All the Way Down

Once of the things I’ve most appreciated about Brandom has been his unwillingness to reduce normativity and value judgments to non-normative factors. Repeatedly in Making It Explicit, he speaks of norms “all the way down”. There is even a subheading for “all the way down” in the index entry for “norms” (p. 732). But in conjunction with this, he repeatedly suggests that the relation between pragmatics and semantics, while symmetrical in many respects, also includes an asymmetry, according to which it is more appropriate to say that normative pragmatics grounds representational semantics than vice versa. This is in distinction both to common views that privilege representation over inference and semantics over pragmatics, and to the purely symmetrical view of semantics and pragmatics that he seems to propound in Reasons for Logic, Logic for Reasons.

The symmetrical view can be seen in the favorable light of other symmetries that Hegel argues for in his campaign against “one-sidedness”. But it also implies that there is no sense in which normative pragmatics ought to be seen as coming before representational semantics.

Brandom’s 1976 dissertation, which is partly framed as the elaboration of a new form of pragmatism, makes links between the pragmatism it advocates, and a priority of pragmatics over semantics in philosophy of language. But as mentioned above, this year’s Reasons for Logic, Logic for Reasons, while applying inferentialist explanation to semantics in new ways, and while remaining as much as ever committed to an inferentialist order of explanation in general, nonetheless seems to back off from claiming any priority for pragmatics over semantics.

My worry is that this new symmetry and parity between pragmatics and semantics could end up weakening the commitment to “normativity all the way down”. The new thesis of full symmetry builds on his previous analogy between normativity and modality or subjunctive robustness, which I take to be sound. It may be that normativity all the way down does not really require the relative priority of pragmatics over semantics that Brandom claims in the dissertation and Making It Explicit, but I think more on this needs to be said.

What Meaning Is

Brandom has characterized the focus of his interests as the theory of meaning. Recent additions to his website include a fascinating 1980 typescript “Assertion and Conceptual Roles”. This early piece has a programmatic character. It goes even further than the 1976 dissertation in anticipating the leading ideas of his major works. (I will omit the also interesting mathematical-logical formalization that he experiments with here, but steers away from in Making It Explicit and A Spirit of Trust.)

While Brandom is resolutely modern in his identifications, this sort of investigation was pioneered by Aristotle. Meaning and truth are approached in terms of a kind of normative “saying” that is up to us. But the paradigmatic kind of saying is what Aristotle calls “saying something about something”, so it is not entirely up to us. Finally, the paradigmatic use of language is dialogical, imbued with a Socratic ethic of dialogue and free-spirited inquiry. And what we most fundamentally are is dialogical talking animals.

As Brandom puts it in the first sentence, “The paradigmatic linguistic activity is saying that-p, in the sense of asserting, claiming, or stating that-p for some declarative sentence p” (p. 1).

Today “declarative” is also an important if ill-defined concept in the theory of programming languages, where its use has a close relation to the logical use that is given ethical significance here. In that context, it is often glossed as focusing on the what not the how (or the end and not the means), although that is a simplification.

The deep issue underneath both these disparate cases is something like the meaning of meaning. In what follows, I think Brandom makes some real progress in clarifying what is at stake. It has both ethical and formal dimensions.

“Frege shows in the Begriffschrift that the ways in which sentences can occur as significant constituents of other sentences require us to distinguish the content of such an assertion (what is asserted) and the force of the assertion (the asserting of that content). For when a sentence appears as the antecedent of a conditional, it must have something, let us call it the ‘content’, in common with its occurrence as a free-standing assertion, or there would be no justification for detaching the consequent of the conditional when one is prepared to assert its antecedent. On the other hand, the asserting of the conditional does not include the asserting of the antecedent, since the asserter of the conditional might well take the former to be true and the latter to be false. It is a criterion of adequacy for any account of either of these features of declarative discourse that it be compatible with some correct account of the other” (ibid).

I had not realized that the Fregean distinction of Sinn (sense or force) and Bedeutung (reference) arose in this context of reference relations between parts of compound sentences. It seems likely that this point attributed to Frege was a source for Michael Dummet’s work on compound sentences in which one part refers to another, which Brandom had made significant use of a few years earlier, in the dissertation. Dummet was a leading Frege scholar.

It strikes me also that in a formal context, this inter-reference between components of compound sentences could serve as an inductively definable and thus paradox-free version of “self” reference. In a more discursive, less formal context, it recalls Kantian-Hegelian “reflection” and other interesting weakenings of strict identity like Hegel’s “speculative” identity or Ricoeur’s “narrative” identity. Instead of a formally strict and thus empty global self-reference, it is a matter of specifiable internal cross-reference.

Further below, Brandom will explicitly connect this with the theme of anaphora or internal back-reference that he later develops at length in Making It Explicit as a way in which identities are constituted out of difference. In the current text he will also relate it to the “prosentential” theory of truth. Prosentences like “that is true” are the sentential analogue of pronouns — they refer to sentences that express definite propositions in the same way that pronouns refer to nouns. Brandom is saying that concrete meaning involves both Fregean sense and Fregean reference.

“Exclusive attention to the practice of asserting precludes understanding the conceptual significance which such linguistic performances express and enable, while the complementary exclusion must cut off semantic theory from its only empirical subject matter, talking as something people do” (ibid).

Standard bottom-up compositional approaches to semantics focus exclusively on the “content”, and not on the related doing.

“[I]t might be tempting to think that such a theory offers special resources for a theory of asserting as representing, classifying, or identifying. It is important to realize that the same considerations which disclose the distinction of force and content expose such advantages as spurious” (ibid).

“There is no reason to suppose that the semantic representability of all sentences in terms of, say, set-membership statements or identity statements, reflects or is reflected in the explanatory priority of various kinds of linguistic performances” (p. 2).

“It then turns out that giving a rich enough description of the social practices involved in assertion allows us to exhibit semantic contents as complex formal features of performances and compound dispositions to perform according to those practices. In other words, I want to show that it is possible to turn exactly on its head the standard order of explanation canvassed above” (p. 3).

“To specify a social practice is to specify the response which is the constitutive recognition of the appropriateness of performances with respect to that practice…. But in the case of discursive practices, the constitutive responses will in general themselves be performances which are appropriate (in virtue of the responses the community is disposed to make to them) according to some other social practice. The appropriateness of any particular performance will then depend on the appropriateness of a whole set of other performances with similar dependences. Each social practice will definitionally depend upon a set of others” (p. 4).

This notion of practice is thus inherently normative or value-oriented. Brandom compares his holistic view of practices with Quine’s holistic view of the “web of belief”.

“Definitional chains specifying the extension of one practice in terms of its intension, and that intension in terms of another extension, and so on, may loop back on one another. We will say that any system of social practices which does so … is a holistic system…. Such a system of practices cannot be attributed to a community piecemeal, or in an hierarchic fashion, but only all at once.”

The key point about such a holistic system is that there are mutual dependencies between parts or participants.

“It follows that in systems containing essentially holistic practices, the norms of conduct which are codified in such practices are not reducible to facts about objective performances. The appropriateness or inappropriateness of any particular performance with respect to such a practice cannot ultimately be expressed in terms of communal dispositions to respond with objectively characterizable sanctions and rewards…. The norms themselves are entirely constituted by the practices of socially recognizing performances as according or not according with them” (p. 5).

“Facts about objective performances” have a monological character. In technical contexts this can be of great value. But ethical and general life contexts have an inherently dialogical or mutual character.

“A community ought to be thought of as socially synthesized by mutual recognition of its members, since a plausible sufficient condition of A‘s being a member of some community is that the other members of that community take him to be such…. This simple Hegelian model of the synthesis of social entities by mutual recognition of individuals has the advantage that it preserves the basic distinction between the individual’s contribution to his membership in a group and the contribution of the other members” (p. 6, emphasis added).

Here we have the first appearance of the great theme of mutual recognition in Brandom’s work. Brandom has dug deeply into this particular aspect of Hegel, making very substantial contributions of his own. In ethics, mutual recognition has roots in Aristotelian philia (friendship or love) and the so-called golden rule (do and do not do to others as you would have them do and not do to you). Brandom sees that Hegel treats mutual recognition not only as an ethical ideal but also as a fundamental explanatory principle.

