Tag: Assertion

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

What Meaning Is

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Next in this series: Conditionals and Conceptual Roles

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

Habermas on Intersubjectivity

“The formal-pragmatic approach to meaning theory begins with the question of what it means to understand an utterance — that is, a sentence employed communicatively. Formal semantics makes a conceptual cut between the meaning [Bedeutung] of a sentence and the meaning [Meinung] of the speaker, who, when he uses the sentence in a speech act, can say something other than it literally means” (Habermas, Theory of Communicative Action vol. 1, p. 297).

His use of the adjective “formal” seems chosen to contrast with “empirical”. Pragmatics comes out looking better than semantics. Unlike Brandom, he does not also invent a new semantics to complement his new pragmatics.

“We understand a speech act when we know what makes it acceptable. From the standpoint of the speaker, the conditions of acceptability are identical to the conditions for his illocutionary success. Acceptability is not defined here in an objectivistic sense, from the perspective of an observer, but in the performative attitude of a participant in communication. A speech act may be called ‘acceptable’ if it satisfies the conditions that are necessary in order that the hearer be allowed to take a ‘yes’ position on the claim raised by the speaker. These conditions cannot be satisfied one-sidedly, either relative to the speaker or to the hearer. They are rather conditions for the intersubjective recognition of a linguistic claim” (pp. 297-298, emphasis in original).

Brandom treats something very like this intersubjective acceptability as a normative judgment, and refers to a background requirement of mutual recognition.

“Registering a validity claim is not the expression of a contingent will; and responding affirmatively to a validity claim is not merely an empirically motivated decision…. And one who doubts the validity of the underlying norms has to give reasons…. Validity claims are internally connected with reasons and grounds. To this extent, the conditions for the acceptability of directions can be found in the illocutionary meaning of the speech act itself; they do not need to be completed by additional conditions of sanction” (pp. 301-302).

Habermas is saying that validity is necessarily intersubjective. It could not be private.

“In general, no special obligations follow from the meaning of constative speech acts” (pp. 303-304).

“Not all illocutionary acts are constitutive for communicative action, but only those with which speakers connect criticizable validity claims” (p. 305).

“The fact that the intersubjective commonality of a communicatively achieved agreement exists at the levels of normative accord, shared propositional knowledge, and mutual trust in subjective sincerity can be explained in turn through the functions of achieving understanding in language” (p. 308).

“Semantic investigations of descriptive, expressive, and normative sentences, if only they are carried through consistently enough, force us to change the level of analysis. The very analysis of the conditions of the validity of sentences itself compels us to analyze the conditions for the intersubjective recognition of corresponding validity claims” (p. 316).

Here he does gesture in the direction of a more interesting semantics.

“It is part of understanding a sentence that we are capable of recognizing grounds through which the claim that its truth conditions are satisfied could be redeemed” (p. 317, emphasis in original).

This should be recognized as elementary. Understanding an assertion is not only concerned with vocabulary and grammar, but also with grounds and consequences.

“As with the meaning of assertoric sentences, it can also be shown for expressive and normative sentences that semantic analysis pushes beyond itself. The discussion that stems from Wittgenstein’s analysis of first-person sentences makes it clear that the claim connected with expressions is genuinely addressed to others. The intersubjective character of the validity of norms is even clearer” (p. 318).

Empathy as an Ethical Stance

Ethically, empathy belongs in the same space as Aristotelian friendship, in which the friend is as another self; and with the golden rule; Kantian respect for others; and Hegelian mutual recognition. It is a prescription for non-egotism and avoidance of self-centeredness. Nothing is really more important than genuinely caring for others, which must include listening to them, and not simply doing or telling them what we think is right for them.

There is a fine line between making and asserting our own independent judgments of what is right — which every ethical being needs to be able to do — and imposing them on others. Empathy is what helps us navigate these gray areas.

I personally see a complementary principle that helps complete this. That is that we should in general as much as possible mean what we say, and say what we mean. I see this partly as a matter of personal integrity, and partly as a way of helping others understand us as best possible, when they may not themselves see things as we do. This can also be understood as a kind of more specific empathy for the listener on behalf of the speaker.

Aristotle on Being

In book Delta (V) of the Metaphysics, devoted to things meant in more than one way, Aristotle has a chapter on “being”. This is worth quoting in full. What I want to draw attention to is Aristotle’s own very modest, “deflationary” approach in contrast to other writers. His emphasis is on ordinary use of “to be” as a verb, not some grand “ontology”. The word translated as “being” (einai) is literally the infinitive “to be”.

