Realism, Nominalism, Modality

There is an important intersection between the 14th century debate about realism and nominalism and contemporary questions about the status of modality in logic that ought to be of interest to non-specialists. Both of these topics probably sound obscure to most people. At sound-byte level, the first is about the status of universals, and modality is something we implicitly presuppose any time we try to reach for something “more” than allegedly pure phenomena or mere appearance.

Both sides of the medieval debate often wanted to enlist the support of Aristotle, who took a remarkably even-handed approach to these questions we have yet to clarify. The debate was often invested with a great moral significance, and provoked a number of intemperate claims. But at the same time, both sides were able to use the technical vocabulary of the theory of “supposition” — along with shared familiarity with Aristotle — to discuss semantic issues of concrete meaning and word use in detail, in terms both sides could in large measure agree upon. This led to a very high quality and sophistication in many contributions to the debate on both sides.

On some slight acquaintance, many modern readers can easily sympathize with nominalist critiques of the premature and illegitimate use of universals. We may think of vulgar platonism, excessive abstraction, reification, alienation, and so on. On the other side though, there are premature and illegitimate claims that universals can be explained away entirely. But Hegel’s Frau Bauer could not even recognize her individually named cows, if there were no such thing as legitimately reusable reference, naming, and vocabulary. I think most people should be able to see that there are two sides to the coin here.

If we ask how legitimate repeatabilities in ordinary language are constituted and used, something like modality inevitably comes into play. It now occurs to me that Brandom’s emphasis on the priority of hypotheticals over alleged categoricals in real-world material inference — a point to which I am deeply sympathetic — really calls for something like the notion of modality that he develops.

Anaphora and Reason Relations

Applying Brandom’s 2025 concept of reason relations to his 1980 expansion of anaphora, it seems that the new reason relations codify and make explicit the same material inferences that are expressible in terms of anaphoric back-reference between sentences in a non-logical base language. Reason relations are constructed formal objects that are designed to codify an explicit formal representation of the material inferences expressed by anaphora. They provide a conservative extension and explanation of the material inferences expressible in the base language.

Anaphora and Prosentences

This will conclude an examination of Brandom’s early programmatic work “Assertion and Conceptual Roles”. At one point he pithily comments that he is developing an account of saying that does not depend on a prior account of naming. Once again, at a broad level I think that is also something that Aristotle does. Saying viewed this way is more oriented toward valuation than toward representation.

I would suggest that naming is a kind of shorthand for a description or classification that is sufficient to pick something out from other things in the applicable context. What a name cannot be counted on to do is to unambiguously specify an essence or an adequate definition. The very first topic raised in Aristotle’s Categories — which was traditionally placed first in the order of instruction — is “things said in many ways”.

The young Brandom says, “Our strategy now is to use the conditionals we have constructed to develop precise representations of the conceptual contents sentences acquire in virtue of playing a material inferential role in some justificatory system. The most sophisticated use of the notion of a conceptual role has been made by Sellars, who in Science and Metaphysics and elsewhere develops a theory of meaning couched in terms of dot-quoted expressions, where such dot-quotation of an expression results in a term referring to the conceptual (inferential-justificatory) role of that expression” (p. 34).

Every concept worth its salt carries its justification with it. We don’t properly understand an expression if we are unable to justify its use. As Aristotle says, the mark of knowing something is the ability to explain why it is the case. I would maintain that there isn’t any knowing “never you mind how”. The latter is rather the mark of what Plato calls mere opinion.

“According to the present view, it is the defining task of a logic or logical construction that it make possible the explicit codification in a conceptual role of what is implicit in the inferential and justificatory employment of an expression…. [C]onceptual roles in Frege’s and Sellars’ sense can be expressed, using the conditionals of our formal logic not only as the means of expression of roles, but also as providing the model according to which we understand such roles.”

On this view, ordinary if-then reasoning turns out to be a kind of key to understanding meaning. But considerable care is required in working out the details. The conditional that codifies material inferences has different detailed behavior than the common one based on a truth table, and that is a good thing, because the truth table one has significant defects.

“The key to this line of thought is the observation that the only sentences whose roles we understand explicitly are the conditionals. We understand them because we constructed them, stipulating their introduction conditions, and deriving the consequences of such introduction (the validity of detachment)” (ibid).

If-then conditionals allow us to explicitly express the reasons and dependencies that implicitly guide judgment and thought.

“We propose to generalize this clear case, and conceive the mastery of the use of an expression which one must exhibit in order to properly be said to understand it (‘grasp’ its conceptual role) as consisting of two parts, knowing when one is entitled to apply the expression, and knowing what the appropriate consequences of such application are (what justifies using the expression, and what inferences one licenses by so doing). Applying the expression is thus assimilated to performing an inference from the circumstances of appropriate application of the expression to the consequences of its application” (ibid).

But “applying the expression” is just what assertion is. By these lights, every asserting is an inferring.

“On this model, suggested by the later Carnap’s use of partial reduction forms, the conceptual role of any expression is the pair of its circumstances of appropriate application and the consequences of such application, that is, of its (individually) sufficient conditions and of its (jointly) necessary conditions. The application of that expression is to be thought of as an inference from the former to the latter. Assertion thus becomes a limiting case of inference” (p. 35).

It is inference that grounds assertion, not the reverse. Only through inference can anyone understand the significance of an assertion.

“More must be said, however, about the ramifications of taking conditionals to be the models for the conceptual roles of basic sentences, insasmuch as our strategy has been to construct a conditional as stating explicitly (as a license) what is implicit in an inference from its antecedent to its consequent, and then to assimilate the content of basic statements to the model of these constructed conditional statements” (ibid).

“In general, one might think that it was incoherent or circular to define the contents of the categorical sentences of an idiom in terms of the contents of hypothetical sentences of that idiom…. Our construction avoids this worry, since we define conditionals in terms of the contents of basic sentences only in the sense in which those contents are implicit in the informal inferential practices which are the use of the basic sentences.” (pp. 35-36).

Kant already questioned the primitiveness of categorical judgments. My take is that they constitute a form of shorthand for what are really reasonings or interpretations.

“Nor is there anything peculiar about taking a sub-class of sentences as the paradigms to which all others are assimilated in a theory of meaning. Frege, for instance, treats all sentences as implicit identity statements (involving names of the True or the False)…. Thus Frege constructs a theory of meaning based on terms explicated with the logical device of identity, where we base our account on sentences explicated by means of the logical device of conditionals” (p. 36).

Brandom has a complex relation to Frege, championing some of his early work and questioning some of his later work.

“We attempt to give a direct account of saying and what is said which does not appeal to naming and what is named” (ibid).

“This is the essential difference between conceptual role semantics inspired by the sort of concerns articulated by the later Wittgenstein, and referential semantics inspired by Frege” (ibid).

“As Dummett points out, the later Frege broke from previous logicians in treating logic not as the study of inference, but of a special kind of truth…. This view seems to have been motivated by his presentation of logic as an axiomatic system, where some truths are stipulated and other truths are derived from them by a minimum of purely formal inferential principles. The philosophical critique in terms of linguistic practice of the distinction between meaning-constitutive stipulated truths and empirically discovered truths, together with Gentzen’s achievement of parity of formal power between proof-theoretic methods of studying consequence relations and the truth-oriented methods epitomized by matrix interpretations … require us to reassess the relations of explanatory priority between the notions of inference and truth” (p. 36).

