's challenge would thereby shift the burden of proof to the challengee. If the scorekeeper can attribute inherited entitlement to one of the incompatible assertions and only default entitlement to the other, then she is authorized to treat the former as a challenge of the latter and to demand of its endorser that he demonstrate entitlement to it. The problem with this type of objection is that it is entirely ad hoc. According to the norms of the game of giving and asking for reasons, players are permitted to demonstrate entitlement; they are not obliged to do so on pain of subsequent changes to their deontic score. It is true that were one of the players in the situation to 'spontaneously' justify her claim, the effect would be to detach the other player's conditional responsibility. However, the original demonstration itself could not be treated as the fulfillment of a justificatory responsibility, since the player was not obliged to do anything. For this response to succeed, the theorist must require players to make moves that the game itself merely permits. While there are alternative objections, I think each rests on a similar ad hoc modification to the model. Rather than pursuing each possible response, I will consider ways the model might be altered once the problem of justificatory stalemate is accepted. To resolve the problem of stalemate, the inferentialist can deny any one of the claims 1–5. But claims 2–5 are intuitively plausible and reflect familiar features of ordinary discourse. On the other hand, claim 1 is a philosophically loaded assumption, one that derives its plausibility from the declarative fallacy. It is a deliberately restrictive claim about the kinds of speech acts a speaker must be capable of performing in order to treat others as making assertions. In ordinary discourse, however, we have all sorts of devices for eliciting justifications, only one of which is the sort of challenge achieved by asserting something incompatible with the claim for which we seek reasons. The inferentialist ought to reject claim 1. However, in order to do so within the constraints of parsimony placed on the scorekeeping model, she will need to identify a unique, non-assertional speech act capable of detaching an asserter's conditional responsibility to provide reasons. To avoid stalemate, this speech act must not stand in a symmetrical relation of incompatibility to the challenged assertion. 6 REASON-SEEKING QUERIES Ordinary discourse offers numerous candidates for the structural role of non-assertional challenges. Perhaps the most obvious of these are speech acts in which a speaker directly asks another for reasons. Indeed, philosophers looking to account for the norms governing assertions often appeal to the fact that questions like "How do you know that p?" are prima facie challenges to a speaker's assertion that p [10, 11, 13, 16]. The tradition of conversational analysis in empirical linguistics has also produced evidence that utterances of interrogatives are uniquely suited to the task of soliciting agents to provide accounts of their actions and claims [4]. There are thus some prima facie reasons to treat queries, in particular, reason-seeking queries (RSQs), as performing the structural role of challenging in (minimally) discursive practices. Introducing queries with the illocutionary force (though not the logical complexity) associated with interrogative utterances of the form "How do you know that p?" into the DSK model is a complicated business. First, there is the problem that questions do not stand in obviously inferential relations to one another in the way that the contents of declaratives do.4 This problem is not nearly as daunting as it first appears. The notion of 'inference' with which Brandom's model operates is quite liberal. Deferring to the authority of an interlocutor, issuing observation reports, even acting intentionally are all performances that get analyzed in terms of dispositions to adopt normative attitudes, and are, thus, the exercise of broadly inferential capacities. So long as normative statuses and attitudes can be coherently associated with queries, their content ought to be explicable within an extended inferentialist framework. Indeed, the questionanswer relation looks custom-made for representation in normativepragmatic terms. 4 Even if it can be shown, as [17] has, that a model-theoretic semantics for declaratives can represent relations of implication among interrogatives- what he calls erotetic implication, from the Greek erőtésis, meaning 'that which pertains to questions'-it remains doubtful that there are material erotetic inferences of the sort Brandom's account demands. The chief difficulty is that even the simplest questions, polar questions, can only be expressed in languages that contain negation. Thus, inferential relations among even polar questions appear to be unavailable to minimally discursive agents. Second, there is the problem of assigning normative statuses to RSQs. One way to do so would be to take the querier as imputing a particular commitment to the queried agent, namely, a commitment to defeasibly license the querier to (re)assert p herself. Such a commitment can be called apokritic-from the Greek verb apokrino, which, when