Moreover, being for Aristotle in all of its primary senses is always being this way or that. Aristotle mainly thinks about being in a “transitive” way. In a derivative sense, he speaks of ordinary “beings” we encounter in life. I note his strong emphasis on ways things are meaningfully said, and the parallel series of assertions about truth. One might conclude that there are as many kinds of being as there are of assertions and of categories. Aristotle’s Categories seems to deal with assertions and kinds of being together, and scholars have debated over which aspect predominates.

“Being is meant in one sense incidentally, in another sense in its own right; in the incidental sense, we say, for example, that the just person is educated, or the human being is educated, or the educated one is a human being, in much the same way as if we were to say that the educated one builds a house because it is incidental to the housebuilder to be educated, or to the educated one to be a housebuilder (for here this is means that this is incidental to this). And it is this way too in the case of the things mentioned; for whenever we say that the human being is educated or the educated one is a human being, or that the white thing is educated or this is white, we mean in some cases that both are incidental to the same thing, in others that something is incidental to a being, and in the case of the educated human being, that the educated is incidental to this person. (And in this sense even the non-white is said to ‘be’ because that to which it is incidental is.) So things that are said incidentally are said to be so either because both belong to the same being, or because one of them belongs to a being, or because the thing itself is, to which belongs that to which it is attributed.”

“But just as many things are said to be in their own right as are meant by the modes of predication; for in as many ways as these are said, in so many ways does to be have meaning. Since, then, of things predicated, some signify what a thing is, others of what sort it is, others how much it is, others to what it is related, others what it is doing or having done to it, others where it is, and others when it is, being means the same thing as each one of these. For it makes no difference whether one says a person is healing or a person heals, or a person is walking or cutting rather than that a person walks or cuts, and similarly in other cases.”

“Also, to be and is signify that something is true, and not to be signifies that it is not true but false, alike in cases of affirmation and denial; for instance, that Socrates is educated indicates that this is true, but that the diagonal is not commensurable means that this is false.”

“Again, being and what is mean in one sense something that is definite as a potency, but in another sense what is fully at work, among these things that have been mentioned. For we say of both one who is capable of seeing and one who is fully at work seeing that he sees, and similarly of both one who is capable of using knowledge and one who is using it that he knows, and also both of that to which rest already belongs and that which is capable of being at rest that it rests. And it is similar in the case of independent things, for we say that Hermes is in the block of stone, and that the half belongs to a line, and that which is not yet ripe is grain. When something is potential and when it is not must be distinguished in other places” (ch. 7, Sachs tr., pp. 86-88).

Next in this series: The Knowledge Sought

Toward Essence

What does it mean to really explain something, as opposed to just making claims about it? According to Robert Pippin, this question underlies what he calls the key transition of Hegel’s Logic, between the “logic of being” addressed in several recent posts and what Hegel calls the “logic of essence”.

The logic of essence will itself eventually be superseded by the logic of the concept. With very broad brush, it seems to me one might expect that the logic of essence will be a representation of important insights Hegel attributes to Aristotle, whereas the logic of the concept is supposed to be a representation of what he claims as his own (and Kant’s).

“[Hegel’s] general approach [is] to begin with the least ‘mediated’, least theoretically committed determination and argue for the further determinations, further theoretical commitments, without which even these relatively simpler determinations would not be possible” (Hegel’s Realm of Shadows, p. 211).

Hegel assimilates all simple predications or assertions to the logic of being, the inadequacy of which we have seen in some detail. Every word, phrase, or assertion taken in strict isolation reduces to meaningless noise, just like the attempt to “say” indeterminate Being. Only taken together and in some sort of context do words and assertions begin to mean something.

According to Pippin, “a mere list of contingent properties and quantitative measures cannot count as having determined any subject of those determinations as such” (ibid). Hegel “summarizes this problem by calling it the problem of indifference” (ibid). We still lack any even quasi-stable things to talk about.

An explanation is more than just a generalization. Explanation requires distinguishing the essential from the nonessential.

Hegel thinks that even something as sophisticated as the use of Newton’s inverse square law to account for the elliptical shape of planetary orbits is still only a compact way of making a complex assertion about relational properties, and does not give us a reason. This corresponds to the level of the “force and understanding” chapter of the Phenomenology, which reaches a purely relational point of view on mathematical physics, but still lacks the features Hegel associates with self-consciousness.

