Reason Relations

“The construction gestured at so far foreshadows an argument for understanding reason relations of consequence and incompatibility as constituting a structure common to representational meaning and to practical use, to truth-making and to justificatory practices, to the objective world talked about and to the activities of talking about it, to what is represented and to the representing of it. That these same reason relations show up from the two otherwise disparate perspectives afforded by (the right kind of) semantic and pragmatic metavocabularies offers some reason to think of those relations as central to language or discourse as such” (Brandom in Hlobil and Brandom, p. 11).

Hlobil and Brandom’s Reasons for Logic presents major new results. In the technical part, Hlobil presents not just one but two very detailed new isomorphisms that unexpectedly seem to unify previously disparate areas of research in a convincing way. I will barely skim the surface of all that is afoot here. My goal is just to work through a few more pages of the motivational part, which also briefly summarizes the whole.

This notion of reason relations is already quite fascinating.

“Such an approach is unusual, and so perhaps surprising in how it discerns rational forms amphibious between these different dimensions” (p. 12).

It is the “amphibious” or hylomorphic character of what is going on here that is so amazing. This is not just something on the horizon offered to aim at as a goal, but an actual concrete accomplishment. This could make it possible to specify in detail what the substantiality of reason will amount to in particular cases. Brandom’s work has clearly taken on a life of its own, and is now being carried forward by others in new ways.

One of the many ideas afoot here is a suggestion that relations come before “things” in the order of explanation. This has been one of my favorite themes throughout the years. It even appears that this amphibious character of reason relations could enable us to say what constitutes objectivity in particular cases, and not merely gesture at it. If so this is huge, from the point of view of perennial human deficits and conflicts. It could be as big a leap for talking animals as the introduction of Platonic dialogue. Of course, we should anticipate that people will still find things to argue about.

Earlier, it was Brandom who convinced me to take Kant and Hegel seriously, and to take analytic philosophy seriously as actual philosophy and not just a technical endeavor. This greatly elevated appraisal, especially of Kant and Hegel, naturally led me to direct attention to Kant and Hegel themselves. In this context, I almost came to think of Brandom primarily as a very innovative expositor of their work. The products of this collaboration in the Research Group on Logical Expressivism that are reported here leave no doubt that there is much more to Brandom’s work than that.

“One important criterion of adequacy for both semantic and pragmatic metavocabularies as we understand them is that they offer expressive resources sufficient to provide explanations of the reason relations of arbitrary base vocabularies. They are able to say, each in their own distinctive idiom, both what it means for some sentences to stand to others in relations of implication or incompatibility and why they do…. Our preferred version of semantics offers, in effect, truth-makers for the claims that Γ#A (Γ is incompatible with A) and Γ|~A (Γ implies A) in alethic modal terms of the impossibility of fusions of truth-making states of A, and truth-making states Γ with falsifying states of A, respectively — that is, in terms of how the sentences of Γ and A represent the world to be. Our preferred version of pragmatics specifies how one must use sentences in order thereby to count as practically taking or treating them as standing in relations of implication or incompatibility. It does that in deontic normative terms of constellations of commitments to accept and reject the claimables they express being improper, inappropriate, or ‘out of bounds’ ” (ibid, emphasis in original).

“Because both of these kinds of metavocabulary appeal to conceptual resources beyond those intrinsic to the base vocabularies of which they are the metavocabularies, and do so in service not just of characterizing the reason relations of those base vocabularies but of explaining them, the sorts of semantic and pragmatic metavocabulary we consider can be denominated ‘extrinsic-explanatory’ rational metavocabularies” (pp. 12-13).

“In addition to extrinsic-explanatory rational metavocabularies, there are also intrinsic-explicative ones. This latter kind of metavocabulary for reason relations restricts itself to the conceptual resources supplied by the base vocabularies whose reason relations it characterizes, and is used to make explicit those reason relations and the conceptual contents they articulate, rather than to explain why they are as they are, or what it is for them to be what they are. The principal phenomenon we initially seek to understand in these terms is logic. The first way logical vocabulary differs from the semantic and pragmatic metavocabularies considered so far is that it is an intrinsic, rather than an extrinsic metavocabulary for codifying reason relations. The rules by which logical vocabulary is introduced to extend any arbitrary nonlogical base vocabulary appeal to nothing more than the reason relations sentences of the base vocabulary stand in to one another” (p. 13, emphasis in original).