used in the middle voice, means 'to give an answer' or 'to reply to a question'. An apokritic commitment obliges the addressee to answer the speaker's question. In the case considered here, answering the question is just a matter of justifying the claim that p. Third, there is the issue of accounting for the second-personal character of these acts-the pragmatic force of queries that directs it at a particular individual, 'you'. To tackle this problem, we can introduce a third deontic attitude, in addition to those of acknowledging and attributing normative statuses. This new attitude, call it addressing, makes a demand upon its addressee to recognize her new status. [9] propose this sort of analysis of second-personal addresses, according to which the demand for recognition is 'inescapable'-no matter what subsequent performances an addressee undertakes, they will either have the significance of acknowledging the demand or rejecting it; there is no way to passively ignore it. Such an attitude may not be as foreign to DSK as first appears. [14] argues that assertions are in fact second-personal addresses, since they bind "asserter and assertee in a normative nexus that, among other things, precludes the possibility of ignoring the address and allows the latter to defer to the former if challenged to do so." Treating addressing as a kind of deontic attitude on level of acknowledging and attributing allows us to make sense of this claim. In asserting that p, an agent addresses entitlement to p to others, calling upon them to reassert p on her authority. Where part of the normative significance of assertions is captured by the address of assertional entitlement, the pragmatic force of queries can be understand as involving an address of commitment, namely apokritic commitment. Addressing a commitment to another player would thus be quite different from attributing one, since in the latter case, there is no prima facie deficiency incurred by ignoring an attributed status. Furthermore, if queries require the speaker to address an apokritic commitment to another player, and if apokritic commitments associated with queries like "How do you know that p?" are demands for justification, then such queries easily satisfy the essential structural role of challenges expressed by claim 5. Fourth, there is the issue of accommodating the distinctive semantic content of interrogatives. Most semantic theories of interrogatives assign to them sets of propositions, rather than single propositions. The members of a set of propositions assigned to any particular interrogative correspond to the propositions expressed by possible answers [3, 8, 7]. Such an analysis is hard to square with the RSQs considered here, since there is no intuitive set of possible answers to questions posed by "How do you know that p?". One way to solve this problem is to treat the content of such questions as a set consisting of a single proposition: p. If the pragmatic force of RSQs also involves a suspension of the addressee's default entitlement to p, then the addressee cannot merely respond to these queries by asserting p itself. She can only discharge her apokritic commitment by demonstrating her entitlement to p. This analysis not only resolves the question of how to assign semantic content to reason-seeking queries; it also ensures that their pragmatic force satisfies another structural role given to challenges, namely, that of cancelling a challengee's default entitlement (claim 4). Finally, there is the task of explicating how RSQs might be evaluated in terms of their own propriety. If it is possible to perform a query inappropriately, then there must be some way for scorekeepers to challenge them. One way to do so would be to reject the address of apokritic commitment as unwarranted. To reject an RSQ, a player can show that she is not committed to p and therefore has no obligation to provide reasons for it. Alternatively, the queried agent can show that the querier is herself committed to p and therefore is not in a normative position to issue RSQs to others regarding p. If RSQs can be challenged in this way, then they satisfy the condition that challenges be susceptible to counter-challenges (claim 3). It is important to note, however, that while queries will serve to challenge assertions, it is assertions that will pose challenges to queries. Assuming that these suggestions for a scorekeeping account of reason-seeking queries pan out, the threat of justificatory stalemate will be averted.5 We have seen that such queries satisfy the conditions laid out by claims 3–5 and are therefore able to serve the structural role assigned to challenges. Moreover, they are distinctly nonassertional in both force and content. This means that introduction of RSQs into the scorekeeping model will force a denial of claim 1, thereby making claim 2, i.e. the symmetry of incompatibility, irrelevant. Unlike purely assertional practices in which challenges are performed by incompatible claims, entitlement to ask a reasonseeking question regarding some assertion is not undermined by the co-instantiation of that very assertion in a practice. Modeling (minimally) discursive practices as those in which players have the ability to both assert and query averts justificatory stalemate and represents a genuine game of giving and asking for reasons. 