“[A] distinction between what is truly real or essential and what appears, or that way of thinking, is now on the Logic‘s agenda…. A practice exists, and we want to know not merely what happens or whether it exists but whether the practice is actually a religious practice. Or a computer wins at chess, but is it actually thinking? Something is displayed in a gallery, but is it actually art?” (p. 218).

“These questions are just examples. The Logic is not concerned with them, and, we should say, is concerned with actuality as such, the possible actuality of anything intelligible” (ibid). “These example questions… depend on ‘the logic of actuality’ as such, which simply means: how we think about what anything ‘really is’. As we have seen, the determinations of such conceptuality cannot be empirical; they must be understood, according to Hegel, as ‘products’ of thought’s self-determination of itself, a process that continually realizes thought’s apperceptive nature. Or: the concept gives itself its own actuality. Hegelian conceptuality has this subjective dimension (‘thought’s autonomy‘), even while also being the articulation of the conceptual structure of reality. This has nothing to do with spinning every actual, contingent species-form out of thought’s self-examination. The topic… is logical or categorical formality as such, not ‘what are the existing species-forms?’ ” pp. 218-219).

“The very title of a ‘logic of essence’ suggests (yet again) immediately the philosopher whom Hegel seems most to admire, Aristotle” (p. 219). “We found in the logic of being that, according to Hegel, it was not possible to specify a thing’s ‘actual’ being by qualitative and quantitative markers…. Since Hegel accepts the Aristotelian premise that actually to be is to be a this-such, where that means it is identifiable by being an instance of a kind, this means we have failed with respect to the question of actuality. We are thereby compelled, in the prosecution of the original task, to consider that, ‘actually’, a thing is not how it simply appears, looks, sensibly manifests itself, however regular or predictable. We have to say that in some way, what a thing actually is lies hidden, must be uncovered, posited, a product of thought, not a simple empirical apprehension as such” (p. 220).

The “original task” is the determination of meaning, which didn’t get very far in the logic of being, even though in the parts Pippin has skipped over, Hegel did develop resources for making broad classes of simple assertions or claims about appearance.

“What we will need is a comprehension of the difference… between the ‘essential’ and the ‘unessential’, and the basis for this differentiation” (p. 221). “[W]hatever seemings are, (in not ‘actually’ being), they exist and are determinate, a determinacy inexplicable, Hegel claims, by the ‘skeptics and idealists’ who claim that the distinction cannot be made, and therefore say, ‘everything is illusory'” (ibid).

Whoever claims that “everything is only mere appearance” turns out to have no basis for making any distinctions within the so-called appearance.

“Someone who had understood everything said onstage, the plot of Shakespeare’s King Lear, and the basic motivations of the characters, as those characters and others voice them, and had understood only that, would not, we feel entitled to say, have understood ‘the play’. Put in the simplest possible way, to understand the play, one has to do more than listen to it; one must think about it, or we can say, using the word most important for Hegel, ‘reflect’ on it, understand what lies ‘beneath’… these facts about plots and characters…. There is no such thing as a hidden meaning in King Lear; there are just the words spoken or found on the page. How we get from this clumsy metaphor to the ‘concept’ of King Lear in itself is the underlying story of the logic of essence” (pp. 223-224).

All meaning that is worth talking about has this same kind of non-thing-like character. It is constituted from relations of connection and disconnection.

“It would be a mistake to sum a person up, attempt to ‘understand’ her in the distinct way persons should be understood, simply by adding up or listing everything she did, from what she had for breakfast to volunteering for a dangerous mission. A person would not be properly understood by attention to such ‘immediacy’ alone (or her qualitative/quantitative/measured appearances, as in the logic of being). We need to understand her deeds as ‘mediated’ by what Hegel calls her ‘inwardness’…, something (and now in the most important difference with the logic of being) that we cannot see, that does not simply present itself” (p. 224).

The relations that constitute meaning do not themselves directly appear. This applies as much to things in general as to human character.

It is certainly ubiquitous that people and things also respond differentially to direct appearances, without anything deeper than a qualitative or quantitative appearance being involved. Mid-20th century behaviorism claimed that was all there is, that the meaning at issue here was a mere figment or conceit.

