<i>Reasons for Logic, Logic for Reasons</i>

Reasons for Logic, Logic for Reasons is as apt as a title can get. In the initial chapters, Robert Brandom gives us reasons for why one would develop a logic. These reasons are that logic studies and explicates reason relations, the foundational notion in a conception of language as a game of giving and asking for reasons. Ulf Hlobil, in the following chapters, gives us such logic(s) for reasons. In a jointly authored conclusion, Hlobil and Brandom ensure that the pieces fit together. The logic(s) for reasons indeed satisfy the reasons for logic. Hlobil adds an optional epilogue in which he presents a speculative metaphysics, derived from taking as Firsts the most general description of what is postulated by the logic(s) for reasons.Brandom’s chapters are, by themselves, a reason for the philosophical pursuit of rigorous logic as well. Writing against the background of the worked-out logics of the latter chapters visibly aids Brandom’s presentation, highlighting the use of logic to achieve clarity. One finds here the most lucid view yet of Brandomian neopragmatism. Some prior (if passing) familiarity is, however, still needed. The neopragmatist moves are made here with renewed perspicuity but not discussed in the same depth as elsewhere. Readers find a clear picture of what it is to rest a philosophy of language on reason relations but must look elsewhere for objections and responses, for the virtues and vices of this strategy compared to other approaches, or for its intellectual history. Such further discussion would, however, be misplaced in this work. The achievement here is to make the view and its upshots as clear as possible, both in its exposition and in its formalization.These initial chapters elaborate familiar Brandomia that are newly suffused with bilateralia, insights derived and elaborated from the expanding literature on bilateral logic. Reasons can occur as reasons for and as reasons against, so there are reason relations of entailment and of incompatibility. Bilateral logic promises an avenue to spell out such bifurcations and the latter chapters make good on the prospect. Overall, then, this is a happy marriage. It is only in the margins that the Brandomia occasionally rub against the bilateralia. For one, Brandom remains committed to the claim that “the fundamental speech act is that of … asserting” (3), but bilateralists require distinct “fundamental acts” of both “affirmation and denial” (30). This has downstream consequences.The book’s running theme is that logical vocabulary is explicative of more fundamental reason relations. To begin, suppose A is a reason for B. This can be expressed in a formal metavocabulary as A⊢B. However, it may not be possible to express in the object-language that A is a reason for B. Only after expanding the language with a symbol ‘>’ for the conditional, one can express that A⊢B with the object-language sentence ‘A>B’. Thus, having the conditional allows one to accept or reject that A is a reason for B, whereas without it one could only use A as a reason for B. Conversely, A may also be a reason against B, which may be expressed in the metavocabulary as A#B. Brandom’s primacy of asserting is thus about the relata of reason relations in the object-language: potential assertions stand in relations of entailment or incompatibility. Bilateralism provides a bifurcated metalinguistic description of the reason relations themselves.More precisely, Hlobil and Brandom define A⊢B to mean that commitment to accepting A precludes entitlement to reject B, and A#B to mean that commitment to accepting A precludes entitlement to accept B. It is clearest here how new bilateralist talk of acceptance and rejection refines old Brandomian talk of commitment and entitlement. But, oddly, the left-hand side of either definition mentions only acceptances while on the right-hand sides there is once acceptance and once rejection. It seems, however, that commitments to rejections can preclude entitlements just as much as commitments to acceptances. One’s commitment to reject ‘Socrates is speaking’ may preclude entitlement to also reject ‘Socrates is mute’ and preclude entitlement to accept ‘Socrates is orating’. Such relations may well be part of the game of giving and asking for reasons—now understood as involving commitments and entitlements to acceptances and rejections, no longer commitments and entitlements tout court—but cannot be expressed in the proposed metalanguage, at least not literally. That rejecting A precludes also rejecting B is equivalent to ‘⊢A,B’ and that rejecting A precludes accepting B is equivalent to ‘B⊢A’. But these expressions, strictly speaking, describe other rules of the game.Reason relations obtain between sentences but the relations themselves are described