“The crucial point is that the reflexive recognition (as social self-recognition) be an achievement requiring the symmetry of being recognized in a particular respect by those whom I recognize in that respect, and presupposing that my recognitions will be transitive…. A community is then any set P which is closed under transitive recognition…. [N]o one member is omniscient or infallible about such membership…, nor is it required that everyone recognize everyone else in the community” (p. 7).

The symmetry of recognizing and being recognized leads to the idea that authority and responsibility ought to be symmetrically balanced. This has tremendous implications.

“Asserting that-p is, among other things, to explicitly authorize certain inferences…. Saying this much does not yet say what the constitutive recognition of this authorizing consists in…. Our account of the authorizing of inferences will draw upon the second major feature of the social role of assertion” (ibid).

The idea of understanding acts of assertion principally in terms of an inferential constitution of meaning is transformative. Others have suggested or implied something like this, but Brandom expresses it with more clarity and thoroughness than anyone.

Reasoning is not a merely technical activity. The constitution of meaning has fundamental ethical significance.

“This second feature is noted by Searle when he says that an assertion (among other things) ‘counts as an undertaking to the effect that p represents an actual state of affairs’. Leaving aside the representationalist expansion of the content ascribed, we can see in the use of the term ‘undertaking’ the recognition of a dimension of responsibility in assertion, coordinate with the previously indicated dimension of authority. In asserting that-p one is committing oneself in some sense to the claim that-p. What sort of responsibility is involved? The leading idea of the present account is that it is justificatory responsibility which one undertakes by an assertion. Justification and assertion will be exhibited as essentially holistic social practices belonging to the same system of practices, internally related to one another. So the recognitive response-type which is the intension of the social practice of assertion must include recognition of the assertor as responsible for justifying his assertoric performance under suitable circumstances…. Authority in this sense consists in the social recognition of a practice as authorizing others” (pp. 9-10).

“What is essential is that the relation between the intensions and the extensions of a family of social practices underwrite a relation of what we may call (extending the usual sense) anaphoric reference between various performances. The term ‘anaphoric’ is used to indicate that this ‘referential’ relation is internal to a system of social practices, where one performance refers to another as one word refers to another in A: ‘Pynchon wrote the book’ B: ‘But has he tried to read it?’, where the pronouns anaphorically refer to the antecedent terms ‘Pynchon’ and ‘the book’. No relation between discursive and non-discursive items is supposed. A prime use of this expressive resource of anaphoric reference to typed utterings is exhibited just below, as a feature of demands for justification” (p. 12).

In Making It Explicit, Brandom uses linguistic anaphora to explain the constitution of objects as objects. Here he gives it an even broader role. Anaphora or back-referencing is the birth of substance, solidity, and modality in meaning. Again the ethical dimension comes to the fore. Assertion as lived concerns neither naked Parmenidean being nor pure objective facts.

“The key to our attempt to offer sufficient conditions for assertion by specifying a class of systems of social practices is the relation of justification which a set of assertions can have to another assertion…. Both the dimension of authority and the dimension of responsibility will be explicated in terms of the recognition of justification. Each of the different types of assertion which play a role in the systems we will examine, free-standing assertions, assertions which are the results of inferences authorized by other assertions, and assertions which are part of the justification which another asserting made its asserter responsible for, each of these types of assertion incurs a justificatory responsibility itself and authorizes further inferences. The relevant responsibility is to produce (what would be recognized as) an appropriate justification, if one is demanded…. The utterance of a conventional request for justification addressed to a foregoing assertion is to be always appropriate, and not itself in need of justification. The cognitive significance of the linguistic practices we describe stems from this universal appropriateness of demands for further justification (as Sellars takes the ‘rational’ structure of scientific practice to consist in its being a ‘self-correcting enterprise which can put any claim in jeopardy, though not all at once’…. An utterance in the conventional style of assertions (utterances which undertake justificatory responsibilities and issue inference licenses whose contents vary as the content of the assertion vary) will constitutively be recognized as possessing that authority only so long as the conditional responsibility to justify if queried has not been shirked…. No more for this distinction than elsewhere in the social practice story need we appeal to intentions or beliefs of performers” (pp. 12-13).

As I’ve mentioned a number of times, other variants of this ethics of dialogue or dialogical ethics have been developed by Plato, Gadamer, and Habermas.

“For just as inference passes the authority of assertion one way along the anaphoric chain, it also passes the justificatory responsibility incurred the other way along that chain” (p. 14).

“The extended responsibility induced by the presentation of a justification is defeasible by the performance of a counter-justification, comprising further assertions…. The categories of justificatory and counter-justificatory performances are not disjoint” (p. 17).

“Each of these conditions codifies some aspect of our ordinary practices of giving and asking for reasons” (p. 18).

“[A] set of basic and extended repertoires related by an accessibility relation will be called a conceptual idiom…. It is in terms of these still rather particularized structures that we will define assertional contents or conceptual roles” (pp. 18-19).

Next in this series: Conditionals and Conceptual Roles

Pragmatics of Inquiry

The third chapter of Brandom’s 1976 dissertation addresses a dispute in 20th-century philosophy of science between “realism” and “instrumentalism”. He aims to overcome this dichotomy with the help of concepts developed by John Dewey (1859-1952). Besides its intrinsic interest, the discussion sheds additional light on several terms that are prominent in Brandom’s later work.

“Within the structure of classical (positivist) philosophy of science there was a genuine and easily formulable issue between realists and instrumentalists concerning the nature of scientific theories. Both parties agreed that statements reporting observations are either true or false, and that the terms used in true observational statements refer to actual objects and properties. The realist claimed that theoretical statements are also true or false, and that if true their terms refer to actual objects and properties. The instrumentalist regarded theoretical statements as convenient codifications of inferential practices concerning observational statements. Theoretical statements are rather to be read as expressing rules for complicated practices of material inference. The origin of this suggestion for reading putative propositions as rules for inferential practices lies in the fact that in a formal logical system one can in general replace any premise such as ‘n is an A‘ with material inferential rules of the form ‘From “All As are Bs” infer “n is a B” ‘ ” (Brandom, “Practice and Object”, p. 71).

Here Brandom already makes use of Sellars’ notion of material inference, which is the foundation of the “inferentialism” that will be propounded in his first big book Making It Explicit (1994). Within the current chapter, he approaches realism and instrumentalism in an even-handed manner, but his references to this discussion elsewhere in this work are slanted in the direction of criticizing instrumentalism. Given that his later inferentialism advocates something closely related to what he criticizes here, it is clear that his thinking on this matter has evolved.

In the current context, “realism” refers not to a direct or naive realism (the idea that we directly interact with objectively real things, which are more or less as we take them to be), but to a commitment to the reality of theoretical objects. Alongside this he implicitly portrays both parties to the dispute as holding to a kind of empiricism that he does not criticize here, but does criticize in his later works.

“Beginning with Pierce, the primary motivation for wanting to eliminate commitment to theoretical objects has been a desire to accommodate the sort of open-ended conceptual change which has characterized scientific inquiry from the beginning…. Appreciation of this sort of conceptual change has taken the form of a regulative principle to the effect that there are to be no claims taken as ‘fixed points’ settled once and for all…. This is referred to by Pierce and Popper as ‘fallibilism’, and by Quine as the ‘revisability in principle’ of our beliefs and the concepts they are couched in” (pp. 71-72).

I hold in addition that this “revisability in principle” applies not only to scientific concepts and theories, but also to the concepts and beliefs that we apply in ordinary life and in any kind of dialogue.

“The realists argue that theoretical statements do not simply license certain inferential moves concerning observation statements, they also explain the efficacy and account for the legitimacy of those practices…. Appreciation of the need for some explanation of the sort the realists seek takes the form of a regulative principle for theories of inquiry which Quine calls ‘naturalized epistemology’. It is just the requirement that we be able to exhibit scientific inquiries as natural processes susceptible of ordinary empirical investigation and explanation” (p. 73).