Brandom makes a good case for seeing the early Frege as a proto-inferentialist concerned with the formalization of material inference. The later Frege propounded an original and rather strange notion of truth and truth-values as foundational. He held that truth is a (unique) object referred to by all true statements, rather than a property.

“One of Frege’s achievements is his formulation of the principle of semantic explanation, according to which the appropriateness of a form of inference is to be accounted for by showing that it never leads from true premises to conclusions which are not true. The usual way in which to exploit this principle is to begin with an account of truth (typically in representational or referential terms) and partition a space of abstractly possible inferences and forms of inference into those which are appropriate and those which are not appropriate according to the semantic principle, as Frege does in the Begriffschrift. Our approach in effect reverses this order of explanation, beginning analysis with a set of appropriate inferences and explaining semantic interpretants, including truth-values, in terms of them” (pp. 36-37).

The idea of this “principle of explanation” is that sound reasoning from true premises cannot yield a false conclusion. This is not a fact, but a definition that also has characteristics of a Kantian imperative. It is up to us to make it true.

He considers possible objections to the idea of treating hypothetical judgments as more originary than categorical judgments. This should not be taken to apply at the level of truths. In a similar vein, he also says that what our words mean does not determine what we believe.

“Just as it is implausible to take what is possible as determining what is actual, so it is implausible to take the totality of conditional truths as determining the totality of unconditional truths. Indeed, the possession by a formal system of this semantic property would be a strong reason to take its conditional as not a reasonable rendering of the English hypothetical construction ‘if … then’. Embarrassingly enough, the standard truth-functional (mis-named ‘material’) conditional which Frege employs has just this property, namely that if the truth-values of all of the conditionals of the language are settled, then the truth-values of all the sentences of the language are settled. This is proven in Appendix II” (p. 37).

This surprising proof really turns things around. I suppose this result is related to the concerns about “logical omniscience” in classical logic. It is not reasonable to suppose that if a human knows A, then she necessarily knows all the consequences of A. But this is independent of the question of whether we really know anything unconditionally (I tend to think not). There is a also question whether we are properly said to “know” abstract tautologies like A = A, without necessarily knowing what A is (I am inclined to use some other word than knowledge for these cases).

“Our genuine conditional, introduced as codifying a set of non-formal inferences, will not have this undesirable property…. We avoid that result by taking the principle that appropriate inference should never lead from true premises to conclusions which are not true as a necessary, but not sufficient condition for appropriateness of inference. The truth-functional conditional results from taking the principle to provide sufficient conditions as well” (ibid).

Again, this falls within the tradition of alternative, “better” definitions of implication.

“Taking Frege’s semantic explanatory principle as a necessary condition on an account of inferential relations settles that the primary semantic notion will be whatever it is that is preserved by appropriate inferences. Frege calls this ‘truth’, but abstractly there are other properties which could also play this role (e.g., justificatory responsibility) and there are good reasons to expect an adequate semantic theory to account as well for the preservation of ‘relevance’ of some kind by appropriate inferences. This primary semantic notion, however, pertains only to the use of a sentence as a free-standing assertive utterance. A full notion of sentential content must specify as well the role a sentence has as a component in other, compound, sentences, paradigmatically in conditionals. It cannot be determined a priori that these two roles coincide. If with Frege we take the first semantic property to be a truth-value either possessed or not by any sentence, then the assumption that the second or componential notion coincides with the first results in classic two-valued truth-functional logic” (p. 38).

It is noteworthy that even the later Frege’s concern in this context was with “whatever it is that is preserved by appropriate inferences”.

He has previously used the term “designatedness”, which names that “whatever it is that inference preserves” that plays a role in multi-valued logics broadly analogous to that played by truth in two-valued logics.

“[M]any-valued semantics requires the assignment to each sentence of two different sorts of semantic interpretant: a designatedness value indicating possession or lack by a sentence used as a free-standing utterance of the property which appropriate inference must preserve, and a multivalue codifying the contribution the sentence makes to the designatedness value of compound sentences containing it, according to the principle … Two sentences have the same multivalue if and only if they are intersubstitutable salva designatedness value in every sort of compound sentence” (p. 39).

He relates the current development to technical work on the algebraic interpretation of logics.

“A matrix is characteristic for a logic if it verifies just the theorems of that logic. Lindenbaum showed that every logic has a characteristic matrix, namely the one gotten by taking the set of multivalues to be classes of inferentially equivalent sentences, and the designated multivalues to be the theorems of the logic in question” (ibid).

“We are now in a position to notice that a repertoire, together with the partial ordering induced on the sentences of a repertoire by the conditionals contained in its formally expanded consequence extension constitute such a Lindenbaum matrix” (ibid).

The conditional as Brandom has defined it provably meets Frege’s criterion of inference preservation. Brandom has extended algebraic logic to include patterns of material inference.

“Theorem 1 above shows that modus ponens preserves designatedness, that is membership in the extended repertoire. Or, to put the same point another way, that result shows that our constructed conditional satisfies Frege’s semantic explanatory principle when membership in a repertoire is taken as the prime semantic notion, and social practice determines an antecedent class of appropriate material inferences. The formally extended repertoire thus is, in a precise sense, the characteristic semantic matrix not for a logic or a set of formal inferences, but for a set of material inferences” (p. 40).

“There are three specific points which should be made concerning this interpretation. First, what is captured by semantic matrices is taken to be a matter of formal inferences first, and logical truths verified by the matrix only second, although this is not how such matrices are usually thought of. Second, we generalize the notion of a characteristic matrix for a set of formal inferences to apply to material inferences as well. Finally, notice that in addition to the structure of material inference codified in each repertoire-matrix we can in fact identify a logic with regard to the whole idiom, insofar as some complicated conditionals will appear in all repertoires. We have not constructed a characteristic matrix for this logic by ordering the sentences of the language according to repertoire-designated conditionals. In some ways it is accordingly more appropriate to say that each repertoire expresses a single matrix valuation characteristic of a set of material inferences, and that the whole idiom comprising all admissible repertoires is characteristic of the formal or logical inferences involving the conditional we used to make explicit the materially appropriate inferences” (ibid).

“In this way, then, we can exploit Frege’s semantic explanatory principle and the truth-oriented matrix semantics it inspired as theoretical auxiliaries useful in the formal analysis of a socially specified set of appropriate inferences” (ibid).

“Seeing logic in the way I have been recommending, however, as a formal tool for the explicit expression of inferential roles, obviates the need for appealing to prior notions of truth or truth-value. We have interpreted Frege’s truth-values as they figure in his semantic principle first as the designatedness values of multivalued logic, and then moving from concern with the codification of formal inference to concern with the codification of material inference, interpreted as expressing membership in a repertoire. Recalling the social practical origins of these repertoires, it would be appropriate to call the two circumstances of membership and non-membership in a particular repertoire assertibility values with respect to that repertoire. We have given a much more precise sense to this term than semantic theorists who advocate the primacy of assertibility over truth typically manage to do, however” (pp. 40-41).