7 QUERIES IN MDPs I have argued that "the game of giving and asking for reasons" cannot be instantiated by purely assertional practices, and have suggested how a normative practice that includes performances of both querying and asserting will qualify as an MDP. But this practice only permits agents to perform a certain small class of queries, namely, RSQs. Arguably, RSQs are species of a genus of queries that seek information more broadly. Information seeking-queries (ISQs) saddle their addressees with apokritic responsibilities to update the querier's deontic score with a license to assert some claim from among a set of alternatives, i.e. to answer the question. RSQs are just those ISQs whose set of alternatives is a singleton and which deny addressees the possibility of fulfilling their apokritic responsibility simply by asserting that claim, that is, they deprive their addressees of default entitlement to the queried claim. Fulfilling the responsibility incurred by RSQs thus requires participants to demonstrate entitlement, either by asserting something from which the queried claim follows inferentially or by deferring to another's assertion of it. Since the force and content of RSQs is a specification of the force and content of ISQs, agents who can perform RSQs must possess the more general capacity to perform ISQs. In this section, I will attempt to formalize the norms governing an MDP whose repertoire consists of ISQs and assertions. The formal treatment is intended to demonstrate how the normative structures of ISQs and assertions are reciprocally dependent speech acts. In order to represent this MDP, our formalism will need to build up the normative structure of assertions and ISQs from primitives that are not themselves speech acts. Nor should these primitives consist of semantic entities such as propositions, since, following Brandom, we treat such entities as explanatorily derivative of pragmatic ones. 5 In chapters 4 and 5 of my dissertation, "How to Ask a Question in the Space of Reasons," I redeem each of these suggestions. The formal theory of MDPs can, however, appeal to normative statuses of commitment and entitlement, as well as to action-types and agents. Although they have no interest in representing MDPs, Rebecca Kukla, Mark Lance, and Greg Restall (KLR) [9] have sketched a formal theory that aims to explain the pragmatic forces of speech acts by mobilizing just these sorts of primitives. For the formal theory of MDPs, I will utilize a modified version of the KLR approach. The formal vocabulary for KLR consist of the following: • α, β, γ ∈ AGENT: a non-empty set of agents • F, G, H ∈ ACTION: a non-empty set of action types • c, e, d ∈ STATUS: a set non-empty set of normative statuses, e.g. COMMITMENT (c), ENTITLEMENT (e), and DOING (d). These primitives are related such that statuses evaluate action types with respect to agents. A basic formula of the theory has the form of the triple s〈F,α〉(abbreviated to sFα) where s is a status, F is an action type, and α is an agent. Basic formulas are normative assignments. A collection of assignments constitutes an agent's 'scorecard'. One of the great advantages of the KLR approach is that normative attributions can be represented as action types. Once we think of a creature as taking α to be committed to F, then we can think of this very taking as yet another act-type, to which it can be entitled or not. Thus, for every α ∈ AGENT, F ∈ ACTION, and s ∈ STATUS, sFα ∈ ACTION. This would be the action type of taking α's F-ing to be s. Sequent calculus versions of formal proof theory can now be applied to explain the constraints on scorecards. If X and Y are sets of attributions, then X ` Y is a structural constraint on scorecards such that a scorecard satisfies it if and only if it is not the case that the it contains every attribution in X and none in Y. General constraints on scorecards are analogous to the normal structural rules for the consequence relation, i.e., reflexivity, weakening, and cut. A special case of the constraint is the form X `. A scorecard is said to violate this constraint when it contains every assignment in X, and respects it when there is some assignment in X that it avoids. X ` says that the assignments in X are jointly incompatible. Where X = {A, B}, X ` can be written as A ⊥ B. This is the primitive notion of incompatibility that the system uses to build up incompatibility relations among specific normative statuses. The most important subsidiary incompatibility relation is that which holds among entitlement assignments. Two actions are said to be entitlement-incompatible or e-incompatible when they cannot be jointly performed with entitlement. For example, suppose that Jim and Susan are sharing a cake and that there is an underlying norm to their practice of cake-sharing such that whoever cuts the cake into pieces must wait until all the other diners have selected their pieces to select his own. Next, suppose that Jim cuts the cake into two pieces and chooses his piece before Susan chooses hers. Jim can no doubt perform both actions-i.e. cake-cutting and selecting the first slice- but he is