The terms “empirical” and “naturalized” can also have broader meanings than they generally do in modern science. For example, I’ve had a lifelong interest in why people believe the things that they do. In this context it is hard to see any kind of dichotomy between justification and explanation. I approach both in terms of “reasons why”. The explanation at issue here, though, is more narrowly causal in a modern sense. (I take both naturalism and “empirical” inquiry in broader, more relaxed senses — empirical as meaning grounded in ordinary experience, and naturalism simply as not appealing to the supernatural as an unexplained explainer.)

“The classical theory/observation distinction simply repeats the Kantian picture of knowledge as the product of a faculty of receptivity (intuition, observation, the passive appropriation of the ‘given’) and a faculty of spontaneity (understanding, theory, the interpretation of the ‘given’)” (pp. 74-75).

More to the point, the common theory/observation distinction in early 20th-century philosophy of science reflects a common dogmatic attachment to empiricism. But at this early point, Brandom still seems to follow Rorty’s negative view of Kant, and he avoids directly criticizing empiricism. But since Kant emphasizes the interdependence of intuition and understanding and says we never find one of these without the other in any real case, it hardly seems fair to treat this as a rigid dualism. In later works, Brandom treats Kant much more sympathetically, and does directly criticize empiricism.

“It is important to realize that the original dispute proceeded as a disagreement about the nature of theories in which the objects immediately given in observation were taken as the measure against which ‘theoretical objects’ were to be laid…. The notion of a theory-neutral, interpretation-free observation language was attacked by Wittgenstein in the Investigations and by Sellars among others, and had fallen into disrepute in the philosophy of science by the 1960s” (p. 75).

That is once again to say that a kind of dogmatic empiricism reigned almost undisputed in early 20th-century philosophy of science. Within analytic philosophy, this commitment to empiricism only began to be questioned in the 1950s, with the work of late Wittgenstein, Sellars, and Quine.

“[T]he current [1976] situation may be put as follows. In the light of many recent criticisms, philosophers of science have denied that there are sharp differences of kind between objects of observation and objects of theory. Contemporary instrumentalists ([such as] Quine, Feyerabend, and Kuhn) may be thought of as taking this work as … showing that [observation] is more like theory as classically conceived than we had previously thought. So observation is to join theory as a matter of holistically criticizable practices. Realists (such as Putnam, Field, and Boyd) have taken the demise of [the observation/theory distinction] as illuminating our notion of theory, letting us see that theoretical objects are as real, causally efficacious, and independent of our knowledge of them as the classical observable objects” (pp. 76-77).

Each of these latter views seems to make a good point.

“It is not clear, however, … that the new positions are incompatible…. I believe that this is precisely the virtue of Dewey’s theory of inquiry” (p. 78). “Dewey’s idiosyncratic and often obscure account of the mechanics of inquiry … exhibits the realist/instrumentalist dispute as a confusion based on insufficient appreciation of the consequences of abandoning the theory/observation distinction” (p. 70).

He goes on to discuss a number of passages from Dewey. Dewey’s “inquiry into inquiry” is grounded in a specialized notion of situation.

Dewey says “The situation as such is not and cannot be stated or made explicit… It is present throughout [inquiry] as that of which whatever is explicitly stated or propounded is a distinction” (p. 79).

Certainly we never have unqualified “mastery” of our practical or epistemic circumstances, but this doctrine of inherently ineffable “situations” goes further than is needed to make that point. What Dewey says here resembles existentialist claims that existence is ineffable in principle. I was unaware that there was such a dimension to his thought. To my knowledge, none of Brandom’s later works builds on this Deweyan theory of situations. But the way Brandom relates this dubious notion to the making of distinctions puts it in a maximally positive light.

Brandom comments “To ‘know’ something, rather than simply ‘having’ the situation is a matter of repeatables ‘instituted’ within an unrepeatable situation. It is this process which we must investigate to understand the nature of inquiry…. What is excluded by the unrepeatable, non-cognitive nature of situations is only that in a given inquiry I should come to know, rather than simply have, the situation which is the context of that very inquiry. I may investigate other inquiries and their contexts, and this is what one must do to produce a theory of inquiry” (p. 80).

The positive idea that universals arise out of our practices that institute “repeatables” is provocative. No human inquiry partakes of perfect reflexivity, but inquiry is possible nonethless.

“From this external point of view situations are sub-types of the natural occurrences which Dewey calls various ‘histories’ or ‘affairs’. These are the basic elements for which our collective name is ‘nature’ ” (ibid).

He quotes Dewey: “[N]ature is an affair of affairs” (ibid).

Then he goes on: “Situations are a class of affairs which contain sentient organisms. These are the most complicated and interesting affairs in nature, for it is within them that cognition occurs. The model of this sort of affair is the transaction between an organism and its environment in which ‘integration is more fundamental than is the distinction designated by interaction of organism and environment’. The environment here is not just that bit of the physical world which happens to surround the organism. It is that part of the surrounding world with which the organism interacts to live. So from the outside, situations are just congeries of objects ‘falling within boundaries’ determined in some way by the inquirer, and considered as unique, datable occurrences.”

I guess this predates the sentience/sapience distinction that Brandom dwells on in Making It Explicit.

“But if situations are thus unrepeatable constellations of objects, how are the repeatables crucial to cognitive inquiry, as Dewey says, ‘instituted’ within them?” (p. 81).

That is indeed the question.

He quotes Dewey again: “A starting point for further discussion is found in the fact that verbal expressions which designate activities are not marked by the distinction between ‘singular’ (proper) names and ‘common’ names which is required in the case of nouns. For what is designated by a verb is a way of changing and/or acting. A way, manner, mode of change and activity is constant or uniform. It persists through the singular deed done or the change taking place is unique” (ibid).

Adverbial ways of being and ways of acting are far more interesting than mere attributions of undifferentiated existence or action. The association of these adverbial “ways” with a formal characteristic of verbs that is agnostic to the distinction between particulars and universals is unfamiliar and intriguing.

Brandom notes, “Practices, modes of activity involving the objects making up the situation, are to be the basis for repeatability in inquiry” (p. 82)

Now he says it more categorically. Universals become instituted through commonalities in practice, rather than through putative resemblances in perceptual experience. No universal is simply passively acquired.

He quotes Dewey again: “We are brought to the conclusion that it is modes of response which are the ground of generality of logical form, not existential immediate qualities of what is responded to…. ‘Similarity’ is the product of assimilating different things with respect to their functional value in inference and reasoning” (p. 82).

This resembles Brandom’s later critique of assumptions about resemblance.

Brandom comments, “Dewey wants to be able to present a ‘naturalized epistemology’, a theory of inquiry which will account for the practices of an inquirer in the ordinary empirical way, in terms of a set of objects existing antecedent to any activity of the inquirer, and which causally condition his behavior in explicable ways. One of the terms by means of which Dewey formulates the results of his ‘inquiry into inquiry’ is thus the situation. The situation of any particular inquiry we choose to investigate may well contain objects unknown to the inquirer who ‘has’ the situation…. With this introduction to the notion of a situation, we are prepared to approach Dewey’s notion of inquiry” (pp. 83-84).

The way he uses “empirical” here seems to straddle the boundary between empirical science on the one hand, and ordinary experience and natural language use on the other.

“[Dewey’s] official definition of inquiry is: ‘the controlled or directed transformation of an indeterminate situation into one that is so determinate in its constituent distinctions and relations as to convert the elements of the original situation into a unified whole.’ Dewey later decided that this was ill-put, and his considered view is that ‘the original indeterminate situation and the eventual resolved one are precisely initial and terminal stages of one and the same existential situation’. We will see that the ‘transformation’ which is inquiry according to Dewey is a transformation of practices of reporting, inferring, eating, etc. Dewey’s talk of ‘existentially transforming’ situations by inquiring will seem less paradoxical if we recall that the paradigm of a situation from the external point of view is an organism in its environment” (pp. 84-85).