“We represent the matrix valuation on the language induced by a formally expanded repertoire by associating with each sentence its repertoire-relative conceptual role, consisting of inferential circumstances and consequences of assertion. It is clear that this is an adequate representation in that this set of roles, together with the repertoire generating them, determines the partial order of the language by the conditional which is the Lindenbaum matrix. These conceptual roles are thus taken as multivalues, with repertoire membership identified as designatedness with respect to the semantic principle. The multivalues must, of course, determine compounding behavior according to our motivation…. It is … a criterion of adequacy of this representation that sentences with the same conceptual role, that is, multivalue, should be intersubstitutable in conditionals preserving both designatedness values and multivalues” (p. 41).

So far he has focused on a notion of the conditional that is a primitive “arrow” rather than something defined by a truth table. He briefly considers how to define other connectives that work off of the designatedness that plays a truth-like role in multi-valued logics, but again affirms the special importance of conditionals.

” ‘Truth-functional’ connectives can now be introduced using designatedness values as the extensions of sentences…. We would like to be able to semantically interpret all forms of sentence compounding by means of functions taking conceptual roles, or sets of them, into conceptual roles, as we can do for conditionals…. Our use of the conditional as both the model of and a tool for the expression of conceptual roles embodies the belief that the contribution a sentence makes to the roles of conditional it is a component in suffices to determine its role in other compounds” (p. 42).

He quotes Frege saying that the kernel of the problem of judgment splits into that of truth and that of what he calls “a thought”, which refers to some declarative content. Given Frege’s unitary view of “truth”, this thought-content identified with saying and conceptual roles has to be responsible for all differentiation.

“By a thought, Frege makes clear, is intended what is referred to in English by that-p clauses. We have identified these judged contents as conceptual roles. In what follows, we try to exhibit a representative variety of uses of such that-p clauses in terms of conceptual roles” (p. 43).

Finally we come to prosentences.

“Our starting point is the prosentential theory of truth of Grover, Camp, and Belnap. That account can best be sketched as the product of three different lines of thought: i) the redundancy theory of Ramsey and others, which says that the conceptual content of ‘it is true that-p‘ is always just the same as that of p…. ii) an account of truth in terms of infinite conjunctions and disjunctions…. [T]he best succinct statement of this view is in Putnam’s Meaning and the Moral Sciences…. ‘If we had a meta-language with infinite conjunctions and infinite disjunctions (countable infinite) we wouldn’t need “true”!…. [F]or example, we could say … “He said ‘P₁‘ & P₁” (ibid).

“iii) Finally, and this is what is distinctive to the view under discussion, it is observed that pronouns serve two sorts of purposes. In their lazy use, … they may simply be replaced by their antecedents (salva conceptual role). In their quantificational use, as in ‘Each positive number is such that if it is even, adding it to 1 yields an odd number’, the semantic role of the pronoun is determined by a set of admissible substituends (in turn determined by the pronomial antecedent)” (p. 44).

“Thus ‘Everything he said is true’ is construed as a quantificational prosentence, which picks up from its anaphoric antecedent a set of admissible substituends (things that he said), and is semantically equivalent to their conjunction” (ibid).

“The authors of the prosentential theory are concerned that ‘is true’ be taken to be a fragment of a prosentence, not a predicate which characterizes sentence-nominalization…. The authors are worried that if the first part of a sentence of the form ‘X is true’ is taken to be a referring sentential nominalization that, first, ‘is true’ will inevitably be taken to be a predicate, and second, the anaphoric prosentential reference of the whole sentence will be passed over in favor of the view that the nominalization does all the referring that gets done, and would vitiate the view” (p. 45).

“In fact this is a situation in which we can have our cake and eat it too. We consider ‘X is true’ as composed of a sentence nominalization X which refers to sentences, and a prosentence-forming operator ‘is true’.” (ibid).

“Our construction of conceptual roles in terms of conditionals of course presents natural criteria of adequacy for translation functions between repertoires contained in a single idiom, or which are members of different idioms” (p. 51).

“We show now how those semantic facts about the idiom can be expressed explicitly as the content of claims made within that idiom. We use the logical vocabulary of conditionals and repertoire attributions we have already constructed to define a further bit of expressive machinery, that-clauses, which will thus have a logical function in making explicit semantic features implicit in the idiom” (p. 53).

“[T]he account of conceptual roles is novel in being entirely non-representational. In the formal idiom we develop, it is not a necessary feature of a saying that-p that the sentence involved represent some state of affairs. Of course sentences used to say things may also be representations, and this fact might be crucial for the understanding of the use of language in empirical inquiry. But our model is broader, and we may hope that it can find application in the explication of other forms of discourse (e.g., literary and political discourse) where the representational paradigm is less apt than it perhaps is for scientific idioms” (p. 55).

“Perhaps the most important feature of our account is the crucial place given to logic, as providing the formal means by which an idiom can come to express explicitly crucial semantic facts which are implicit in the system of justificatory practices which are the use of a language. We argued that the function thus assigned to logic as a formal auxiliary in a theory of meaning is that which Frege originally envisioned and pursued. Our own development looked at he codification of inferential practices in conditionals in some detail, and somewhat less closely at the codification of repertoires in prosentences containing ‘is true’ and in propositional attitudes, and at the codification of roles in ‘that’-clauses. The basic claim here is that logic must not be restricted to the analysis of the meanings sentences acquire in virtue of the formal inferences they are subject to, as is the usual procedure). Logic should not be viewed as an autonomous discipline in this way, but as a tool for the analysis of material inference, and for making explicit the roles played by sentences in systems of material inferential practice. Using logical devices so interpreted, we were able to specify not only what role a performance needs to play in a system of social practices in order to be a saying (asserting, professing, claiming, etc.) that-p, but also to show what it is about that system of practices in virtue of which the content of such a saying can be that someone else has said (asserted, etc.) something. Indeed the only sort of ‘aboutness’ we ever employ is the reference of one bit of discourse to another (anaphoric reference if performance or sentence tokens are at issue, and mediated by conceptual roles otherwise)” (pp. 55-56).

When Aristotle discusses saying something about something, implicitly that second something is also something said. This phrase refers to that phrase. The kind of reference that is most relevant in all this is what I think of as constitutive cross-reference, or as Brandom calls it, back-reference or anaphora. Less adequately, it has been called “self” reference, but if we examine this closely, it does not involve a unitary self or a pure undifferentiated reflexivity, but rather parts referring to other parts.

Conceptual content emerges out of a sea of cross-reference. A constitutive molecular cross-reference of Fregean declarative “thoughts” or “content” or Aristotelian “sayings” precedes sedimentation into molar subjects and objects.

Epilogue to this series: Anaphora and Reason Relations

Conditionals and Conceptual Roles

Saying something is more than the material fact of emitting sounds in conventionalized patterns. We ought to be able to say more about that “more”.

This is part two of a look at an early programmatic document in which Brandom first develops his highly original approach to meaning and logic. Brandom’s “logical expressivism” treats logic as a tool for explaining meaning, rather than a discipline with its own distinctive subject matter. That logic is such a tool and not a science is an Aristotelian view (or, I would say, insight) that has been mostly ignored by subsequent traditions.

The dominant modern tradition treats meaning as representation by pointing or reference. But pointing is rather trivial and uninformative. By contrast, I normally think of meaning in terms of something to be interpreted. But this hermeneutic approach tends to focus attention on concrete details. Brandom ambitiously wants to say meaningful things about meaning in general, and I think he succeeds.