Pippin continues his previous example, “For example, we can’t really understand what she did except by some attention to her own formulation of the act description and to her avowed motive (her ‘intention’). Sometimes what happens should not count as a deed because there is not the proper connection of inner and outer. An accident happens. Something prevents her from realizing her intention; that is, something happens to her. She does not do something. What happens is not an expression of her character. On the other hand, as Hegel states the central claim of the entire logic of essence in a phrase, we must concede that any such inner self-construal can ‘prove itself’… only in what manifests that outwardly, in the deeds. (It is immediately important that this ‘test’ can fail.) Too radical a separation and we have someone trying to disown what she in fact did, to fabricate excuses. (‘Mistakes were made’; ‘It was never my intention to deceive/hurt/offend anyone’, etc.) We need this distinction, but we can’t establish which deeds are true manifestations of essence and which are merely aberrations by any statistical analysis of frequency, any simple inspection of what happens. We need to understand how ‘what shows’, ‘what manifests itself’ (Schein), can be said to reflect these deeds’ essence when it does (if it does, then as Erscheinung, appearance), even if, as appearance, no one deed is ever a manifestation or simple representation of essence as such ” (pp. 224-225).

It was this sort of point about the ethical meaning and use of actuality in Hegel’s Practical Philosophy that initially greatly impressed me in Pippin’s work (see especially Hegel on Willing). According to Pippin, this kind of question about the relation of actuality to appearances is just what Hegel’s “logic of essence” is all about.

Unexpectedly for me at least, this now provides the occasion for Pippin to tell us more specifically what he thinks “mediated immediacy” means in Hegel. As I mentioned before, I have always thought first of things like the experience of riding a bicycle or recognizing an object, which properly speaking are examples of “immediatized mediation”, bridging the gap between the intrinsic emptiness of immediacy in itself and our undoubtedly non-empty “immediate” uptake of things in ordinary experience. In other words, my attention was drawn to the way in which complex results of some previous synthesis can be pre-consciously associated to what we experience “immediately” in a new synthesis of imagination.

Hitherto, in thinking about the term “mediated immediacy”, I have focused on ordinary appearances of meaning, in contexts that according to Hegel are not adequate to “immediately” support the constitution of that apparent meaning. This is admittedly to disregard the surface grammar of the phrase.

Pippin here starts to give “mediated immediacy” a sense that is aligned with the surface grammar, and is also closely aligned with what he has just said the logic of essence is all about.

He continues, “Understanding this relation properly is what Hegel thinks allows him to speak of a mediated immediacy. The appearances are not denied as unreal. They ‘shine’ in their immediacy. But they can be understood in their determinate immediacy only as the manifestation of the thing that they are appearances of, and so are always mediated…. We can’t derive the appearances from a mediated (‘posited’, ‘reflected’, ‘thought-over’) essence. That would be a denial of their immediacy. But we don’t apprehend such appearances on their own, in pure immediacy, and then infer what appears. What appears is appearing in what manifests itself…. What a person does is tied to that person’s character, whatever it is. And understanding that character is nothing other than rightly understanding what that person has done. With respect to all the reflected dualisms introduced in the logic of essence, this thought in various forms remains the kernel of that logic throughout” (p. 225).

This is Hegel’s recovery of something like Aristotle’s qualified common-sense realism about experience. We say that we experience not just phenomena but also things, even if we are wrong about them sometimes. At the simplest level, though not itself thing-like, essence is what enables the distinction of things from arbitrary collections of appearances.

“This is also why essence is a retrospective reflection of what has been made manifest, why it is rooted in gewesen, the past participle of sein [to be] or ‘what has been’, a feature somewhat counterintuitive in an account of action. It is also why Hegel is happy to accept the Wesen/gewesen suggestion of temporality. It links his account with one he admired, Aristotle’s, whose term for what has often been translated as essence is to ti en einai, something like ‘the what it was to be’ of a thing” (p. 226).

Essence, I would suggest, subsists independent of time once constituted, but the constitution of essence for both Aristotle and Hegel has a dependency on appearances in time. It therefore could not be pre-given. We have to actively discover or construct it, often taking into account long sequences of appearances in time. These may wander in various directions or sharply reverse our previous expectation. Parts of them we will judge to be irrelevant. This is only the beginning of the story of essence, not the end.