in terms of commitments and entitlements to acceptances and rejections. The role of commitments to rejections is absent. So the bilateralism of acceptance and rejection does not seem to map perfectly onto the bifurcation of entailment and incompatibility. Here is another reason to think so. As the conditional makes explicit the turnstile, negation is supposed to make explicit the pound sign. But negation alone is insufficient to express A#B in the object-language, as negation is unary and incompatibility is binary. One requires additional expressive power, conjunction, to say ‘not (A&B)’. So although negation can make explicit (unary) rejection, it cannot by itself make explicit (binary) incompatibility.My even being able to raise such fine-grained complaints is a testament to the clarity and rigor of the presentation here. That they even are complaints is a testament to the ambition of the project. The goal is to be able to make explicit any and all possible reason relations. This ambition is fulfilled to a remarkable degree. The matter of rejective commitments can be tentatively set to the side, as equivalent reason relations are covered.In chapter 3, Hlobil introduces the Non-Monotonic, Multi-Succedent (NMMS) logic. It has the property that for any set of atoms that stand in any configuration of entailment/incompatibility relations (given minimal constraints), each such relation can be expressed by an NMMS sentence. The logic is starkly substructural, so as to avoid making any undue demands on the foundational reason relations. Using a suite of charming examples, it is demonstrated that both entailment and incompatibility could be nonmonotonic and nontransitive. Then, since logical vocabulary is what allows one to explicate a reason relation, logical validity can be construed as whatever is valid regardless of the underlying reason relations. Hlobil demonstrates that these logical validities include the classical validities (consequence is, of course, still substructural). The examples and the results are so compelling that one could easily miss how sophisticated NMMS really is.For one, some operational rules are nonstandard. The usual right-rule for conjunction is to conclude Γ⊢A&B from Γ⊢A and Γ⊢B, but Hlobil adds a third premise, Γ⊢A,B. As before, Γ⊢Δ means that accepting all members of Γ precludes rejecting all members of Δ. Thus, a situation in which the two standard premises hold, but not the added third one, is one in which accepting Γ precludes rejecting A and rejecting B but does not preclude rejecting both. It is initially puzzling how this could be and, so, what work the third premise does. Earlier, Hlobil explains that Γ⊢A is merely a necessary condition for it being proper to accept A based on Γ. Thus, one can extrapolate, it can be that Γ⊢A without it being proper to accept A based on Γ. Then, the desired situation is one in which necessary conditions for the proper acceptance of A and B obtain (Γ⊢A and Γ⊢B), but it is still improper to do so since a necessary condition for accepting either does not obtain (not Γ⊢A,B).Similarly, the left-rule for disjunction lets one infer Γ,A∨B⊢Δ from Γ,A⊢Δ and Γ,B⊢Δ and Γ,A,B⊢Δ. The first two say that, given Γ, accepting A precludes rejecting Δ and accepting B precludes rejecting Δ. One may be inclined to shorten this to say that accepting A or B precludes rejecting Δ, so the third premise may seem superfluous. But, again, two necessary conditions for accepting Δ may obtain (namely, that accepting A precludes rejecting Δ and that accepting B precludes rejecting Δ), but a third necessary condition fails (namely, that accepting both A and B precludes rejecting Δ). For instance, Γ might have consequences not blocked by A and not blocked by B, that are yet blocked by A and B together. Thus, Hlobil logic has a three-legged disjunctive syllogism.These may be counterintuitive readings of the bilateral language. Readers are regularly reminded of the technical definitions, but some examples for the new rules would have helped. It seems that the Nixon Diamond will do for conjunction. That Quakers are pacifists is a necessary condition for properly accepting “Nixon is a dove” based on his religious affiliation; and that Republicans are interventionists is a necessary condition for properly accepting “Nixon is a hawk” based on his party affiliation. Yet it would not be proper to accept either conclusion, since either one is a reason against the other and, so, a necessary condition for accepting either fails. Hlobil’s third premise is therefore not met here and, thus, works to block the bad conclusion that Nixon is both a hawk and a dove. The initial puzzlement is resolved by reading the normative terms themselves as nonmonotonic: it could be precluded to reject A but still proper to reject A and also reject