not entitled to do both. He is only entitled to perform one of them. Thus, the actions of cake-cutting and choosing the first slice, when performed by the same agent, are e-incompatible. E-incompatibility is thus defined as the incompatibility between a set of attributions X when all of its statuses are replaced with DOING and that same set when all of its statuses are replaced with ENTITLEMENT. ⊥e X iff ⊥ X[c := d, e := d] ⋃ X[c := e, d := e] The notion of e-incompatibility is of particular importance to the formulation of the norms of asserting. In order to represent an agent as contradicting herself, scorekeepers must be able to take each other as making assertions to which they are not jointly entitled. This is just what they do when they attribute e-incompatible assertions to each other. Within this formal system, KLR identifies the following normative constraints on assertions. A1: d〈A(F, β), α〉 ` d〈dFβ, α〉 A2: e〈A(F, β), α〉 ` e〈dFβ, α〉 A3: If⊥e{d〈A(F, β), α〉, d〈A(G, γ), α〉} then ⊥e{d〈A(F, β), α〉, d〈A(G, γ), δ〉} A1 says that to assert that something is the case (e.g. β's F-ing) is, in part, to practically take something to be the case (e.g. to take β to have F-ed). Similarly, A2 states that entitlement to assert something implies entitlement to the corresponding practical attitude. The third constraint, A3, says that if an agent cannot make two assertions without contradicting herself, then when those assertions are made by two different agents, each contradicts the other. This constraint is intended to capture the sense of agent-neutrality that KLR take to characterize entitlement to assertions-the sense that when one agent is entitled to assert something, then, ideally, such entitlement is available to all discursive agents. While the conditions that KLR provide for assertion are necessary, they are by no means sufficient. Importantly, they fail to capture the justificatory responsibility a speaker incurs when making an assertion.6 Since the institution of justificatory responsibility is essential to the DSK model of assertion, the formal treatment of MDPs will need to be able to represent it. To formalize justificatory responsibility, we first need to be able to represent default entitlement, since detachment of the conditional responsibility to justify one's claims is, in part, dependent upon the loss of default entitlement. In order to capture the propriety of default entitlement, we will need to define a nonmonotonic structural constraint on scorecards using some modified notions of default logic. Let W be the set of all normative assignments belonging to members of {AGENT} and letCn(X) represent the closure of a set of assignmentsX under `. Our system has a single default theory 〈W,D〉 where D is a set of defaults composed of instances of the following form with particular action-types substituted for F and particular agents for α, β. dFα : eFα eFα Rules of this form say that if an agent has F-ed and there is no assignment incompatible with its entitlement, then the agent is entitled to F. Extensions of 〈W,D〉 are defined by fixed point construction. For any set of normative assignments, X , let Γ(X) be the least closed set that includes W and satisfies the following condition: If dFα : eFα/eFα, and dFα ∈ Γ(X), and X 6⊥ eFα, then eFα ∈ Γ(X). Conflicts between defaults will be resolved cautiously, so that when two actions are performed whose default entitlement (together with their performance) is incompatible, both are denied default entitlement. Since all defaults in 〈W,D〉 are of the normal form, we will use |∼ to represent cautious default consequence. Following [1] we take |∼ to satisfy conditions of reflexivity, cut, supraclassicality, and cautious monotonicity. 6 This lacuna is in part a consequence of KLR's emphasis on the regulative ideals of normative discursive functions and their commitment to an I-We model of discursive sociality [9]. We thus have the following default consequence relation: DE1: dFα |∼ eFα Substituting an assertion for F then yields the default entitlement practice in Brandom's MDP: A4: d〈A(F, β), α〉 |∼ e〈A(F, β), α〉 This condition states that if α asserts something, then she is entitled to that assertion, so long as no one occupies a normative position incompatible with its entitlement. It follows from A3 that an agent will not be awarded default entitlement to an assertion if someone else has performed an entitled assertion that is incompatible with it. For example, if Jim asserts that whales are cold-blooded but Susan has asserted that whales are mammals, then Jim does not receive default entitlement to his claim. However, since |∼ is interpreted cautiously, when two e-incompatible assertions have been made, neither is treated with default entitlement. Thus, if Susan's claim that whales are mammals is only attributed default entitlement, then following Jim's claim, her assertion would (also) lose its default entitlement. Such a scenario would exemplified the kind of justificatory stalemate that we have seen paralyze Brandom's pragmatic theory. In other words, were we to follow Brandom and treat assertions as challenges, the default theory above would lead to justificatory stalemate. We must, therefore, make good on the promise that queries