“Ultimately on Hegel’s account, if we want to know whether this lie reveals a person to be a ‘liar’, what we need is not to have deeper insight into some thinglike essence, but to observe what else the person does over time and to understand the relation among these deeds, to interpret them or ‘think them over’ in their relation to each other. This will be a crucial point throughout the logic of essence, and it obviously raises the question of how to make, what guides us in making, this relational connection.”

It is relatively easy to express the openness of Aristotelian practical judgment. But we still have to do the work of judgment in each case, and due to the openness we will have committed to with Aristotle, there could not be a precise roadmap telling us how to do the work. But Kant already argued that at least at a sufficiently high level of abstraction, universals can meaningfully guide practical judgment, so perhaps something more could be achieved. Any such progress on how to judge what is essential would be priceless indeed.

“Finally, it is important to stress that this topic is being introduced very broadly. No particular theory of ‘essentialism’ is being entertained, and as already noted, making the general distinction just discussed could be achieved even by an account of the difference between transcendental and empirical subjectivity, or between categories and empirical concepts” (ibid).

Essence as such need not be taken as a specific “ontological commitment”. It means what is reasonably, reflectively judged to be important. That is part of the hermeneutics of things and of life, which we encounter as soon as we begin asking if someone or something is really or actually something-or-other. (See also Essence and Explanation; Hegel on Reflection.)

Next in this series: Essence and Explanation

What We Saw

In passing in the last post I argued that “because I saw it” is not a reason, but a mere reiteration of an assertion. I claimed that we ought always to be able to say something more about why we believe what we do, and suggested that in the current example, this would typically take the form of more detailed claims about what we saw. (See What and Why.)

Previously, I argued against John McDowell’s claim that the space of reasons includes cases in which empirical claims may be non-inferentially justified by reference to other empirical observations. In the current analogy, what McDowell counts as justification in such cases amounts to saying “because I saw something else”. In effect, it is an appeal to another completely indeterminate “seeing”.

By contrast, when we make more detailed claims about what we saw, even though these supplementary claims are not themselves inferences, because they analyze the initial “what”, they may provide the basis for subsequent inference to the original “what”. The axis of justification shifts from other immediate observations to articulated claims about the original observation.

Because the justification now appeals to articulated content rather than to other seeings that are as completely indeterminate as the first, it can now be inferential. Such inferential justification is weaker than deductive proof; unlike a mathematical proof, for instance, it is potentially refutable. But now we have truly entered the space of rational dialogue.

In the situation of “he saw X, she saw Y“, no dialogue is possible. “He saw, she saw” is just as vacuous as “he said, she said”. In both these latter cases, one mere assertion is merely counterposed to another mere assertion, and we can say categorically that no insight could ever be gained from the exchange.

By contrast, as soon as the discussion shifts from a contest of assertions to the articulation of content, something can potentially be learned from it, whether or not we end up endorsing what is said.

An empirical observation may still provide a useful heuristic basis for belief about the world. Additional observations may add to the heuristic “weight” of that basis. But contrary to McDowell, I would not count that heuristic basis as part of the space of reasons. I call something a “reason” if and only if it provides a basis for some reasoning, which is to say some inference or inferences. To call something a non-inferential “reason” makes no sense.

And contrary to both McDowell and Brandom, I do not recognize the existence of non-inferential “knowledge” at all. Every observational report is just a claiming about appearance, and no mere claiming about appearance should count as knowledge.

What we have in the putative case of “observational knowledge” is observational belief. An observational belief may turn out to be well-founded, but any such well-foundedness depends on factors that go beyond the brute fact of the existence of observations.

We can have dialogue about claims about other claims. We cannot have true dialogue about claims about raw appearances — or indeed, properly speaking, about first-order claims at all.

This, I think, is part of the upshot of Hegel’s “logic of being”. Any first-order claim “A is B” considered in isolation fares no better than Parmenides’ saying of Being. It is logically vacuous, just because it is isolated. Isolation would mean, for instance, that we have no definition for A or B.

(The way I am using “first order” here for claims is different from the way it is used in predicate logic. In standard mathematical logic, what I am calling an “isolated first-order claim” corresponds to a proposition, rather than any construct in predicate logic. According to Frege, a proposition can only mean either “true” or “false”, so we have a similar lack of information.)

In Aristotelian terms, the claim then reduces to a mere saying, which is actually charitable, because for Aristotle, in the absence of meanings for A and B, we would have failed to express a proposition at all. Mere saying in this sense actually fails to properly say anything at all. If we don’t know what A and B are, “A is B” is the logical equivalent of arbitrary noise.