something else.Apprehending this reading is rewarded with a better understanding of how Hlobil and Brandom conceive of reason relations. Based on this understanding, however, some pragmatists may now say that the reason relations are once-removed from language use. There could be reason relations that never show up in the game of giving and asking for reasons since these relations express merely necessary conditions for something whose sufficient conditions are never (and perhaps cannot ever be) fulfilled. Then again, one may also take this to mean that the reason relations are the underlying subject matter of semantics beyond surface use, roughly akin to how representationalists study truth conditions that may never be met. Hlobil and Brandom go some way navigating this dialectic in the remaining chapters.The bilateral normative-pragmatic metavocabulary is merely used for the first formulation of NMMS. Chapter 4 explores the semantic-representational metavocabulary, in which entailment and incompatibility are alethic relations of inclusion and impossibility. This leads to a development of a truth-maker semantics for reason relations—and a natural definition of truth-maker consequence that is isomorphic to NMMS. Hlobil and Brandom note that both the normative-pragmatic and the semantic-representational viewpoints involve conceptual resources that go beyond the mere idea of reason relations. This makes them extrinsic metavocabularies.Thus, although both metavocabularies are about entailment and incompatibility, they do not share a notion of content. Chapter 5, then, presents a third route to NMMS, implication-space models, whose metavocabulary only involves conceptual resources derived from the reason relations themselves (making it intrinsic). This yields a definition of contents as inferential roles that requires nothing more than that the bearers of such contents stand in reason relations. This is a remarkable achievement and a significant contribution to the study of (propositional) contents. To compare: one might think of content as what is truth-apt. But to spell this out, one typically requires a host of additional notions (such as properties or truth-makers). Hlobil and Brandom present a notion of content free from such additions.The formal work is, therefore, deep and significant. Hlobil and Brandom make a conciliatory move in the debate between inferentialists and representationalists. Both approaches, they maintain, are just two ways of talking about one subject matter. Representationalists study reason relations in alethic terms; inferentialists study them in normative terms. This is a striking intervention. Both inferentialists and representationalists can speak of the same contents by using the intrinsic metavocabulary. Previously, given some suitable completeness result, they could at most agree on equivalent consequence relations among very different contents. Hlobil and Brandom thus open an avenue for conciliation also on the metaphysics of meaning.Naturally, this can only go so far. Not all representationalists (nor all inferentialists, for that matter) will agree that their object of study is reason relations. In the end, the pragmatics first order of explanation (the primacy of giving and asking for reasons) remains nonnegotiable to Hlobil and Brandom. One may also wonder whether the conciliation survives conflict. Given two contents, an inferentialist might claim that they are (normatively) incompatible while a representationalist denies that they are (alethically) impossible. A Moore paradox might lead to such a situation, as it is normatively precluded but alethically possible. To resolve disagreement about a common subject matter of reason relations, perhaps either normative or alethic relations must take priority. The authors seem to disagree here. Hlobil’s epilogue contains a derivation of “the world” as setting an alethic standard of correctness. Brandom dissents in an endnote.Besides these grander implications, neopragmatists will also benefit from (finally!) possessing a rigorous notion of content, as some problems related to the former lack of such a notion may now be answerable. For instance, neopragmatists are pressed to say not just what it is to believe or assert some content (or otherwise use it in the game of giving and asking for reasons) but also what it is to hope, fear, or regret that same content. They now have a fighting chance.Reasons for Logic, Logic for Reasons is thus a key achievement in neopragmatism, presenting a long-desired formal treatment of its version of the doctrine. Its formal innovations, especially the notion of content and the conciliatory project it enables, are apt to reshape the debate in semantics. This work improves our understanding not just of meaning but of the study of meaning itself.