As in the first installment, I will continue to focus on the discursive parts of the text, while skirting around the formal development. (There is more formal logical development in this text than anywhere else in Brandom’s corpus, at least until this year’s publication of the collaborative work Reasons for Logic, Logic for Reasons, which returns to the current text’s aim of implementing his program of logical expressivism.)

Brandom begins with the early work of Frege, who pioneered modern mathematical logic.

“To make out the claim that the systems of social practices we have described implicitly define assertion, we need to supplement that account of assertings with a story about the contents which are thereby asserted. Our starting point is Frege’s discussion in the Begriffschrift, where the distinction between force and content was first established…. First, Frege identifies conceptual content with inferential role or potential. It is his project to find a notation which will allow us to express these precisely. Second, sentences have conceptual contents in virtue of facts about the appropriateness of material inferences involving them. The task of the logical apparatus of the conceptual notation which Frege goes on to develop is to make it possible to specify explicitly the conceptual contents which are implicit in a set of possible inferences which are presupposed when Frege’s logician comes on the scene. The task of logic is thus set as an expressive one, to codify just those aspects of sentences which affect their inferential potential in some pre-existing system” (“Assertion and Conceptual Roles”, p. 21).

Meaningful “content” is to be identified with the inferential roles of things said, which are each in turn defined by the pair consisting of the conditions of their application and the consequences of their application. The novelty of what is expressed here is tactfully understated by the reference to “facts” about the appropriateness of material inferences. This tends to downplay the “fact” that the inquiry into conditions of application is really a normative inquiry into judgments about appropriateness more than an inquiry into facts.

What is being said here also needs to be sharply distinguished from the nihilistic claim that there are no facts. There are facts, and they need to be respected. The point is that this respect for facts ought to be opposed to taking them for granted.

“We will derive conceptual contents from the systems of practices of inference, justification, and assertion described above. Following the Fregean philosophy of logic, we do so by introducing formal logical concepts as codifications of material inferential practices. First we show how conditionals can be introduced into a set of practices of using basic sentences, so as to state explicitly the inference license which the assertion of one sentence which becomes the antecedent of the conditional can issue for the assertion of another (the consequent of the conditional). With conditionals constructed so as to capture formally the material inferential potential of basic sentences, we then show how conceptual contents expressed in terms of such conditionals can be associated with basic sentences on the model of the introduction and elimination rules for compound sentence forms like the conditional” (ibid).

Introduction and elimination rules are characteristic of the natural deduction and sequent calculi due to Gentzen. This style of formalization — common in proof theory, type theory, and the theory of programming languages — is distinctive in that it is formulated entirely in terms of specified inference rules, without any axioms or assumed truths.

Until Sellars and Brandom, modern logic was considered to be entirely about formal inference. Brandom argues that the early Frege correctly treated it instead as about the formalization of material inference. Brandom also endorses Quine’s logical holism against atomistic bottom-up views like that defended by Russell.

“We cannot in general talk about ‘the consequences’ of a claim (for instance, that the moon is made of green cheese) without somehow specifying a context of other claims against the background of which such consequences can be drawn. (Can we use what we know about the mammalian origins of cheese and take as a consequence that at one time the moon was made of milk, for instance?) Quine, in “Two Dogmas [of Empiricism]”, may be seen as arguing against the possibility of an atomistic theory of meaning (e.g. one which assigns to every sentence its ‘conceptual content’) that such meanings must at least determine the inferential roles of sentences, and that the roles of each sentence in a ‘web of belief’ depends on what other sentences inhabit that same web. In particular, whether anything counts as evidence for or against a certain claim … depends on what other sentences are held concurrently. Given any sentence, … and given any second sentence there will be some webs in which the second counts as evidence for the first, and some where it counts as evidence against the first, where what ‘web of belief’ is considered determines what other sentences are available as auxiliary hypotheses for inferences. Accepting the general Fregean line that meanings as theoretical constructs are postulated to express inferential potentials, Quine reminds us of basic facts about our inferential practices … to impugn the comprehensibility of assignments of conceptual role to individual sentences, unrelativized to some doxastic context. Conceptual roles can only be specified relative to a set of other sentences which are all and only those which can be used as auxiliary hypotheses, that is, as Quine puts it, at the level of whole theories-cum-languages, not at the level of individual sentences” (pp. 22-23).

Much of the ensuing discussion will revolve around conditionals, and what logicians call the implicational fragment of a logic, in which only implication is considered. This is a kind of minimal form for what constitutes a logic — if you specify a notion of implication, you have a logic. But the common modern truth-table definition of implication has been criticized from many quarters. Much work has been done on the precise definition of alternate or “better” notions of implication. This is one of the things Brandom will be doing here.

One of the most important questions about implication is whether it is “primitive” — i.e., something in terms of which other things are defined, which is itself considered to be defined only operationally (indirectly, by its use) — or whether it is to be defined in terms of something else, such as a truth table. For instance, category theory (by which all of mathematics can be interpreted) can be elaborated entirely in terms of primitive “arrows” or morphisms, which generalize both the notion of a mathematical function and that of logical implication. Arrow logics, which generalize modal logic, also start from a primitive notion of arrows. Later in this text, Brandom will develop his own notion of arrows as a primitive, alternate form of implication.

In the context of the debate about holism and atomism, it is interesting to consider the scholastic practice of debating for and against individual propositions. At top level, it seems atomistic, in that the propositions are taken up one at a time. But at a detailed level, the arguments turn out to be mostly about the consequences of accepting or rejecting the proposition under discussion. Brandom will argue that propositions are to be understood by the combination of their consequences and their conditions of appropriate use.

He turns to the question of what assertion is. The novelty here is that assertion will be explained in terms of primitive conditionals, rather than treated as primitive.

“The first step in our account of the semantic contents or conceptual roles sentences acquire in virtue of being used according to the practices expressed in some idiom is the introduction of some logical vocabulary. We understand the inference-licensing function of assertion by our model of justificatory systems of social practices. We will introduce the conditional as a compound sentence-form constructed out of the basic sentences on which some idiom is defined. The conceptual content of the conditionals will be stipulated; a sentence of the form p→q is to have as content the inference-license of a statement of the appropriateness of an inference from the assertion of p to the assertion of q. Various formal inferential connections between such conditional sentences will then be elicited. For these formal principles to comprise a logic is for them to make possible the explicit formal codification of the material inferential and justificatory practices of some conceptual idiom. This is the task Frege sets for logic in the Begriffschrift — although in that work he succeeded only in completely codifying the formal inferences involving his logical constructions, his discussion makes clear that the ultimate criterion of adequacy for his conceptual notation is its capacity to express explicitly and precisely the contextual material inferences which define the conceptual roles of non-logical sentences” (p. 23).

We see here too some of the motivation for focusing on compound sentences — all sentences that include explicit conditionals are compound. But according to his analysis, it will turn out that simple sentences of the form “A is B” implicitly express a sort of minimal form of material inference.

I would suggest that the allegedly unconditional or categorical judgment “A is B” is best understood as a kind of shorthand for a judgment like A(x)→B(x). Aristotle’s concern with sayings leads him to treat the sentences that express propositions in a non-atomic way. He glosses “A is B” as expressing “combination” and “A is not B” as expressing “separation”. I have suggested that “combination” could be read as a relation of material consequence, and “separation” as a relation of material incompatibility. This means that for Aristotle too, a proposition can be considered a kind of minimal material inference. (See Aristotelian Propositions.)