Conversely, when we do take a first-order claim as meaningful — as we indeed do all the time — we must always already have some higher-order perspective on it that makes it meaningful. All meaningful saying is saying something at a higher-order level.

A Logic of Being?

We’ve reached part 2 of Robert Pippin’s important Hegel’s Realm of Shadows. Despite recently mentioned peripheral caveats, I’m enormously impressed with the way he makes sense of Hegel’s Science of Logic, possibly the most difficult philosophical work ever written.

He now begins a high-level survey of the three separate “logics” Hegel develops. It is essential to Hegel’s scheme that the first two will be regarded as failures in the explanation of what is involved in making things intelligible. For Hegel, failures of thought play an essential, irreducible role in the attainment of new insights. The perspectives achieved by thought are not “refuted” by other perspectives external to those achieved; instead, the achieved perspectives metaphorically “discover” their own inability to solve their own problems.

We’ve already seen the first move of the first of these failed accounts of what it is to be intelligible, the logic of being.

Hegel uses the further development of this account as a vehicle for discussing the Kantian categories of quantity and quality. If his first point was that being qua being is utterly sterile because intelligibility depends on the ability to make definite determinations, the elaboration begins to show the relational character of all determination, and at the same time the failure of any simple assertion of properties of things (“judgment”, in the severely truncated early modern form that reduces it to predication) to adequately make those things intelligible.

Pippin does not go into detail on Hegel’s lengthy discussion of quantity and quality, so for instance there is no more mention of the issue about good and bad infinity, though this is where Hegel treats it. Pippin reserves the most space for the final logic of the concept that is supposed to be successful, and gives the least to the logic of being, which according to Hegel is the least adequate.

In discussing the logic of being, Pippin is mainly concerned to extract takeaway points relevant to understanding the high-level “movement” of Hegel’s logic as a whole. I have been highlighting his suggestion that this notorious “logical motion” is teleological in a genuinely Aristotelian sense, rather than being either deductive, or somehow univocally driven forward by contradiction. It is all oriented toward the merely hypothetical necessity of what is required if we aim to reach a deeper truth. Pippin is at pains to point out that for Hegel as for Aristotle, every teleological actualization involves contingency.

“The idea is to begin with the thought of anything at all, in its immediate indeterminacy, simply being, Sein. But the thought of anything at all is not the thought of anything…. Nothing is excluded, so nothing is included…. It is a failed thought, not the thought of this failure or even just the enactment of the failure. This is the beginning of everything of significance in the Logic; it (the thought of Sein being nothing other than Nichts [nothing]) is the reflective relation to what is being thought that is inseparable from anything possibly being thought. It is thought’s apperceptive moment…. Just thereby, thinking is thinking its failure to be thinking, not thinking of a strange object, Nichts. It is only in this sense that the first moment has a second moment, a realization of what thinking must be to be thinking of anything” (p. 186).

“Such a reflective determination reveals both that such putative immediate indeterminacy must itself already be a determination, and that such a putative content, anything at all in its immediate indeterminacy, has not been transformed, has not ‘become’ Nichts, but that it always already was” (p. 187).

“Hegel here is doing something like making a case for, or at least in some way showing us, the apperceptively discursive nature of any possible discursive intelligibility. This also means that in judging anything, I am always also implicitly holding open the possibility of the self-correcting of judging…. Or, any judgment always implicitly applies, is implicitly applying, the concept of judgment to itself” (p. 189).

That apperceptive judgment always implicitly applies the concept of judgment to itself follows from its apperceptive, reflective nature. To be apperceptively reflective is to be self-referential, Pippin has been saying.

“As Kant insisted, in any such case I must be able to ‘stand above’ what I judged and what I now judge correctly and take the latter to be a correction of the former in order for it to be that, a correction. Otherwise, there is just a succession of episodes. This is why he could say that the understanding, the power of claiming, is the synthetic unity of apperception (in the same way, I am ultimately claiming in this book, Hegel is claiming that what he calls the concept is the synthetic unity of apperception)” (ibid).