“Gentzen’s basic innovation was to treat reason relations, paradigmatically implications, as objects, called ‘sequents’, that can be referred to and manipulated, and their metainferential relations made explicit in a mathematical metavocabulary. The sequent-calculus metavocabulary can be thought of as applying to an arbitrary nonlogical base vocabulary…. This sequent-calculus metavocabulary allows for efficient expression of the reason relations that hold in any base vocabulary, including metainferential relations. But it is essentially just a notation, requiring no substantial additional conceptual resources beyond what is provided by the base vocabulary whose nonlogical implications and incompatibilities it specifies explicitly.”

“Perhaps surprisingly, the spare sequent-calculus notation… turns out to be sufficient to formulate rules for adding logical vocabulary to any arbitrary base vocabulary, and (most importantly), computing the reason relations of the extended vocabulary from those of the base…. The idea is first to extend the lexicon of the base vocabulary, by syntactic rules that specify that the base lexicon is included in the logically extended lexicon, and that if A and B are sentences in the extended lexicon, then so are [A implies B, A and B, and A or B]…. The complete logically extended vocabulary… can then be computed from the base vocabulary. We say that a corresponding logically extended vocabulary can be elaborated from any arbitrary base vocabulary. Implications and incompatibilities (and metainferences involving them) that hold in every logical extension of a base vocabulary, no matter what base vocabulary it is elaborated from, can then be said to hold in virtue of logic alone” (pp. 13-14).

“The sequent-calculus vocabulary is accordingly a rational metavocabulary — a vocabulary for specifying the reason relations of some other vocabulary — that has the special feature that it permits the elaboration of arbitrary base vocabularies over lexicons that extend the lexicons of the base vocabularies by adding logically complex sentences formed by combining the sentences of the base vocabulary with logical operators. Rules for those operators formulated in the sequent-calculus vocabulary conservatively extend the reason relations of the base vocabulary, in the sense that the implications and incompatibilties that hold among logically atomic sentences in the logically extended vocabulary are just those that already held among them in the base vocabulary. And the connective rules formulated in the sequent-calculus vocabulary do this while appealing to no resources outside of those provided already by the reason relations of the base vocabularies” (p. 15, emphasis added).

“”That is, sequent-calculus metavocabularies are intrinsic rational metavocabularies…. And they elaborate all the reason relations of the extended vocabulary solely from the reason relations of the base vocabulary…. When the reason relations of the logically extended vocabulary are suitably elaborated from those of a base vocabulary, it becomes possible for the first time to say explicitly, in the extended vocabulary, what implications and incompatibilities hold in that base, and also in its logical extension” (ibid, emphasis in original).

“The constellation of the sequent calculus metavocabulary and the logical vocabulary it introduces stands in an intrinsic-explicative relation to the reason relations of any base vocabulary whatsoever…. The rules of the logics we propose can be shown to be expressively complete in a strong sense…. [A]lmost all extant logics either presuppose that the base vocabularies they extend satisfy strong global structural constraints — paradigmatically the monotonicity and transitivity at the core of traditional understandings of specifically logical consequence as a kind of closure operator — or retroactively impose some such global structure, thereby failing to be conservative over some substructural base vocabularies. While we believe that specifically logical consequence does have a global closure structure (and that logical consistency is monotonic), we argue that this is not in general true of nonlogical reason relations” (p. 16, emphasis in original).

Next in this series: Implication Spaces

The Role of Reasons

In a brand-new book co-authored with logician Ulf Hlobil — Reasons for Logic, Logic for Reasons: Pragmatics, Semantics, and Conceptual Roles (2025) — Robert Brandom introduces results from the Research Group on Logical Expressivism, which is inspired by a major strand of his work. Logical expressivism is a highly innovative approach that takes the primary purpose of formal logic to be not the proving of truths, but a kind of making explicit of all kinds of real-world reasoning that are carried out in natural language.

The book introduces quite a number of big ideas — among them logical expressivism, reason relations, implication spaces, conceptual roles, and important new technical results that highlight the importance of nonmonotonic logic and substructural logic. Established Brandomian themes such as normativity and its relation to modality, inferentialism, material inference, and the close connection between semantics and pragmatics also show up here in new light. Brandom has written the more philosophical chapters, and Hlobil the more technical ones.

One interesting surprise is that Brandom explicitly calls the new approach “neo-Aristotelian”. This “neo-Aristotlian metalinguistic bimodal conceptual realism” will be “hylomorphic in a recognizably Aristotelian sense. For it identifies a kind of rational form that is understood as common to thoughts and things…. [T]he relations of consequence and incompatibility that show up in different guises in a whole constellation of intimately interrelated metavocabularies… are those that in the end underwrite practices of reasoning, by determining what is a reason for and against what” (p. 9, emphasis in original).