Inquiry is something existentially transforming that occurs within a broadly natural context.

“By insisting on the role of pre-cognitive situations in inquiry, Dewey enforces the constraint of practices and changes of practice by causal relations of pre-existing objects which make those practices possible” (p. 85).

Here Brandom aims to show that Dewey addresses the concerns of the realists.

An interesting sentence in one of his quotations from Dewey is that “The attitude, when made explicit, is an idea or conceptual meaning” (p. 87). The phrase “making explicit” appears here at several important junctures in this discussion of Dewey. The title of Making It Explicit may reflect a Deweyan inspiration. This also sheds light on Brandom’s later talk about the attitude-dependence of normative statuses. The attitudes in question are not purely or shallowly subjective. They are practical stances in situations, subject to concrete give-and-take in the situations, and therefore to objective constraints that go into making the situation what it is.

Young Brandom explains, “A situation is indeterminate insofar as it is uncertain what to do in it, what past situation to assimilate it to…. An inquirer enters any situation with a repertoire of practices differentially elicitable by features of that situation…. The situation is determinate or resolved insofar as a concordant set of practices is unambiguously elicited by the situation. Inquiry is the process of producing such settled situations by applying high-order practices of criticism and refinement of initially conflicting claims made in accord with established practices whether inferential or non-inferential” (ibid).

The notion of a differentiating elicitation does occur in his later work.

“For Dewey, as for Pierce, inquiry is a matter of refining one’s practices toward an ideal in which no situation would elicit discordant or ambiguous activity in accord with those practices. Every time a problematic situation does arise, a re-assessment of the practices involved is required, an adjustment and refinement of that set of practices until concord is reached in the concrete situation” (p. 89).

Brandom’s later works express this repeated re-assessment in terms of the ongoing re-constitution of Kantian unities of apperception. Pierce and Dewey apparently put too much stock in a sort of universal movement toward consensus.

“It is important to this picture of inquiry that the inquirer and the habits which determine his practices are part of the situation. This means that altering one’s practices is a way of transforming one situation into another” (pp. 89-90).

“The essential feature of language is that ‘it compels one individual to take the standpoint of other individuals and to see and inquire from a standpoint that is not strictly personal but is common to them as participants or “parties” in some conjoint undertaking’ ” (p. 90).

Language in part presupposes and in part constitutes intersubjectivity. (Intersubjectivity is not something added onto individual subjectivity, but rather a precondition for its possibility. We could not be talking animals at all without others to talk with.)

“Common sense inquiries and scientific inquiries are alike, in that the same general description as ‘controlled transformation of problematic situations into resolved ones’ applies to both. They are different in that the practices of scientific inquiry are developed, inculcated, and criticized in social institutions unparalleled in the extra-scientific community” (p. 91).

I would say that any serious inquiry is an instance of what Habermas calls communicative action, and involves many considerations that do not apply to action in general.

“By looking thus from the outside at an inquirer and his situation in terms of the best scientific theory we have of them, we can also in principle describe conceptual change in an ordinary empirical way” (p. 93). “By describing their practices with respect to the objects which our best theories tell us make up their situations, we provide the framework for an ordinary empirical investigation of inquiry and conceptual change in terms of the physiological and sociological basis of their practices…. According to Dewey, the activity of the physiologist and sociologist investigating the basis in relation of objects for the practices of various groups of inquirers is itself to be thought of as a set of practices which occur within some non-cognitive situation (had but not known) and transformed as inquiry progresses. Inquiry into inquiry shares with all other inquiries the utilization and adaptation of practices forged in previous inquiries, and hence the revisability-in-principle of all these practices and the claims made in accordance with them” (p. 94).

This seems to treat natural-scientific explanation rather than discursive inquiry into meaning as the paradigm for explanation in general. As evinced by the work of Habermas, revisability in principle is an attribute of discursive or dialogical inquiry in general.

“It should be clear at this point that the realist’s claims and the instrumentalist’s claims as they appear in Dewey’s view of inquiry are completely compatible. Objects and practices occupy correlative functional roles in describing inquiry. Conceptual change is indeed viewed as a change of practice, but neither the practices nor the change is viewed as inexplicable” (pp. 95-96).

This is the main point that young Brandom wants to make here. Issues with classical pragmatist sources notwithstanding, I think he is basically successful.

“On the contrary, any practice or change of practice may in principle be explained by appealing to the objects reported, inferred about, or manipulated in any of the practices which are not then in question. This does not mean that there is any practice which cannot be explained or changed, and which is somehow a basis for the rest. We simply cannot change or explain all of our practices at once” (p. 96).

Any particular belief or concept we may have is subject to revision. But we doubt one thing in light of other things that are provisionally held constant. In real life no one doubts everything at any given time.

“There is a certain sort of circularity here, but it is the familiar non-vicious circularity of any self-regulating enterprise, a formal characteristic acknowledged by contemporary philosophy of science as applying to empirical inquiries, capsulized most vividly in Neurath’s famous figure of a ship making repairs at sea” (ibid).

This idea of practical mutual dependence among the elements of inquiry makes foundationalism untenable.

“The difficulty with the instrumentalists is that, having noticed the problems resulting from an ontology of objects, they sought to put epistemology on a firm footing by substituting an ontology of practices, claiming that objects were derivative entities, ultimately reducible to practices which, as we say, involve them…. Dewey teaches us that the problem is with the notion of ontology itself. Once we have become naturalistic, accepting a thoroughgoing fallibilism means eschewing the notion of a categorization of the kinds of things there are which is outside of and prior to any empirical investigation. Objects and practices are mutually dependent functional notions. We cannot account for the changing roles objects play in our conceptual economy without appealing to practices as well, and we cannot individuate practices without reference to objects” (p. 96n).

Objects are derivative entities, and there is a problem with ontology itself, whether it be taken merely as an a priori enumeration of kinds of things, or as something supposedly more fundamental.

“The problem which faced the realists, as we have argued, is allowing for fallibilism in their account of scientific activity. On the face of it, the explanation which the realist wants to be able to offer of the success of current practices, in terms of the actual existence and causal efficacy of the objects purportedly referred to in the theory will not explain why previous views which we have good empirical reason to believe false worked as well as they did. Nor is it obvious how believing in all those unreal objects enabled us to reach our present privileged position of believing in real ones (i.e., the ones which ‘really’ enable us to engage in the practices we do). Finally, fallibilism dictates that we be willing to accept the possibility of revisions in our current view as radical as those which have occurred in the past” (p. 97).

Here there is a clear parallel to the entry conditions for dialogue developed by Gadamer and Habermas. These apply not only to scientific discourse, but to discourse in general.

“According to Dewey’s view, each time our scientific view of things changes sufficiently, we will have to rewrite our account of the history of inquiry in terms of the sorts of objects which we have new practices of making claims about. But this fact no more impugns the project of explaining how previous practices worked as well as they did, than it impugns any other empirical project which may have to be rethought in view of the results of subsequent inquiry” (p. 98).

Naive views of the history of scientific progress as a linear accumulation toward presumed present truth cannot be sustained. When one view supersedes another in any context, it is not a simple matter of truth versus error. For example, geocentric astronomy had an important practical use in navigation that was not negated by the greater “truth” of heliocentric astronomy.

“As long as knowledge is thought of on the Kantian model, as the product of the collaboration of a faculty of receptivity and a faculty of spontaneity (and the observation/theory distinction is a straightforward version of this model, it will seem that there is a philosophical task of explaining the relations of these faculties. (Even Quine falls into this view in the very midst of a recommendation of a Deweyan naturalism about knowledge.) On this picture, philosophers are to tell us how theory relates to evidence, concept to intuition, in every possible cognition. This project stands outside of and prior to any empirical investigation. Dewey, having wrestled free of the picture generating the classical epistemological project, is able to present inquiry into inquiry as an ordinary empirical matter…. Thus Dewey’s naturalized account of inquiry can retain a distinction between inferential and noninferential practices, and between repeatable and non-repeatable elements. These categories are now meant to have only the same force that any empirical classification has, however. They can be discarded when an empirically better idea comes along. Once we give up the receptivity/spontaneity distinction, and with it the project of a philosophical discipline called ‘epistemology’ which is to relate the operations of the two faculties, we lose also the means to formulate a dispute between realism and instrumentalism concerning which faculty is to be given pride of place” (pp. 98-100).