“Once the conditional has been introduced as codifying the consequence relation implicit in material inferential practice, and its formal logical properties have been presented, we will use such conditionals both as models for the conceptual roles of non-logical sentences (which will have analogues of introduction and elimination rules, and will be given content as licensing inferences from their circumstances of appropriate application to the consequences of such application) and as tools for making those roles explicit” (ibid).

Treating conditionals as models for the conceptual roles of simple “non-logical” sentences like “A is B” begins from the intuition that these simple assertions are the potential antecedents or consequents of inferences, and that this role in possible inferences is what gives them specifiable meaning.

“We may think of the relation between basic and extended repertoires in a conceptual idiom as defining a consequence function on admissible sets of sentences. For the extended repertoire … comprises just those sentences which an individual would socially be held responsible for (in the sense that the relevant community members would recognize anaphoric deference of justificatory responsibility for claims of those types to that individual) in virtue of the dispositions that individual displays explicitly to undertake such responsibility for the sentences in his basic repertoire. The extended repertoire consists of those claims the community takes him to be committed to by being prepared to assert the claims in his basic repertoire. These community practices thus induce a consequence function which takes any admissible basic repertoire and assigns to it its consequence extension. The function only represents the consequences of individual sentences relative to some context, since we know what the consequences are of p together with all the other sentences in a basic repertoire containing p, but so far have no handle on which of these various consequences might ‘belong’ to p. Thus we have just the sort of material inferential relations Frege presupposes when he talks of the inferences which can be drawn from a given judgment ‘when combined with certain other ones’…. The idiom also expresses a material consistency relation…. The sets which are not idiomatically admissible repertoires are sets of sentences which one cannot have the right simultaneously to be disposed to assert, according to the practices … of the community from which the idiom is abstracted. The final component of a conceptual idiom as we have defined it is the conversational accessibility relation between repertoires” (pp. 23-24).

The accessibility relation will turn out to correspond to whether a sentence makes sense or is categorial nonsense like “Colorless green ideas sleep furiously”.

“Given such an idiom defined on a set of non-logical sentences, we will add conditional sentences p → q to each of the consequence-extended repertoires in which, intuitively, p is inferentially sufficient for q, in such a way that the newly minted sentences have the standard inferential consequences of conditionals such that this formal swelling of the original repertoires is inferentially conservative, that is does not permit any material inferences which were not already permitted in the original idiom” (p. 24).

He defines an idiom as a triple consisting of a set of sets of sentences or basic repertoires, a function from basic repertoires to their consequence extensions, and a function from repertoires to the other repertoires “accessible” from each.

“Recalling the constitutive role of recognitions by accessible community members in determining consequence relations, we may further define p as juridically (inferentially) stronger than q at some repertoire R just in case p is actually stronger than q at every repertoire S accessible from R. This natural modal version of inferential sufficiency will be our semantic introduction rule for conditional sentences…. The conditional thus has a particular content in the context of a given repertoire, a content determined by the inferential roles played by its antecedent and consequent” (p. 25).

“We must show that the important formal properties of idioms are preserved by the introduction of conditionals, and that the conditionals so introduced have appropriate properties. In order to permit sentences with more than one arrow in them, we must swell the basic idiom with conditionals first, and then iterate the process adding conditionals which can have first-order conditionals as antecedents or consequents, and so on, showing that the relevant properties of conceptual idioms are preserved at each stage. Our procedure is this. Starting with a basic idiom …, we define a new idiom … with repertoires defined not just over the original set of non-logical sentences, but also containing first-order conditionals, as well as consequence and accessibility relations between them. The same procedure is repeated, and eventually we collect all the results” (ibid).

“The properties of conceptual idioms which must be preserved at each stage in this construction are these. First is the extension condition, that for any admissible repertoire R, R [is a subset of its consequence extension]. The motive for this condition is that the consequence extension c(R) of R is to represent those claims one is taken to be committed to in virtue of being prepared explicitly to take responsibility for the members of R, and certainly one has committed oneself to the claim one asserts, and licenses the trivial inference which is re-assertion justified by anaphoric deferral to one’s original performance. Second of the properties of conceptual idioms which we make use of is the interpolation condition, which specifies that any basic repertoire R which can be exhibited as the result of adding to some other repertoire S sentences each of which is contained in the consequence extension of S, has as its consequence extension c(R) just the set c(S).” (pp. 25-26).

“The idempotence of the consequence function, that for all [repertoires in the domain], c(c(R)) = c(R), is a consequence of the interpolation property. Of course this is a desirable circumstance, since we want idempotence in the relation which is interpreted as the closure under material inference (as constituted by social attributions of justificatory responsibility) of admissible basic repertoires” (p. 26).

“The consequence relation is contextual, in that a change in the total evidence which merely adds to that evidence may entail the denial of some claims which were consequences of the evidential subset. Allowing such a possibility is crucial for codifying material inferential practices, which are almost always defeasible by the introduction of some auxiliary hypothesis or other…. [B]oth ‘If I strike this match, it will light’, and ‘If I strike this match and I am under water, it will not light’, can be true and justified. Denying monotonicity (that if [one repertoire is a subset of another], then [its consequence extension is a subset of the consequence extension of the other]) forces our logic to take account of the relativity of material inference to total evidence at the outset, with relativity to context made an explicit part of the formalism instead of leaving that phenomenon to the embarrassed care of ceteris paribus [other things being equal] clauses because standard conditionals capture only formal inference, which is not context-sensitive” (p. 27).

Real things are in general sensitive to context, whereas formal logical tautologies are not.

Monotonicity is a property of logics such that if a conclusion follows from a set of premises, no addition of another premise will invalidate it. This is good for pure mathematics, but does not hold for material inference or any kind of causal reasoning, where context matters. The match will light if you strike it, but not if you strike it and it is wet, and so on.

“We are now in a position to investigate the logic of the arrow which this formal, non-substantive expansion of the basic idiom induces. To do so, we look at the sentences which are idiomatically valid, in that every repertoire in the formally expanded idiom contains these sentences in its consequence extension. First, and as an example, we show that if p is in some consequence-extended repertoire, and p→q is also in that repertoire, then so is q, that is, that modus ponens is supported by the arrow” (p. 29).

What he calls a basic repertoire is defined by some set of simple beliefs, assumptions, or presumed facts, with no specifically logical operations defined on it. Non-substantive expansion leaves these unchanged, but adds logical operations or rules.

At this point he proves that modus ponens (the rule that p and (p implies q) implies q, which he elsewhere refers to as “detachment” of q) applies to the conditional as he has specified it. Additional theorems are proved in an appendix.

“[T]he most unusual feature of the resulting logic is its two-class structure, treating conditionals whose antecedents are other conditionals rather differently from the way in which it treats conditionals involving only basic sentences. This feature is a direct consequence of the introduction of first-order conditionals based on material inferential circumstances of the repertoire in question, and higher-order conditionals according to purely formal, materially conservative criteria. Thus it is obvious from inspection of the … steps of our construction of the hierarchy of conditionals that the complement of basic sentences in a consequence extended repertoire is never altered during that construction, and that the novel repertoires introduced always have first-order restrictions which are elements of the original set…. Higher-order conditionals, of course, are what are added to the original idiom, and … those conditionals obey a standard modal logic. The principles governing conditionals with basic sentences as antecedents or consequents, however, are those of the pure implicational fragment of Belnap and Anderson’s system EI of entailment” (ibid).