This is well short of the more full-blooded re-visioning of an open Aristotelianism that I have been suggesting here, but within its scope it does seem genuinely Aristotelian to me — particularly the idea that there are forms common to thought, things, language, and practices of reasoning. This is a nice vindication of the “Aristotle and Brandom” theme with which I began this blog almost six years ago.

“[T]he strategy of addressing philosophy’s perennial concern with the nature of understanding or reason in general by investigating language…. has been developed in two quite different directions…. The first, dominant, better worked out tradition focused on logic, and later, also formal semantics, as perspicuous mathematical metalanguages…. The other tradition focused rather on language as a kind of social practice” (p. 1, emphasis in original).

Brandom has always been interested in both of these. At the beginning of his career he worked on logic, but for most of his maturity he has tended to favor the pragmatic side. Here at one point he ends up suggesting that they may be equally important. The book presents new results in mathematical logic that help bridge the gap.

“Where the formalist tradition is oriented by a conception of understanding and reasons as codified in artificial logical calculi and semantic metalanguages, the pragmatist tradition looks instead directly to natural languages, thought of as social practices and forms of life. In place of the exclusively monological character of reasoning as deriving, modeled on proof, characteristic of the other tradition, understanding shows up in this tradition as a social achievement, and reasoning as essentially dialogical: a matter of discursive practices of giving and asking for reasons, defending and challenging claims that amount to taking up positions in a contestable, public, normative space” (p. 2).

“The two traditions ought by rights to be understood as focusing on different aspects of language: roughly, on the meanings of linguistic expressions, and on their use. In suitably broad senses, we might understand semantics as the study of meaning, and pragmatics as the study of use or discursive practices and abilities. So understood, semantics (even a semantics inspired by and paradigmatically applicable to logic) and pragmatics show up as complementary theoretical endeavors. The goal should be to synthesize semantic and pragmatic theories…. Perhaps the combination of those thoughts recommends rather a more balanced view that eschews claims of explanatory priority in favor of understanding each aspect as in principle intelligible only in terms of its relation to the other” (pp. 2-3, emphasis in original).

“The lesson that emerges, we will argue, is a kind of discursive or linguistic rationalism. Language becomes visible as at base the medium of reasons, and reasoning as the beating heart of language. On the side of pragmatics, the fundamental speech act is that of making claims. The basic speech act of making claims, asserting, is to be understood in terms of practices of defending and challenging those claims, by making other claims that have the practical significance of giving reasons for and against them. Understanding claiming this way provides a path to understanding the claimable contents expressed by declarative sentences in terms of the role they play in relations of being a reason for or against — what we will call ‘reason relations” (p. 3, emphasis in original).

He continues, “On the side of semantics, worldly represented states show up as what determines the reason relations of consequence and incompatibility that the sentences whose truth-makers and falsifiers they are stand in to one another: their roles in reason relations. By understanding the common topic that semantic and pragmatic metalanguages articulate aspects of, not just under the vague rubric of ‘language’, but more specifically as the implicit reason relations that distinguish discursive practices as such, we can better understand not only the relations between the meaning and the use of linguistic expressions, but also the relations between truth (the central concept of traditional semantics) and justification (the central concept of pragmatics, according to linguistic rationalism), in the form of practices of defending claims by giving reasons for them and challenging claims by giving reasons against them” (pp. 3-4, emphasis in original).

“At the core of this book, then, is the rationalist explanatory strategy of understanding the nature of language in terms of what we will call ‘reason relations’. As addressed here, that is a genus with two principal species: implication and incompatibility. They correspond to being a reason for and being a reason against” (p.4).

“A closely related term of art is ‘vocabulary’. We use it in a technical sense, to mean a lexicon or set of declarative sentences, together with an implication relation and an incompatibility relation defined on those sentences. To begin with, we can think of an implication relation as holding between a set of sentences that are its premises and a single sentence that is a conclusion that follows from, is a consequence of, or is implied by those premises. An incompatibility relation holds between a set of premises and a further sentence that those premises exclude, or rule out, or are incompatible with” (p. 5).

He continues, “By calling them (declarative) ‘sentences’ we just mean that they are what in the first instance stand to one another in reason relations of implication and incompatibility…. In virtue of standing to one another in reason relations of implication and incompatibility, what thereby count as declarative sentences express conceptual contents. Those contents can be thought of as the functional roles the sentences play in constellations of implications and incompatibilities” (ibid).