As I noted earlier, in later works Brandom never blames Kant for the bad idea that there is such a thing as pure observation without any interpretation. That is an empiricist prejudice that ought in fact to be regarded as decisively refuted by Kant. Broadly construed, “naturalism about knowledge” is a good thing, provided it does not lead us back to empiricism.

Next in this series: Truth and Assertibility

Implication Spaces

“Logical vocabularies make reason relations explicit in terms that appeal only to the conceptual resources supplied by the base vocabularies from which they are conservatively elaborated. They are in that sense intrinsic vocabularies for specifying reason relations. Logical vocabularies, however, are not purely metavocabularies, in the sense in which semantic and pragmatic rational vocabularies are. The sequent-calculus vocabularies in which we say how to elaborate arbitrary base vocabularies into logically extended vocabularies with the capacity to codify reason relations are genuine metavocabularies in that sense. Like semantic and pragmatic metavocabularies, they do not extend the base vocabularies for which they are metavocabularies. They are purely metalinguistic, talking about expressions in the base vocabulary, rather than using them” (Brandom in Hlobil and Brandom, Reasons for Logic, pp. 17-18, emphasis in original).

“Logical vocabulary is a hybrid or mongrel kind of metavocabulary. It plays the expressive role of explicitating reason relations: making them explicit, constructing sentences intelligible as saying that relations of implication and incompatibility hold. That is a broadly metalinguistic function. But logical vocabulary performs that explicative expressive function by using the sentences whose reason relation it articulates, rather than by talking about them (mentioning them).”

“These observations raise the question whether there is a purely intrinsic-explicative vocabulary for specifying reason relations that is a rational metavocabulary in the sense of being genuinely and wholly metalinguistic. The answer is ‘yes’…. Our candidate, informed by work due to Dan Kaplan (2022), is an implication-space metavocabulary for specifying both reason relations and the conceptual role sentences play in virtue of standing to one another in such reason relations. Very roughly, where Gentzen’s sequent-calculus metavocabulary treats implications as basic objects in a proof-theoretic formalism, Kaplan’s implication-space metavocabulary treats them as basic objects in a model-theoretic formalism. It represents the current state of the art in inferentialist semantics.”

“Inferentialists have long thought that the universe from which semantic interpretants are drawn or from which those interpretants are built — the analogue of the universe of mereologically structured worldly states out of which semantic interpretants (propositions) as pairs of sets of truth-making states and falsifying states are built — should consist of implications (including incompatibilities coded as implications) and sets of them” (p. 18, emphasis in original).

This is vital stuff. At the risk of sounding dogmatic in the Kantian sense myself, I have long thought that the world is made of implications. What this really means is that the determinacy in it is made of implications.

“Kaplan’s (2022) first conceptual innovation was the idea that thoroughgoing inferentialists ought to treat the most basic units being interpreted, no less than the semantic interpretants assigned to them, as being implications, rather than the sentences that make up their premises and conclusions. Only at a second, subsequent stage would semantic interpretation be extended from implications to the sentences they contain. He accordingly begins with a universe of candidate implications, together with a partition of that universe into a distinguished set of good implications — ones whose conclusions really follow from their premises — and the rest. This universe of candidate implications with a distinguished subset is an implication space.” (p. 19).

Note that he speaks of implications containing sentences, rather than of sentences “having” implications. This reflects the implication-first point of view: implications are “the most basic units being interpreted”.

“Any base vocabulary determines such an implication space, since the lexicon of the vocabulary suffices to define the points (candidate implications as ordered pairs of sets of sentences of the lexicon), and the reason relations of the vocabulary suffice to determine the distinguished set of good implications” (ibid).

“We are exploring the idea of understanding meaning to begin with in terms of reasons instead of understanding it in terms of truth. That is to understand meaning in terms of a dyadic relation (between sets of sentences) instead of in terms of a monadic property (of sentences). On the approach that takes truth as basic, one starts with assignments to sentences of a truth value: as true or false, correct or incorrect, good or bad (as a representation). However, although assignments of truth values are the beginning of semantic interpretation on this approach, they are not the end. To get a notion of meaning that corresponds to what one grasps (however imperfectly) when one understands a sentence, one must advance from consideration of truth values to consideration of truth conditions. (One must add to a semantic conception of Fregean Bedeutung of a sentence a semantic concept of its Fregean Sinn.)” (pp. 19-20; see also Brandom on Truth).

When we contrast appeal to reasons with direct appeals to truth, the problem with direct appeals to truth is that there is no good way to separate them from what Kant would call dogmatic assertions.

It seems to me that the truth-first approaches to meaning inevitably end up assuming particular truths. Such assumptions may be entirely innocent and tentative, or not, and there is no way to easily distinguish the innocent ones. On many traditional views, the necessity of such assumptions is simply taken for granted. Here is an alternative to all of that that respects natural language, but can also be made mathematically rigorous. I did not expect such a thing to even be possible.

I think Aristotle and Plato already took a reasons-first approach, but it was purely hermeneutic, without mathematical underpinning, in spite of Plato’s great interest in mathematics.

Ultimately I do more hermeneutics than mathematics myself, but for quite some years I was keenly interested in mathematics. In my day job, I implicitly lean on both constructive mathematics and a kind of hermeneutics on an everyday basis, in doing a kind of logically oriented engineering modeling of “real world” use cases. So whereas records in a database may be taken as expressing sentences that are supposed to be true, I do all my design in terms of the functional dependencies of one thing on another (where the value of one is a simple mathematical function, fully determined by others that can be finitely enumerated and are usually very few). These can be thought of as if-then rules that apply to all practically relevant cases, without claiming to represent universal truth. This applies a kind of lightly formalized inferentialism in the engineering world, which can also be very pragmatic and adaptable to new hypotheses. I do indeed find that these practical judgments (even well outside of the broadly ethical domain that I am mainly concerned with here) have all the characteristics that Brandom talks about. So naturally I found Brandom’s explicit inferentialism very appealing.

“At the extensional semantic ground level, one can say that a sentence is true, and in the reason-based setting one correspondingly can say at the extensional semantic ground level that an implication is good or an incompatibility holds. Given that analogy, the question becomes: what stands to implication (reason relation) values (good/not-good) as truth conditions stand to truth values?”

This is a distinction that Aristotle also makes in his own way. The more elementary stages of inquiry are concerned with a preliminary mapping out that some characterization of something in the domain is at least pragmatically true. The more advanced stages are concerned with why it is true, or what makes it true.

“The idea behind truth conditions (and Fine’s generalization to truth-makers and falsifiers) is that apart from the question of whether a truth-candidate actually is true or false, there is the question of what it would take to make it true — what things would have to be like for it to count as correct in this distinctive semantic sense. The idea behind the first stage of implication-space semantics is that apart from the question of whether a candidate implication actually is good (according to the partition of the space of candidate implications into good and bad determined by the underlying base vocabulary), there is the question of what it would take to make it good. In the special case of reason relations that already do hold, candidate implications that are good, this takes the form of asking about the circumstances under which it would remain good. That is the range of subjunctive robustness of the implication” (p. 20).

This notion of a scale of subjunctive robustness is where the hermeneutics meets the math.

“The range of subjunctive robustness of a candidate implication is its semantic counterpart in the form of its good-makers, as in Fine’s truth-based semantic setting the semantic interpretants are their truth-makers (and falsifiers).

“Grasping ranges of subjunctive robustness in this sense is an essential part of understanding reason relations in ordinary vocabularies” (pp. 20-21).