Belnap and Anderson worked on relevance logic, which restricts valid inference to the case where premises are relevant to the conclusion. The premises of a material inference are always “relevant” in this sense. Formal inference on the other hand doesn’t care what the underlying terms or propositions are. It is entirely governed by the abstractly specified behavior of the formal operators, whereas material inference is entirely governed by the “content” of constituent terms or propositions.

That there would be two distinct kinds of conditionals — first-order ones that formally codify material inferences, and higher-order ones that operate on other conditionals in a purely formal way — seems consonant with other cases in which there is a qualitative difference between first-order things and second-order things, but no qualitative difference between second-order and nth-order for any finite n.

“We may view the conditionals which end up included in the consequence extensions of formally extended repertoires as partially ordering all of the sentences of the (syntactically specified) language. Since according to our introduction rule, a repertoire will contain conditionals whose antecedents and consequents are not contained in that (extended) repertoire, the ordering so induced is not limited to the sentences of the repertoire from which the ordering conditionals are drawn. Although the conditional induces an appropriately transitive and reflexive relation on the sentences of the language, the ordering will not be total (since for some p, q and R [in the domain], it may be that neither p→q nor q→p is in c(R)), and it will not be complete, in that sentences appearing only in inaccessible repertoires will have only trivial implication relations (e.g. p→p)” (ibid).

“The conditionals which do not have antecedents in c(R) are counterfactual with respect to R. These are of three kinds: i) those taken true by the theory codified in the repertoire, that is, counterfactuals in c(R), ii) those taken not to be true, i.e. conditionals not in c(R) but on which R induces non-trivial entailments, and iii) inaccessible counterfactuals, assigned no significance by the extended repertoire (e.g. ‘If the number seventeen were a dry, well-made match’, an antecedent generating counterfactuals which, with respect to a certain set of beliefs or repertoire simply makes no sense). Entailment relations between counterfactuals of the first two kinds and between each of them and base sentences will be underwritten by the induced partial ordering, all depending on the original material inferential practices involving only base sentences” (pp. 29-30).

There are many counterfactuals that we take to be true. For example, if I had left earlier, I would have arrived earlier. In fact counterfactuals are essential to any truth that has any robustness. Without counterfactuals, what Brandom is calling an idiom could apply only to some exactly specified set of facts or true statements. This would makes it very brittle and narrowly applicable. For example, any kind of causal reasoning requires counterfactuals, because causes are expected to operate under a range of circumstances, which by definition cannot all hold at the same time. Counterfactuals play an important role in Brandom’s later work.

“The repertoire which induces such a partial ordering by its conditionals will then be a distinguished subset of the sentences it orders, one which Theorem 1 assures us is deductively closed under modus ponens. Each repertoire is in short a theory or set of beliefs, embedded in a larger linguistic structure defining the implications of the sentences in that theory. Not only do different repertoires codify different theories, but they assign different significances to syntactically type-identical sentences of those theories, in that p as an element of c(R) may have one set of inferential consequences, and as an element of c(R’) have a different set of consequences. The repertoires ordered by their indigenous implication relations thus deserve to be called ‘webs of belief’ in Quine’s sense, as the smallest units of analysis within which sentences have significance. The idiom, comprising all of these repertorial structures of implicational significance and embedded belief, is not a set of meanings common and antecedent to the repertoires, but is the structure within which each such web of belief is a linguistic perspective made possible by a justificatory system of social practices” (p. 30).

Each repertoire counts as a “theory” or set of beliefs.

“The systematic variation of the significance of those sentences from one individual to another expressed in a formally expanded idiom then exactly answers to whatever communication is going on in the original set of practices. The possibility of communication consists in [a] kind of coordination of significances across repertoires codified in a formally expanded idiom” (p. 31).

The success or failure of communication depends on something like a kind of translation from your repertoire to mine.

“We have described the practical origins and effects of elements of extended repertoires which are first-order sentences of the language, in terms of attributions and undertakings of justificatory responsibility and the issuing and recognition of inferential authority. What, in these terms, should we take to be the significance of a conditional p→q? The presence of such a conditional in the formally expanded consequence extension of the repertoire exhibited by an individual should signify, first, that that individual recognizes others who are prepared to assert p as licensing the inference to q, and, second, that he recognizes the assertion of p as justifying the assertion of q” (p. 32).

“So if all those recognized by the individual exhibiting R are responsible for the conditional p→q and p [is in] c(R), then q [is in] c(R), which means that p→q plays the proper role as codifying the recognition of inferential licensing and appropriate justification of q by p” (ibid).

“Finally, we state a more general condition under which the arrow we have defined will be a practically complete expression of a justificatory system” (ibid).

Next in this series: Anaphora and Prosentences

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

Reason Relations

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

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

This notion of reason relations is already quite fascinating.

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

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

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

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

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

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

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

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

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

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

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

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

Next in this series: Implication Spaces

The Role of Reasons

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Next in this series: An Isomorphism

Identity, Difference, Reflection

Reflection is also the key to Hegel’s often misunderstood views on identity and difference.

“Reflection is the shining of essence within itself. Essence, as infinite immanent turning back is not immediate simplicity, but negative simplicity; it is a movement across moments that are distinct, is absolute mediation with itself. But in these moments it shines; the moments are, therefore, themselves determinations reflected into themselves” (Hegel, Logic, di Giovanni trans., p. 354, emphasis in original).

He goes on to discuss identity, difference, and the notorious “contradiction” as principal moments or determinations of reflection. Sometimes he uses these terms in the conventional way — of which he is highly critical — and sometimes he gives them his own meaning.

On Aristotelian grounds, I have long had doubts about appeals to an implicitly immediate simplicity or “identity” of substance in traditional metaphysics. I take these to be a form of Platonizing that originated in the neoplatonic commentaries on Aristotle. Hegel’s alternative suggestion of a “negative simplicity” seems much more plausible generally, as well as more consistent with the Aristotelian texts. We just have to get past the difficulty of Hegel’s idiosyncratic metaphorical straining of language about “negation”, and recognize that he is inventing ways to talk about the limits of representation, rather than grossly abusing the “classical” negation of formal logic.

Hegel’s remarks about identity are actually pretty clear, and worth quoting at length. As with negation, in Hegel identity, difference, and “contradiction” only have the meanings that they have in classical logic when he is pointing out their limitations. The alternative meanings that he actually endorses deeply reflect his critique of representationalism.