“This also means, as we have been stressing, that given certain concepts of the power of knowing — say, a knowing that must be indeterminate and immediate, a ‘resolve’ to begin with such a notion — we already have thereby the concept of the object of such pure knowing, Being. If we are talking about a case of knowing, as we are, the two are, must be, inseparable…. There is no question, here or anywhere in the Logic, of the need to ‘move’ from the order of knowing to the order of being. If that were claimed to be necessary, how would we have begun with a case of knowing?” (pp. 189-190).

This intimate connection between the form of knowing and the object of knowing is Hegel’s alternative to the difficult “transcendental deduction” by which Kant in the Critique of Pure Reason aims to establish that the categories of thought really are relevant to experience. Pippin suggests that Hegel generally reinterprets Kantian dualities as cases of Aristotelian hylomorphism, and notes that even Kant occasionally makes remarks tending in this direction. In this particular case, reinterpreting the duality as a hylomorphism eliminates the “gap” between thought and being that in Kant creates the need for the transcendental deduction.

I confess, though, that it was not obvious to me that we had begun with a case of knowing. I have trouble identifying any kind of failed thought or thought that fails to have a content with knowing; I am not used to recognizing the possibility of an empty “knowing”.

But we are at least implicitly talking about an instance of thought here, even if it is a degenerate instance. Pippin is arguing that even that failed, empty thought must still be self-referential, just in being a case of thought in Hegel’s sense at all. By virtue of its form as thought or apperceptive judgment, it is already reflectively turned back on itself. I think Pippin is suggesting that that turning back on itself counts as a kind of knowing at the meta level, even though the thought failed at ground level.

“[T]here is no objection in Kant or among the relevant post-Kantians, in their denial that thinking is a kind of perceiving or primarily receptive, to the general form of such claims as ‘I know it because I saw it’, especially because that is the invitation to establishing that it can be seen by anyone…. But for thinking as such, there is nothing like: ‘I know that is the essence because I had an essence-intuition…'” (p. 190).

I am more reserved about claims like “I know it because I saw it”. Plato would not accept this as an instance of knowledge, and I am inclined to follow suit. I would say, “I believe it with confidence because I saw it”. But Pippin makes a good point here about the implicit invitation to treat this as the claim that it could be seen by anyone.

As I have noted before, what I prefer to call belief and others call a form of immediate, noninferential empirical “knowledge” are not just arbitrary assertions. Though we arrive at such beliefs “spontaneously” (in the ordinary sense, which is nearly the inverse of the Kantian sense), after the fact it is always possible to ask about the reasons for them.

I am claiming that after the fact, it should always be possible to express something of why we believe what we do. “Because I saw it” is not a reason, but a reiteration that it appeared that way to me. Intrinsically, it has no more value than “because I said so”. The kind of reasons that can be provided in this case will be persuasive (or, in Aristotle’s usage, “probable”) to some degree or other, but also potentially refutable. Typically they will take the form of more detailed claims about what we saw.

“Fichte insists on the same point that is made in the first move in the Logic… by pointing out the difference logically between ‘A’ and ‘A = A’. For the latter, we need… an ‘I’ that is ‘= I’…. But this identification is something done, a Tat [deed], the equivalent here of ‘bringing contents to the unity of apperception’ in Kant’s account, an active unifying necessary for the I to be continuously that I in experience” (p. 191).

As Aristotle pointed out, merely saying something (“A”, “Being”, or whatever) is not yet saying something about something, which turns out to be the minimal condition for truth or falsity. This formulation points to some kind of self-relatedness in the attitude toward content that seems to be a minimal condition for any kind of assertion. This self-relatedness in the content of assertions seems to be related to the inherent self-referentiality of thought for which Pippin is arguing, as if the one were a sort of hylomorphic reflection of the other.

I used to misunderstand the above argument of Fichte as additionally requiring the existence of an “I” like a rabbit out of a hat, but again we are only dealing with hypothetical necessity here. If I want to be able to conclude “A = A”, then I need to be able to apply the same identification “A” twice within the context of one judgment. That the two identifications of “A” must be combined within the context of one judgment is the sole import of Fichte’s “I = I”. If there is any existence of an I involved here, it is by hypothesis.

Pippin stresses that although Hegel speaks of logical “movement” in temporal metaphors, each part of the “movement” has always already occurred. Once again, Hegel is not talking about what drives the course of events, but something like the conditions of possibility of the constitution of intelligibility and normativity.

He goes on to discuss more problems related to immediacy, and the transition to the logic of essence, each of which I’ll address separately.

Next in this series: Problems of Immediacy