“The ranges of subjunctive robustness of candidate implications are their ‘goodness’ conditions, as truth conditions are the ‘goodness’ conditions of sentences. For an implication to be good in the reasons-first semantic setting is for its premises to provide reasons for its conclusion (or reasons against, in the case of incompatibilities), while for a sentence to be good in the truth-first semantic setting is for it to be true. The advance from a conception of semantic goodness to a conception of meaning is the advance to consideration of circumstances under which a reason relation or sentence would be good….. In the implication-space setting, the circumstances are additional premises (and, in the fully general multisuccedent case also additional conclusions) that would make or keep the reason relation good. By contrast to the truth-maker setting, in the implication-space setting, those further premises and conclusions are just more sentences of the lexicon of the base vocabulary. That is why implication-space semantics counts as intrinsic” (pp. 21-22, emphasis in original).

“In this way, a model-theoretic inferentialist semantics becomes available that is sound and complete for the aforementioned expressive logic NMMS [NonMonotonic MultiSuccedent logic]. The implication-space semantics shows how to compute the conceptual roles of arbitrary logically complex sentences from the conceptual roles of logically atomic sentences of any base vocabulary — even when the base vocabulary, and so its (conservative) logical extension, are radically substructural, including those that do not satisfy the metainferential structural closure conditions of monotonicity and transitivity. To do this, the implication-space rational metavocabulary must make explicit the conceptual roles played by sentences of all those base vocabularies, as well as their logical extensions. It is universally explicative of sentential conceptual roles. And since implication spaces can be constructed using no resources other than those supplied by the spare specifications of arbitrary, even substructural base vocabularies — just sentences and set-theoretic constructions from them representing their reason relations — the implication-space model-theoretic semantics qualifies as a universal intrinsic-explicative rational metavocabulary” (pp. 22-23, emphasis in original).

“Metainferences of various kinds can be defined precisely, systematic combinations of them recursively constructed, and the effects of those combinations computed. The result is a principled botanization of constellations of metainference that offers revealing characterizations of a number of logics that have been the subject of intense interest among logicians and philosophers of logic over the past few decades…. In treating metainferential relations among conceptual roles as objects that can be combined and manipulated, this calculus stands to conceptual roles as the sequent calculus stands to the sentences that are the relata of the implication relations it codifies as sequents. This intrinsic rational metavocabulary, built on top of the implication-space inferentialist model-theoretic semantics for conceptual roles, provides the expressive power to make explicit a hitherto unexplored level of metainferential reason relations among those roles, and thereby offers an illuminating new semantic perspective on the relations among a variety of well-studied logics.”

“The implication-space metavocabulary provides a model-theoretic semantics for the conceptual roles sentences play in virtue of standing to one another in reason relations of implication and incompatibility. It is a reason-based inferentialist semantics, rather than a truth-based representational semantics like truth-maker semantics. By contrast to the proof-theoretic treatment of reason relations by the sequent calculus, the implication-space metavocabulary assigns sets of implications as the semantic interpretants of sentences, and set-theoretic constructions out of those sets as the semantic interpretants of sentences, and then operates on and manipulates those semantic interpretants to codify reason relations and conceptual roles. In fact, it does so in a way that can be shown to be isomorphic to truth-maker model-theoretic semantics…. In both cases, the universe is taken to be structured by a commutative monoid (fusion of states and a corresponding operation combining candidate implications according to their ranges of subjunctive robustness). Nonetheless, the implication-space metavocabulary provides an intrinsic semantics, since it appeals to nothing that is not made available by the base vocabulary to which it is applied: sets of sentences and their reason relations. Implication-space semantics is something like the intrinsification of truth-maker semantics — in a way formally analogous to, but expressively more powerful than, Fine’s use of intrinsic ‘canonical models'” (pp. 23-24).

The abstract algebraic notion of a monoid is also ubiquitous in contemporary functional programming. Per Wikipedia, a monoid is a set equipped with an associative binary operation and an identity element. One easy example is the set of positive integers with addition as the associative operation and 0 as the identity element, but there are a great many others as well.

“When this structural isomorphism of implication-space and truth-maker semantics — which holds between the universes from which semantic interpretants are drawn, the interpretants themselves, and the way reason relations of consequence and incompatibility are determined for sentences in terms of their semantic interpretants — is appreciated in detail, and considered in context with the orthogonal isomorphism at the level of reason relations between the truth-maker alethic modal semantic metavocabulary and the deontic normative bilateral pragmatic metavocabulary, it becomes clear that the implication-space semantics makes explicit the abstract rational forms common to those two extrinsic-explanatory metavocabularies of meaning and use. Those rational forms are just the conceptual roles the implication-space semantics characterizes” (p. 24).

Epilogues to this series: Anaphora and Reason Relations; All the Way Down

An Isomorphism

“The present point is that if the claim that it is possible to identify a rational structure common to what is expressed in pragmatic and semantic metavocabularies could be made out in detail, it would cast light on issues of much wider philosophical significance. For we can look at the relations between what is expressed in normative pragmatic and representational semantic metavocabularies in another way: as articulating the relations between the activities of talking and thinking, and what is being talked or thought about. This is the intentional nexus between subjects and objects, between mind and the world, knowers and the known.” (Brandom in Hlobil and Brandom, Reasons for Logic, p. 8).

Brandom uses the term intentionality in a non-psychological sense that he elsewhere attributes to Kant. We are implicitly in what I think of as Aristotelian-Hegelian territory, where a Cartesian-style division into Subject and Object is not assumed. Brandom’s low-key summary of what to me are the rather dramatic stakes in this issue focuses on the American pragmatists, whom he discussed in the recent Pragmatism and Idealism lectures.

“The American Pragmatists inherited from the German Idealists — who in turn inherited it from Romantic critics of the Enlightenment — the idea that the Cartesian tradition failed structurally, making itself a patsy for skepticism, by attempting to define subjects and objects independently of one another, and then later on facing the problem of how to bolt together things understood as having wholly disparate natures…. The better strategy, they thought, was to start with a conception of intentionality as successful cognition (and action)…. One way to work out such a strategy begins with the thought that there is a kind of structure common to what normative pragmatic metavocabularies make it possible to say about the practices of discursive subjects using declarative sentences to manifest practical attitudes and undertake commitments, on the one hand, and what representational semantic metavocabularies make it possible to say about the modal relations among matter-of-factual states of the world those sentences come to represent by being so used, on the other” (ibid).

Here he references the classic pragmatist emphasis on “successful” thought and action. But especially since he is about to explicitly invoke an Aristotelian (and Scholastic) connection on the next page, this suggests to me that even a very elementary mainstream notion of pragmatism could be recast as evincing a kind of Aristotelian teleological concern with ends and that-for-the-sake-of-which, but in language that hides this angle and is suited to survive in the climate of uncomprehending modern antipathy to Aristotle. The main difference is that Aristotle says much more clearly that the ends that matter are those that are sought for their own sake, and not as means to other ends.

I used to think that logical and linguistic pragmatics as a field of study had nothing in particular to do with pragmatism as a view of the world. Brandom’s recent writings provocatively suggest that there is indeed a connection.

The emphasis on structure is also significant. Although Brandom does not identify with it as I did especially in my youth, French so-called structuralism and poststructuralism represent another major strand of non-Cartesian, non-subject-centered thought in the 20th century. Brandom’s usage seems closer to mathematical structuralism, and perhaps to the structural functionalism of the sociologist Talcott Parsons and the cognitive psychologist Jean Piaget that attracted Jürgen Habermas, whom Brandom has called a personal hero.

“For the worldly version of the relations that articulate the structure we are calling ‘conceptual’ are relations of necessity and impossibility whose existence owes nothing to the activities of discursive practitioners. They are objective relations, specified in the alethic modal vocabulary used to state laws of nature, and more generally to specify subjunctively robust relations” (pp. 8-9).

Brandom has consistently highlighted the significance of modality and modal logic for formulating what he likes to call subjunctive robustness. Next he invokes non-Cartesian strands within analytic philosophy.

“We take the view we develop to be a way of understanding what Frege means when he says ‘A fact is a thought that is true’. It is also one way of understanding the Tractarian [early Wittgenstein] claim that the world is the totality of facts…. John McDowell (1996) explores the same sort of conceptual realist view in Mind and World under the slogan ‘The conceptual has no outer boundary’.”