“According to this order of explanation, the key question is: what do we mean by talk of reason relations of implication and incompatibility? In virtue of what does something deserve to count as a consequence or incompatibility relation?” (ibid).

“The idea is to identify reason relations in terms of the various vocabularies that can be used to specify them. Because these are vocabularies for talking about (the reason relations of) other vocabularies, they are metavocabularies. Because it is in particular the reason relations of base vocabularies that they address, we can call them rational metavocabularies” (pp. 5-6, emphasis in original).

“Semantic metavocabularies explain reason relations of implication and incompatibility by specifying what the sentences that stand in those relations mean, in the sense of how the world must be for what they say to be true. The sentences stand to one another in relations of implication and incompatibility because the objective states of affairs that are their semantic truth conditions stand to one another in modally robust relations of necessitation and noncompossibility” (p. 6).

“Pragmatic vocabularies explain what is expressed by reason relations of base vocabularies by saying what features of the discursive practice of using those sentences it is, in virtue of which practitioners count as practically taking or treating the sentences as standing to one another in relations of implication and incompatibility. Pragmatic metavocabularies make it possible to say what it is that language users do in virtue of which they are properly to be understood as practically taking or treating some sentences as implying others in the sense of taking assertion or acceptance of the premises as providing reasons for asserting or accepting the conclusions, and practically taking or treating some sentences as incompatible with others in the sense of taking assertion or acceptance of the premises as providing reasons against asserting or accepting the conclusions. Reason relations show up from the expressive perspective provided by pragmatic metavocabularies as normative standards for assessment of the correctness of rational defenses of and challenges to claims, made by offering other claims as reasons for or reasons against those claims” (p. 6).

“As we will see later in much more detail, to do their job properly, semantic metavocabularies must use alethic modal vocabulary to make claims about what states and combinations of states of the world the base vocabulary talks about are and are not possible. To do their job properly, pragmatic metavocabularies must use deontic normative vocabulary to make claims about what acts, practical attitudes, and combinations of them are and are not appropriate, and what other acts and attitudes would and would not entitle an interlocutor to them. What can be said in alethic modal terms is substantially and importantly different from what can be said in deontic normative terms. The one concerns features of the objective world, the other features of the practice of discursive subjects. These are the two poles of the intentional nexus that links knowers and the known, minds and the world they understand and act in, representings and what is represented. We want to understand both kinds of thing, and the important relations between them” (p. 7).

“Alethic” is from the Greek aletheia, for truth. The parallelism or isomorphism between the “alethic modal” notion of measuring the subjunctive robustness of assertions, and a “deontic normative” Kantian articulation of the compelling or necessary character of ethical conclusions, which Brandom has long stressed, is very substantially elaborated in the new book.

“In the terms used above to introduce the idea of reason relations we propose to understand the alethic modal semantic metavocabulary and the deontic normative pragmatic metavocabulary as offering different (meta)conceptual perspectives on a common object: the incompatibility of what is expressed by the declarative sentence p and what is expressed by the declarative sentence q. Corresponding claims apply to reason relations of consequence or implication” (pp. 7-8, emphasis in original).

Next in this series: An Isomorphism

What We Mean by Meaning

Returning to Brandom’s Spinoza lectures, he has been clarifying his relation to the tradition of American pragmatist philosophy, which is largely mediated by the work of his former teacher and colleague Richard Rorty.

“At the core of the capacious ‘big tent’ tradition Rorty retrospectively rationally reconstructs under the rubric of ‘pragmatism’ is this broadly naturalistic, anthropological-ecological conception of language as an evolving population of discursive practices that is a, indeed the, distinctive feature of the natural history of creatures like us” (Pragmatism and Idealism, p. 41).

Aristotle defines humans as animals that have logos, or meaningful discourse. Hegel says that “language is the Dasein [“existence”, literally “being there”] of spirit”. The pragmatists Pierce and Dewey were interested in Hegel, and notably took a down-to-earth attitude toward his work. Brandom picks up this somewhat loose link to Hegel, and strengthens and sharpens it.

“This is what motivates and justifies [Rorty’s] use of this term [pragmatism] to characterize not only philosophers such as Pierce and Dewey, who embraced it themselves, but others such as Wittgenstein and Heidegger, and Sellars, Quine, and Davidson, who (sometimes explicitly and emphatically) did not. Rorty sees a stark contrast between this way of thinking about language and the analytic representationalist tradition that runs from Frege, Russell, and the Wittgenstein of the Tractatus through Carnap and Tarski to his colleague David Lewis. This tradition models language on formal monological logistical calculi, justification on proof of theorems from axioms, and truth conditions on model-theoretic semantics for such artificial languages. What, Rorty asks, does any of that have to do with what users of natural languages do?” (ibid).