“In its positive formulation, A = A, [the principle of identity in classical logic] is at first no more than the expression of empty tautology. It is rightly said, therefore, that this law of thought is without content and that it leads nowhere. It is thus to an empty identity that they cling, those who take it to be something true, insisting that identity is not difference but that the two are different. They do not see that in saying, ‘Identity is different from difference’, they have thereby already said that identity is something different. And since this must also be conceded as the nature of identity, the implication is that to be different belongs to identity not externally, but within it, in its nature. — But, further, inasmuch as these same individuals hold firm to their unmoved identity, of which the opposite is difference, they do not see that they have thereby reduced it to a one-sided determinateness which, as such, has no truth. They are conceding that the principle of identity only expresses a one-sided determinateness, that it only contains formal truth, truth abstract and incomplete. — Immediately implied in this correct judgment, however, is that the truth is complete only in the unity of identity and difference, and, consequently, that it only consists in this unity. When asserting that formal identity is incomplete, there is vaguely present to one’s mind the totality, measured against which that identity is incomplete; but the moment one insists that identity is absolutely separate from difference and in this separation takes it to be something essential, valid, true, then what transpires from these two contradictory claims is only the failure to reconcile these two thoughts: that identity as abstract identity is essential, but that, as such, it is equally incomplete. What is lacking is awareness of the negative moment as [that by] which, in these claims, identity itself is displayed. — Or when this is said, that identity is identity essentially as separation from difference or in the separation from difference, then right there we have the expressed truth about it, namely that [formal] identity consists in being separation as such, or in being essentially in the separation, that is, it is nothing for itself but is rather moment of separation.”

“As to the other confirmation of the absolute truth of the principle of identity, this is made to rest on experience in so far as appeal is made to the experience of every consciousness; for anyone presented with this proposition, ‘A is A’, ‘a tree is a tree’, immediately grants it and is satisfied that the proposition is self-evident and in need of no further justification or demonstration.”

“On the one hand, this appeal to experience, that every consciousness acknowledges the principle universally, is a mere manner of speaking. For nobody will want to say that the abstract proposition, ‘A is A’, has actually been tried out in every consciousness. The appeal to actual experience is therefore not in earnest but is rather only an assurance that, if the experiment were made, universal acknowledgement of the proposition would be the result. — And if it is not the abstract proposition as such that is meant, but the proposition in concrete application, from which application the abstract proposition would then have to be developed, then the claim to the universality and immediacy of the latter would consist in the fact that every consciousness assumes it or implies it as a foundation, and indeed does so in every utterance. But the concrete and the application are precisely in the reference that connects simple identity with a manifold which is different from it. Expressed as a proposition, the concrete would be first of all a synthetic proposition. From this concrete itself, or from the synthetic proposition expressing it, abstraction could indeed extract the principle of identity through analysis; but, in actual fact, it would not then leave experience as it is but would have altered it, since in experience the identity was rather in unity with difference. And this is the immediate refutation if the claim that abstract identity is as such something true, for what transpires in experience is the verry opposite, namely identity only united with difference” (pp. 358-359, emphasis in original).

“Identity, instead of being in itself the truth and the absolute truth, is thus rather the opposite; instead of being the unmoved simple, it surpasses itself into the dissolution of itself.”

“More is entailed, therefore, in the form of the proposition expressing identity than simple, abstract identity; entailed by it is this pure movement of reflection in the course of which there emerges the other, but only as reflective shine, as immediately disappearing…. The propositional form can be regarded as the hidden necessity of adding to abstract identity the extra factor of that movement…. Consequently, if appeal is made to what appearance indicates, then the result is this: that in the expression of identity, difference also immediately emerges” (p. 360, emphasis in original).

“From this it is clear that the principle of identity itself, and still more the principle of contradiction, are not of merely analytical but of synthetic nature” (ibid, emphasis in original).

Here he uses Kant’s distinction of analytic from synthetic judgments. Analytic judgments are purely formal and tautological; canonically, the predicate is considered to be literally implied by the subject. Synthetic judgments on the other hand go beyond what is already implied by the subject or premises. This includes most judgments in ordinary experience. Synthetic judgments involve the material inference that Robert Brandom has particularly expounded in recent times.

“Thus the result of this consideration is this: (1) the principle of identity or contradiction, when meant to express merely abstract identity in opposition to difference as a truth, is not a law of thought but expresses rather the opposite of it; (2) these two principles contain more than is meant by them, namely this opposite, absolute difference itself” (p. 361, emphasis in original).

Contradiction and Nonmonotonicity

In standard formal logic, even one pair of contradictory assertions is traditionally deemed to make any possible conclusion vacuously derivable. Ex falso quodlibet, as the scholastics used to say — from a contradiction, anything at all follows. Meaning is thus destroyed.

As an alternative to this, Hegel in the 19th century anticipated what 20th and 21st century logicians and artificial intelligence researchers have called “nonmonotonic” reasoning. In a nonmonotonic setting, a contradiction only invalidates what is contradictorily asserted. Something must still be wrong with one of the contradictory assertions, but the damage does not spread arbitrarily.

“[W]hat is self-contradictory does not resolve itself into a nullity, into abstract nothingness, but essentially only into the negation of its particular content; … such a negation is not just negation, but is the negation of the determined fact…, and is therefore determinate negation ” (Science of Logic, di Giovanni trans., introduction, p. 33, emphasis in original).

Robert Brandom has pointed out that material inference — the kind of reasoning based on meaning that most humans really rely on most of the time — has this nonmonotonic character:

“Gil Harman sharpens the point in his argument that there is no such thing as rules of deductive reasoning. If there were, presumably a paradigmatic one would be: If you believe p and you believe if p then q, then you should believe q. But that would be a terrible rule. You might have much better reasons against q than you have for either of the premises. In that case, you should give up one of them. He concludes that we should distinguish relations of implication, from activities of inferring. The fact that p, if p then q, and not-q are incompatible, because p and if p then q stand in the implication relation to q, normatively constrains our reasoning activity, but does not by itself determine what it is correct or incorrect to do” (Brandom, Reasons: Three Essays on their Logic, Pragmatics, and Semantics, pp. 4-5).

“Monotonicity… is not a plausible constraint on material consequence relations. It requires that if an implication (or incompatibility) holds, then it holds no matter what additional auxiliary hypotheses are added to the premise-set. But outside of mathematics, almost all our actual reasoning is defeasible. This is true in everyday reasoning by auto mechanics and on computer help lines, in courts of law, and in medical diagnosis. (Indeed, the defeasibility of medical diagnoses forms the basis of the plots of every episode of House you have ever seen — besides all those you haven’t.) It is true of subjunctive reasoning generally. If I were to strike this dry, well-made match, it would light. But not if it is in a very strong magnetic field. Unless, additionally, it were in a Faraday cage, in which case it would light. But not if the room were evacuated of oxygen. And so on” (p. 6).

Pure Reason?

Hegel’s “logic” takes what Kant calls pure reason as its subject matter. Hegel regards Kantian pure reason as a world-changing revolution, because in contrast to early modern views, it seeks not to imitate the formal character of mathematical reasoning, but rather to achieve the discipline of a kind of self-sufficiency that does not appeal to anything external to it. Kant and Hegel differ on the scope of this self-sufficiency, but that is a different matter.

Early modern views of the world generally rely on many substantive assumptions. There is strong motivation for them to do so, because in order to yield any substantive conclusions, reasoning of a broadly formal kind requires substantive assumptions. The assumptions are typically of a sort analogous to those that Aquinas regards as grounded in the natural light of reason, which is not itself reason, but a kind of originating intuition of truth given to us by God. Descartes, for example, explicitly appeals to a variant of the Thomistic doctrine of natural light.