While I am highly sympathetic to the non-Cartesian ambitions here, I think that facts alone are too shallow a basis to constitute a world. I am not a Wittgenstein scholar, but I think he later moved away from this attempt to ground everything on atomic facts. But what else is needed is something like the subjunctive robustness or modal aspect of things that Brandom dwells upon. This emerges naturally as we move from world-as-totality-of-fact to the idea of a world constituted from implications and distinctions (the latter being my preferred way of thinking about what Brandom calls incompatibilities).

“These are deep waters. These pronouncements by great philosophers are mentioned to indicate that the stakes are high for the enterprise of explicating any form of conceptual realism. Here is a sketch of how we go about it. One of the key arguments we appeal to in filling in this neo-Aristotelian metalinguistic bimodal conceptual realism is a technical result…. Greg Restall and David Ripley have worked out what they call a ‘bilateral’ normative pragmatic understanding of the turnstile that marks implication relations in multisuccedent sequent calculi [which looks approximately like |~ and means that if all formulae on the left (often represented as a context capital gamma Γ) are true, then at least one formula on the right is true.]…. The Restall-Ripley bilateral normative pragmatic metavocabulary turns out to be related in surprising ways to what we take to be the most sophisticated contemporary heir of Tarskian model theory and later intensional semantics in terms of possible worlds (Lewis, out of Kripke, out of Carnap), namely Kit Fine’s truth-maker semantic framework…. The representational content of declarative sentences is then understood in terms of assignments to them of sets of states as truth-makers and falsifiers. Global structural conditions on modally partitioned state spaces (for instance requiring that all the mereological parts of possible states be possible) interact with conditions on assignments of truth-makers and falsifiers (for instance forbidding the truth-makers and falsifiers of logically atomic sentences to be overlapping sets).”

Sequent calculi are proof-theoretic notations due to Gerhard Gentzen in the 1930s. They generalize Gentzen’s system of natural deduction. In sequent calculi, every line is a conditional or sequent, rather than an unconditional assertion. In effect, the primitive terms are implications. This is a formal analogue of Brandom’s idea that the common structure of the world and of thought is at root constituted out of implications (and distinctions) rather than simple facts. Hlobil and Brandom’s book shows that it is general enough to support radically nonmonotonic and nontransitive cases.

“We show below that if one defines semantic consequence in just the right way, a powerful, fruitful, and detailed isomorphism can be constructed relating truth-maker modal semantic metavocabularies and bilateral normative pragmatic vocabularies” (pp. 9-10).

Serious logicians mainly study the properties of different logical systems, or logics, and develop new ones. Alternate logics have hugely proliferated since the first half of the 20th century. He is alluding to the fact that many differently detailed notions of logical consequence have been proposed. What is the “right” one depends in part on its conditions of use.

An isomorphism is a structure-preserving mapping that works bidirectionally. The existence of an isomorphism — like the one mentioned further below between algebra and geometry, or the one Brandom is talking about immediately below, between semantics and pragmatics — is an extremely nonrandom, rare occurrence, and therefore is often taken to be deeply significant.

“Assertion and denial line up with truth and falsity, combinations of commitments (to accept and reject) in a position line up with fusion of truth-making and falsifying states, and normative out-of-boundness (preclusion of entitlement to the commitments incurred by those assertions and denials) of a compound practical position lines up with the modal impossibility of such a fusion state.”

“When Spinoza looked back on the relations between algebraic equations and geometric shapes on which Descartes modeled mind-world relations, he saw that the key feature distinguishing that new, more abstract notion of representation from earlier atomistic resemblance-based conceptions is the existence of a global isomorphism between the algebraic and geometrical vocabularies. Spinoza’s slogan for the holistic insight that animated the representational revolution was ‘The order and connection of ideas is the same as the order and connection of things’ (Spinoza, Ethics II, Prop. vii). The isomorphism between normative pragmatic and alethic representational metavocabularies turns out to make possible in our setting a precise, tractable, and productive specification of that shared rational ‘order and connection’. We think this is a good way to rationally reconstruct some central aspects of Aristotelian (and Scholastic) intelligible forms. This isomorphism is the core of our version of bimodal (deontic/alethic) metalinguistic conceptual realism” (p. 11).

Brandom has been a consistent critic of standard versions of representationalism, but he has always been careful not to reject too much. The more affirmative reference to representation and Tarskian model theory here specifically involves not just any representation but an inferentialist semantics that undoes many conventional assumptions. Apparently there is a formal result to the effect that inferentialist semantics can be expressed not only in terms derived from Gentzen’s proof theory, but also in terms of an evolved variant of Tarski’s model theory in which the things represented are implications.

Next in this series: Quick Note on Proof Theory

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

Logic for Expression

In recent times, Robert Brandom has pioneered the idea that the role of logic is primarily expressive. In his 2018 essay “From Logical Expressivism to Expressivist Logic”, he says this means its purpose is “to make explicit the inferential relations that articulate the semantic contents of the concepts expressed by the use of ordinary, nonlogical vocabulary” (p. 70).

In my humble opinion, this is what logic was really supposed to be about in Aristotle, but the tradition did not follow Aristotle. Aristotle insisted that logic is a “tool” not a science, but most later authors have assumed the contrary — that logic was the “science” of correct reasoning, or perhaps the science of consequence relations. Several scholars have nonetheless rediscovered the idea that the purpose of logical demonstration in Aristotle is not to prove truths, but to express reasoned arguments as clearly as possible.

Brandom says that “the task of logic is to provide mathematical tools for articulating the structure of reasoning” (p. 71). People were reasoning in ordinary life long before logic was invented, and continue to do so. But the immensely fertile further development of logic in the late 19th and early 20th centuries was mostly geared toward the formalization of mathematics. Reasoning in most specialized disciplines — such as the empirical sciences, medicine, and law — actually resembles reasoning in ordinary life more than it does specifically mathematical reasoning.

According to Brandom, “The normative center of reasoning is the practice of assessing reasons for and against conclusions. Reasons for conclusions are normatively governed by relations of consequence or implication. Reasons against conclusions are normatively governed by relations of incompatibility. These relations of implication and incompatibility, which constrain normative assessment of giving reasons for and against claims, amount to the first significant level of structure of the practice of giving reasons for and against claims.”

“These are, in the first instance, what Sellars called ‘material’ relations of implication and incompatibility. That is, they do not depend on the presence of logical vocabulary or concepts, but only on the contents of non- or prelogical concepts. According to semantic inferentialism, these are the relations that articulate the conceptual contents expressed by the prelogical vocabulary that plays an essential role in formulating the premises and conclusions of inferences” (pp. 71-72).

“Material” relations of consequence and incompatibility have a different structure from formal ones. Formal consequence is monotonic, which means that adding new premises does not change the consequences of existing premises. Formal contradiction is “explosive”, in the sense that any contradiction whatsoever makes it possible to “prove” anything whatsoever (both true statements and their negations), thereby invalidating the very applicability of proof. But as Brandom reminds us, “outside of mathematics, almost all our actual reasoning is defeasible” (p. 72). Material consequence is nonmonotonic, which means that adding new premises could change the consequences of existing ones. Material incompatibilities can often be “fixed” by adding new, specialized premises. (As I somewhere heard Aquinas was supposed to have said, “When faced with a contradiction, introduce a distinction”.)

Brandom notes that “Ceteris paribus [“other things being equal”] clauses do not magically turn nonmonotonic implications into monotonic ones. (The proper term for a Latin phrase whose recitation can do that is ‘magic spell’.) The expressive function characteristic of ceteris paribus clauses is rather explicitly to mark and acknowledge the defeasibility, hence nonmonotonicity, of an implication codified in a conditional, not to cure it by fiat” (p. 73).

“There is no good reason to restrict the expressive ambitions with which we introduce logical vocabulary to making explicit the rare material relations of implication and incompatibility that are monotonic. Comfort with such impoverished ambition is a historical artifact of the contingent origins of modern logic in logicist and formalist programs aimed at codifying specifically mathematical reasoning. It is to be explained by appeal to historical causes, not good philosophical reasons” (ibid). On the other hand, making things explicit should be conservative in the sense of not changing existing implications.