Brandom himself speaks of “pragmatism” in this same very broad and yet distinctly philosophical way. Here we get a glimpse of how he arrived at that.

“In taking this line, Rorty rightly understands himself as appealing to the Pierce-Dewey tradition of American pragmatism to amplify and radicalize Quine’s and Sellars’ criticisms of Carnap, and following up on Wittgenstein’s advice for philosophers to look not to the [formal, logical, representational] meaning of expressions, but to their use‘” (ibid).

Brandom more commonly cites Wittgenstein’s other formulation, that “meaning is use”. He clearly does not mean that there is no meaning. He means that meaning as use comes before meaning as representation. This focus on order of explanation as an alternative to reducing one thing to another, or denying one in favor of the other, is one of Brandom’s great contributions.

“Rorty sometimes seems to draw the lesson that we should do pragmatics instead of semantics (which he identifies with appeals to the notions of [logical] truth and representation), study use rather than meaning. When talking this way. he is following the later Wittgenstein (who recoils from his semantics-only Tractarian view to a pragmatics-only approach), James, and Dewey, but not Pierce, Sellars, Quine, and Davidson. They should be understood as pursuing pragmatics-first, rather than semantics-first explanatory strategies, but not as trading the traditional neglect of pragmatics by the representationalist semantic tradition for a corresponding dismissal of semantics holus bolus. I think that another genuine strand in Rorty’s thought belongs in this tradition…. [H]ere we see both a subtle interplay and perhaps a residual tension between pragmatist naturalism and an insistence on a Kantian disjunction between norms and causes” (pp. 41-42).

“Rorty inscribes within his Piercean, broadly naturalistic account, a distinction between the social-normative and the nonsocial, so non-normative, merely natural world of vocabulary-less things. The norms that articulate vocabulary use are to be understood functionally, in terms of roles in social practices that include the adoption of normative attitudes. Practitioners adopt such attitudes by taking or treating each other in practice as committed or entitled, responsible or authoritative” (p. 42).

Vocabularies are a characteristic theme of Rorty’s. I take this to resemble my own attitude in examining usages of words — not looking for “the” meaning (as if there could be such a thing), but rather thoughtfully exploring what uses are better or worse, and why.

In contrast to reductionist views, naturalism should be understood in terms broad enough to encompass beings like us who have their being in language and normativity, and thus live mainly in “second nature”.

“In the sort of pragmatics-first order of explanation he recommends, we think of what one is doing in claiming, say, that the frog is on the log, as undertaking a commitment. Doing that is taking up a stance in a normative space, acquiring a distinctive kind of social status. Rorty understands such statuses ultimately in terms of interpersonal practices of justification. In adopting normative stances we make ourselves answerable to each other for doing so. We are liable to be challenged, and obliged to defend the normative statuses we claim. One commitment is treated by community members as providing a reason for another, as providing a justification for it” (pp. 42-43).

Every assertion we make has some kind of ethical consequences.

“The meaning expressed by using some bit of vocabulary is to be understood in terms of the role it plays in these practices of giving and practically assessing reasons: what its application provides reasons for and against, and what provides reasons for and against its application. All there is to confer meaning on our noises is the role they play in our taking up, challenging, and defending the stances taken up by applying them…. Understanding meaning or semantic content in terms of inferential roles read off of justificatory practices is a way of implementing the pragmatics-first order of explanation without giving up on semantics” (p. 43).

Ethics and hermeneutics come before epistemology. This is not to say that a theory of knowledge is impossible, but only that it should not be foundationalist. We never begin a philosophical account of things with certainty, but rather with questions and practices of questioning. The highest kind of certainty we can have is still only a “moral” certainty, not an absolute one.

“Rorty thinks such a pragmatist explanatory strategy can underwrite unobjectionable kinds of truth-talk. We just have to restrict ourselves to properties of truth that can be cashed out in pragmatic terms of what we are doing in taking or treating something as true” (ibid).

I don’t really see this as a restriction. There are ultimately ethical truths of reason and reasoning and emotional reasonableness that can be brought to light by Socratic dialogue, and there is poetic truth. Spiritual truth I take to be one or the other of these, or both. Neither of these is an authoritarian representational Truth with a capital T that I personally claim to know, but never mind how.

“Once the meanings are fixed, it is of course nonsense to think the community can in general make true whatever sentences it likes simply by taking or treating them as true. But our words do not mean what they mean apart from which sentences involving them we actually take to be true” (p. 44).