(The strong Thomistic notion of the natural light of reason and of reason’s relative autonomy from the simple dictates of authority is itself a development of almost inestimable importance, compared to completely authority-bound views of religion such as present-day fundamentalism. Indeed, something like the natural light of reason was never completely absent from the earlier medieval tradition either.)

But for Kant, reason is purely discursive, and cannot appeal to any intuitive source of truth like a natural light. Pure reason is nonetheless supposed to be able to stand on its own. In Kant’s language, it is “autonomous” (see also Kant’s Groundwork; Self-Legislation?). Kant’s critique of dogmatism especially targets assumptions that are naively realistic in the sense of claiming direct knowledge of external or inner objects, but it is broader than that.

Kant in the Critique of Pure Reason is most directly responding to empiricist views broadly associated with Locke, which were dominant in England and France, and popular in Germany in his day; but even more so to the rationalist system of Christian Wolff (1679-1754), which then dominated German academic teaching. (Wolff was an accomplished mathematician who had corresponded with Leibniz, and greatly contributed to popularizing the part of Leibniz’s philosophy that Leibniz had published in his own lifetime. Like Leibniz, he is associated with moderate Enlightenment, while at the same time showing a degree of sympathy for scholastic philosophy.)

Kantian pure reason effectively aims to be free of unnecessary assumptions, especially those of the Wolffian system, but also those of the empiricists. Kant also criticizes Wolff’s and Spinoza’s idea that philosophical reasoning should as much as possible resemble mathematical reasoning. What makes it possible for Kant to avoid assumptions beyond the famous “God, freedom, and immortality” (and for Hegel to avoid any assumptions at all) is a move away from the early modern ideal of reason as formal.

Without ever explicitly saying so, Kant in fact takes up and works with a notion of reason that is close to aspects of Plato and Aristotle that were generally neglected in the intervening tradition. Reason in Plato, Aristotle, Kant, and Hegel is not limited to formal reasoning. It includes what in more recent times Sellars and Brandom have elaborated under the name of material inference.

Formal reasoning is called formal because it is supposed to apply to all things, independent of any analysis of meaning. But this makes it dependent on assumptions in order to yield conclusions. Material inference — which was also present as a minor theme in scholastic logic — is on the contrary grounded in the interpretation of meaning. It is this reflective grounding that can enable reason to be autonomous and “pure”, with no reliance on anything external to it.

Sellars illustrates material inference with examples like “there are dark rain clouds in the sky, so I should take my umbrella when I go out”. Brandom elaborates with an account of how such judgments may be successively refined based on additional information. In general, if I strike a match correctly, it will light. But under certain conditions, it will not light. But under yet more specific additional conditions, it will in fact still light.

Both Sellars and Brandom — working within the tradition of contemporary analytic philosophy — tend to reach for examples that involve empirical facts, and relations of cause and effect in the broad modern sense. But material inference is more general than that. It is grounded in meaning as we encounter it in real life. Its scope is not limited to any particular kind of meaning, nor does it assume any particular theory of meaning.

Pure reason, then — far from excluding meaning, as formal logic does — is concerned with the progressive self-clarification of meaning — or Kantian “taking as”, or judgment — in a reflective context.

For Hegel, “logic is to be understood as the system of pure reason, as the realm of pure thought” (Science of Logic, di Giovanni trans., introduction, p. 29). This is what he calls the “concept of science”, and also “absolute knowledge” (p. 28). As I’ve pointed out before, in Hegel these terms have specialized meanings that are far from their ordinary connotations in English. Science need not be empirical, and “absolute” in this context just means the same thing as “pure” or “autonomous” — that reflective judgment need presuppose nothing outside itself.

For Hegel, the standpoint of pure reason (or “science”, or “absolute” knowing) is that of reflective judgment. The whole effort of the Phenomenology of Spirit is required to reach this point, which he then uses as a starting point in the Logic.

“Pure science thus presupposes the liberation from the opposition of consciousness [between itself and its object]…. As science, truth is pure self-consciousness as it develops itself and has the shape of a self, so that that which exists in and for itself is the conscious concept and the concept as such is that which exists in and for itself” (p. 29, emphasis in original).

The reflective concept has the shape of a “self” — a reflexivity — that is not to be identified with our empirical self, but rather is related to the reflective character of self-consciousness, which overcomes the simple opposition between consciousness and its object.

“This objective thinking is thus the content of pure science. Consequently, far from being formal, far from lacking the matter for an actual and true cognition, it is the content which alone has absolute truth” (ibid).

He calls reflective judgment objective thinking, precisely because it begins only after the separation of consciousness from its object ends. Reflective judgment and self-consciousness will not be separated from “the concept” in which they are embodied. Rather, we have here a case of the Aristotelian identity of pure thinking with what it thinks.

“Logic has nothing to do with a thought about something which stands outside by itself as the base of thought; nor does it have to do with forms meant to provide mere markings of the truth; rather, the necessary forms of thinking, and its specific determinations, are the content and the ultimate forms of truth itself.”

“To get at least some inkling of this, one must put aside the notion that truth must be something tangible. Such tangibility, for example, is carried over even into the ideas of Plato which are in God’s thought, as if they were, so to speak, things that exist but in another world or region, and a world of actuality were to be found outside them which has a substantiality distinct from those ideas and is real only because of this distinctness” (pp. 29-30).

Truths are not objects, and they are not given to us in the way that ordinary consciousness takes objects to be. For Hegel, moreover, spiritual values do not have to do with turning away from this world in favor of another one. They are intended to guide us in life.

“There will always be the possibility that someone else will adduce a case, an instance, in which something more and different must be understood by some term or other” (p. 28).

Reflection and interpretation are inherently open-ended.

“How could I possibly pretend that the method that I follow in this system of logic, or rather the method that the system itself follows within, would not be capable of greater perfection, of greater elaboration of detail? Yet I know that it is the one true method. This is made obvious by the fact that this method is not something distinct from its subject matter and content — for it is the content in itself, the dialectic which it possesses within itself, which moves the subject matter forward. It is clear that no expositions can be accepted as scientifically valid that do not follow the progression of this method and are not in tune with its simple rhythm, for it is the course of the fact [Sache] itself” (p. 33).

Translator di Giovanni comments in his glossary, “In non-technical contexts, [Sache] can and should be translated in a variety of ways, such as ‘substance’, or even ‘thing’. As category, however, ‘fact’ seems to be the best rendering. Sache, like ‘fact’, denotes a thing or a situation which we understand to implicitly contain all the factors required for an explanation of its existence. Its presence therefore cannot be doubted even when those factors have yet to be made explicit. The related word, Tatsache, was first coined… in order to translate the English term ‘matter of fact'” (pp. lxxi-lxxii).

To me, these sound like reasons for calling Hegel’s Sache something other than “fact”. Especially in a work of “logic” that invokes “science”, the English word “fact” would most commonly be taken taken to mean an unambiguous empirical truth. Both what I think Hegel means and the explanation di Giovanni gives of it seem better suited by the more open connotations of an English phrase like “the concrete case” or “the matter at hand”. The Sache is something objective, but it is objective in the indefinite sense of a Gegenstand [“object” in the sense of something standing over and against us, but whose nature has yet to be determined].

I used to think that reason that would be applicable to life (or to anything like Hegel’s Sache) could not possibly be pure. I now think that with the inclusive character of reflective judgment and material inference, it can be pure.