“…[W]e should not emulate the drunk who looks for his lost keys under the lamp-post rather than where he actually dropped them, just because the light is better there. We should look to shine light where we need it most” (ibid).

For relations of material consequence, the classical principle of “explosion” should be replaced with the weaker one that “if [something] is not only materially incoherent (in the sense of explicitly containing incompatible premises) but persistently so, that is incurably, indefeasibly
incoherent, in that all of its supersets are also incoherent, then it implies everything” (p. 77).

“The logic of nonmonotonic consequence relations is itself monotonic. Yet it can express, in the logically extended object language, the nonmonotonic relations of implication and incompatibility that structure both the material, prelogical base language, and the logically compound sentences formed from them” (p. 82).

Material consequence relations themselves may or may not be monotonic. Instead of requiring monotonicity globally, it can be declared locally by means of a modal operator. “Logical expressivists want to introduce logical vocabulary that explicitly marks the difference between those implications and incompatibilities that are persistent under the addition of arbitrary auxiliary hypotheses or collateral commitments, and those that are not. Such vocabulary lets us draw explicit boundaries around the islands of monotonicity to be found surrounded by the sea of nonmonotonic material consequences and incompatibilities” (p. 83).

Ranges of subjunctive robustness can also be explicitly declared. “The underlying thought is that the most important information about a material implication is not whether or not it is monotonic — though that is something we indeed might want to know. It is rather under what circumstances it is robust and under what collateral circumstances it would be defeated” (p. 85).

“The space of material implications that articulates the contents of the nonlogical concepts those implications essentially depend upon has an intricate localized structure of subjunctive robustness and defeasibility. That is the structure we want our logical expressive tools to help us characterize. It is obscured by commitment to global structural monotonicity—however appropriate such a commitment might be for purely logical relations of implication and incompatibility” (pp. 85-86).

“Logic does not supply a canon of right reasoning, nor a standard of rationality. Rather, logic takes its place in the context of an already up-and-running rational enterprise of making claims and giving reasons for and against claims. Logic provides a distinctive organ of self-consciousness for such a rational practice. It provides expressive tools for talking and thinking, making claims, about the relations of implication and incompatibility that structure the giving of reasons for and against claims” (p. 87).

“What” by Inferential Semantics

Brandom’s inferential semantics can be seen as providing a general framework for answering “what is…” questions. Semantics is about meaning — especially of concrete things said — and inferential semantics is about understanding meaning as a kind of practical doing involved with reasons. Looked at this way, a meaning reflects an inferential role, or role in real-world reasoning. Such roles always have two sides — conditions for appropriate use, and consequences of using this rather than that. Brandom identifies conceptual content with such inferential roles, and focuses on a contrast between these and simple definition, but I want to emphasize instead that all simple definition should be understood as a kind of summary of what implicitly distinguishes a particular inferential role from others.

The kind of meaning of interest here is in principle shareable rather than subjective, private, or psychological. Meaning is social and essentially involved with communication, but it is not a matter of empirical fact. Rather than explaining communication in terms of empirical facts, we should ultimately explain what we call empirical facts in terms of well-founded shareable meaning. The more we are able to explicitly spell out conditions of use and consequences of things that are said, the more substantive content we can share with others.

The “what is…” questions classically asked by Plato and Aristotle have an open-ended character because they are concerned with what something means for a reasoning being in general, which is an open-ended context. To have meaning for a reasoning being is to make a difference in the way the being reasons in life. In this way, Plato and Aristotle also were deeply concerned with the inferential roles of things, and practiced a kind of inferential semantics. This is ultimately inseparable from questions of goodness of reasoning. Here, too, inferential semantics depends on normative pragmatics.

Kant and Foundationalism

According to Kant, all human experience minimally involves the use of empirical concepts. We don’t have access to anything like the raw sense data posited by many early 20th century logical empiricists, and it would not be of much use if we did. In Kantian terms, this would be a form of intuition without concepts, which he famously characterized as necessarily blind, and unable to function on its own.

Foundationalism is the notion that there is certain knowledge that does not depend on any inference. This implies that it somehow comes to us ready-made. But for Kant, all use of empirical concepts involves a kind of synthesis that could not work without low-level inference, so this is impossible.

The idea that any knowledge could come to us ready-made involves what Kant called dogmatism. According to Kant, this should have no place in philosophy. Actual knowledge necessarily is a product of actual work, though some of that work is normally implicit or preconscious. (See also Kantian Discipline; Interpretation; Inferentialism vs Mentalism.)

It also seems to me that foundationalism is incompatible with the Kantian autonomy of reason.

Historiography, Inferentialism

Having laid out some preliminaries, I’ve begun to circle back to more questions of historical detail related to the development here, and it seems fitting to summarize the motivations driving these more historical notes. History is all about the details, but in any inquiry, what are actually higher-order questions about methodology ought to inform primary investigations. We never just have data; it always has to be interpreted, and this involves questions about methodology. With history, this often involves critical examination of the applicability of categories that may tend to be taken for granted. Thus, I am adding notes about the application of various categories or concepts in particular historical settings, and about historical details that seem to have larger methodological significance.

I’m looking back at the history of philosophy (and, to some extent, broader cultural developments) from a point of view inspired by the “inferentialism” of Brandom (taking this as a general name for his point of view), as well as by my own ideas for a revitalized Aristotelianism. In Tales of the Mighty Dead and elsewhere, Brandom himself has effectively placed the historical roots of his development in the broad tradition of early modern philosophical rationalism, including the work of Descartes, Spinoza, and Leibniz. I find standard connotations of the term “rationalism” rather problematic, and want to separate Descartes — of whom I am much more sharply critical than Brandom seems to be — from Spinoza and Leibniz, for whom I find additional reasons to be sympathetic. Brandom has contributed to a new understanding of Kant, and has developed a landmark reading of Hegel. I want to help support the broad thrust of these with historical considerations, while reconnecting them with fresh readings of Aristotle, Plato, and other historical philosophers. With some caveats and in spite of Brandom’s own brief comments, I also want to suggest a possible rapprochement with key insights of 20th century French “structuralism”.

A key point common to most of the tendencies mentioned above is an emphasis on the role of difference in making things intelligible. In the context of philosophical arguments, this means that critical distinctions are as important as positive assertions. Contrasts not only greatly facilitate but largely shape understanding. Brandom himself has developed the contrast between inferentialism and the representationalism of Descartes and Locke. He has made large use of Wilfrid Sellars’ critique of a “Myth of the Given” associated with most varieties of empiricism, and has also referenced the critique of psychologism developed by Frege and others in a logical context.

I have been using the term “mentalism” for a privileging of contents that are supposed to be immediately present to a personal “mind” that is itself conceived mainly in terms of immediate awareness. It seems to me that Descartes and Locke’s version of this was a historically specific combination of all the above notions from which an inferentialism would seek to distinguish itself — representationalism, the Myth of the Given, and psychologism. I have been concerned to point out not only that Cartesian-Lockean mentalism has historically specific antecedents that long predate modernity (going back to Augustine, with some foreshadowing in Plotinus), but also that a proto-inferentialist countertrend is actually even older, going back to Plato and Aristotle’s emphasis on the primacy of reason and reasoned development.

In A Spirit of Trust, Brandom has among many other things expanded on Hegel’s critique of Mastery. I find this to be of tremendous importance for ethics, and consonant with my structuralist sympathies. I have been concerned to point out how extreme claims of mastery are implicit in the various historical kinds of voluntarism, which all want to put some notion of arbitrary will — or authority attributed one-sidedly to such a will — ahead of consideration of what is reasonable and good.

Usual generalization caveats apply to statements about “isms”. In any particular case where the terms seem to apply, we need to look at relevant details, and be alert to the possibility that all aspects of a generalized argument may not apply straightforwardly. (See also Historiography; History of Philosophy.)