can fill the role of challenges in an MDP. In order to do so, it will be helpful to refer to some of the following sets. • Ent(sFα) = {A : A ` eFα} • Ent |∼ (sFα) = {A : A |∼ eFα} • Inc(sFα) = {A : A ⊥ sFα} • Ince(sFα) = {A : ⊥e{X, sFα}} Notice that the most obvious formalization of justificatory responsibility is unacceptable: A4∗: d〈A(F, β), α〉 6` cHα where • dHα ∈ Ent (d〈A(F, β), α〉) This condition says that if an agent claims that β F's, then she is responsible for doing something which justifies that claim, typically by making another assertion from which it can be inferred. The problem with this formulation is that the responsibility to do something which entitles one to the assertion on the right-hand side is not a conditional responsibility, as it is intended by Brandom. Recall that in DSK for assertional practices, asserting that p entails the agent's responsibility to demonstrate entitlement if challenged. But A4* states that if an agent asserts something, then she is responsible for justifying that assertion, full stop. Thus, to accurately represent justificatory responsibility, we must define acts of challenging. Following the proposal in section 6, we shall attempt to do so by formulating the structure of RSQs. However, since RSQs are a species of ISQs, we must first formalize ISQs. Semantically speaking, polar questions, or yes-no questions, represent the most basic types of questions in the sense that they have smaller answer-sets than alternative or wh-questions. Indeed it has even been proposed by [18] that under certain constraints, the answerhood conditions for the latter may be reduced to those of sets of atomic yes-no questions. This is a prima facie reason for thinking that institution of polar queries, that is, speech acts of asking polar questions, can proceed that of alternative or wh-questions. Polar queries still require the expressibility of logical constants, namely, negation, so they cannot be included in a Brandomian MDP. Nonetheless, a pre-logical variant of polar queries is available to agents in an MDP using the basic incompatibility relation that holds between normative assignments. Since these 'proto-polar queries' can be directed at any action an agent performs and not just her assertions, they are not strictly speaking information-seeking queries. The following condition represents part of the normative structure of these 'basic proto-polar queries.' Basic Proto-Polar Queries. Q1: e〈Q(F, β), α〉, d〈Q(F, β), α〉 ` cHβ, cIβ where • dHβ ∈ Ent |∼ (d〈dFβ, α〉) and • dIα ∈ Ent |∼ (d〈dGβ, α〉) and • dGβ ∈ Inc(dFβ) This condition says that if α is entitled to query β regarding the act of F-ing, and in fact issues such a query, then β is responsible for either doing something which defeasibly entitles α to take her as having F-ed or for doing something which defeasibly entitles α to take her as having done something incompatible with having F-ed. The left-side of Q1 thus represents β's apokritic responsibility. Following the disjunctive interpretation of the left-side of the consequence relation, this condition is satisfied when β performs actions which license α to take her as having performed incompatible actions. Such a response will no doubt place β in a normatively deficient position, but it will still count as having 'answered' α's query. Specifying different types of queries-e.g. ISQs, advice-seeking queries, self-addressed queries, exam queries, etc.- can be achieved by some combination of a) modifying the sets of assignments which 'proto-negative' responses in Q1 license, b) substituting particular normative assignments for dFβ, and c) adding conditions. In formulating the conditions on proto-polar ISQs we employ all three techniques. Proto-Polar ISQs. ISQ1: e〈Qis〈A(F, β), δ〉, α〉, d〈Qis〈A(F, β), δ〉, α〉 ` cHδ, cIδ ISQ2: ⊥e{d〈Qis〈A(F, β), δ〉, α〉, d〈e〈A(F, β), α〉, α〉} ISQ3: ⊥e{d〈Qis〈A(F, β), δ〉, α〉, d〈e〈A(G, β), α〉, α〉} where • dHδ ∈ Ent |∼ (d〈A(F, β), α〉) and • dIδ ∈ Ent |∼ (d〈A(G, β), α〉) and • d〈A(G, β), α〉 ∈ Ince (d〈A(F, β), δ〉) Condition ISQ1 is interpreted as saying that if α poses an entitled query to β regarding some assertion, then β is responsible for defeasibly licensing α to make that assertion or some other assertion e-incompatible with it. In formulating this condition, we have substituted assertions for the queried assignment in Q1 and weakened the kind of incompatibility relation which must hold between the actions licensed by 'proto-positive' and 'proto-negative' responses. The motivation for both moves is the idea that the normative function of an ISQ is to obtain for the speaker a license to make an assertion. It is not sufficient for appropriate uptake of an ISQ that a querier merely be entitled to take the queried agent has having made an assertion. For other sorts of queries, e.g., exam queries, this result may be appropriate. But for ISQs, at least those present in the austere conditions of an MDP, the relevant normative function aims at a situation in which the querier obtains information that can be used in her own reasoning, even if only defeasibly.7 The additional conditions of ISQ2 and ISQ3 are also motivated by our intuitions regarding the normative structure of genuinely information-seeking queries. Together they state that one cannot pose an entitled query and take oneself (and hence anyone else) to be entitled to assert one of its answers. These conditions are intended to represent the state of ignorance that queriers must be in for answers to provide them with information. Again, such conditions would not be present in the normative structure of, e.g., exam queries, where the function is to discern what someone else takes himself to be entitled to. Among the crucial strutural features of proto-polar queries is that, following from A4, a queried agent can satisfy her apokritic responsibility simply by asserting the queried assertion or some assertion e-incompatible with it. Indeed, the formalism shows that it is precisely because a principle like A4 holds in an MDP, and agents' assertions are typically awarded entitlement, that merely making assertions serves to answer ISQs. For example, according to ISQ1–ISQ3, if Jim is entitled to ask Susan whether whales are mammals, and in fact asks her, then Susan is thereby committed either to informing Jim that whales are mammals or to informing him that something is the case whose assertion is e-incompatible with the assertion that whales are mammals, say, that whales are cold-blooded. If Susan asserts that whales are cold-blooded, then, so long as no one in the discursive community has asserted something incompatible with entitlement to this claim, she is entitled to her claim by default, and Jim now has a license to re-assert it. In such a situation, Susan fulfills her apokritic responsibility.8 We are at last in a position to formulate conditions for RSQs. Reason-Seeking Queries. Let Xα denote all assignments on α's scorecard. RSQ1: ⊥e{d〈Qrs〈A(F, β), δ〉, α〉, d〈e〈A(F, β), α〉, α〉} RSQ2: d〈A(F, β), δ〉, e〈Qrs〈A(F, β), δ〉, α〉, d〈Qrs〈A(F, β), δ〉, α〉 ` cHδ RSQ3: ⊥e{d〈Qrs〈A(F, β), δ〉, α〉, d〈A(F, β), δ〉} iff Xδ 6` dHδ where • dHδ ∈ Ent (d〈A(F, β), α〉) RSQ1 is a carry-over of the 'genuine ignorance' condition on ISQs. Just as one cannot legitimately ask an information-seeking question to which one already knows the answer, one cannot demand reasons for a claim to which one takes oneself (and everyone else) to 7 Further support for this move can be found in the fact that KLR deliberating avoid a biconditional formulation of A2 for the reason that "there are prelinguistic takings that do not constitute issuances of universal re-taking license." [9, 230] 8 The reader may wonder why the apokritic responsibility associated with ISQs can be discharged by the performance of any action that defeasibly licenses the querier to assert the queried claim. The reason is that in ordinary discourse, a query can be answered by a host of linguistic as well as non-linguistic performances. For example, I can satisfy your query regarding the whereabouts of the TV remote by lifting up the couch cushion. Such a performance fulfills my apokritic responsibility without my having to assert anything. be entitled. RSQ2 represents the detachment of conditional justificatory responsibility. It says that if an agent is issued a query regarding the grounds of some assertion she has made, then she is responsible for doing something which licenses her querier to make that very assertion. Since the set of permissible responses to an RSQ are drawn from the set of assignments that strictly (i.e. not defeasibly) entitle one to make the assertion in question, performances that only defeasibly license re-assertion will not provide appropriate uptake. Thus, an agent subject to an RSQ cannot satisfy her apokritic responsibility by simply re-asserting the challenged claim. Rather, she must demonstrate her entitlement to the claim. In this sense, the apokritic responsibility of an RSQ just is the justificatory responsibility associated with assertion. RSQ3 says that an assertion and its corresponding RSQ are eincompatible just in case the queried agent has not demonstrated entitlement to her assertion. This condition gives the sense in which RSQs have the force of suspending default entitlement to a queried assertion. In the absence of a demonstration of entitlement, the posing of an entitled RSQ defeats the default license of the targeted assertion. The formalism offered here indicates how the normativepragmatic structures of queries and of assertions are interdependent. The administration of ISQs is only possible for practices whose repertoire includes the provision of information in the form of assertions that enjoy default entitlement. Conversely, assertions require distinctly non-assertional speech acts, namely, RSQs, to institute the structure of justificatory responsibility. The latter is but the apokritic responsibility associated with RSQs as a species of ISQs. 8 CONCLUSION Brandom's pragmatic theory offers us a picture of the most basic kinds of practical abilities that creatures can exhibit and, thereby, qualify as language-users. The model he presents of MDPs, however, is unsatisfactory. Purely assertional practices do not have sufficient resources to institute justificatory responsibility. In this paper, I have sought to reject the fallacy of declarativism and to look to inquisitive practices to provide the requisite normative structure for MDPs. 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