Tag: Reference

A Triangular Relation?

In the previous post, we saw a sharply binary model of signifier and signified being applied by Roger Bacon and Duns Scotus. At least in Bacon’s case, this goes hand in hand with a new kind of “direct” realism that aims to deal directly with things in the world, and repudiates the subtleties of the indirect account of knowledge and meaning by way of concepts and the passions of the soul that was broadly shared by Aristotle, Augustine, and Boethius. But Scotus complicates the picture considerably by also promoting a triangular model that includes concepts understood in a certain way. Scotus also argues for a non-psychological approach to concepts.

“Does the sign signify the thing itself or the concept in the soul? — We have said that for Scotus, the great semantic controversy of the Middle Age, more fundamental than any other, is constituted by the following question: Is the vocal sound the sign of the thing or of the concept?” (Boulnois, L’Être et représentation, p. 35, my translation throughout).

“The line of the English Franciscans seems to have developed this theory long before him: for Roger Bacon, linguistic signs have been arbitrarily instituted by humans to directly indicate the things themselves. Words are not related to things by means of a conceptual interpretation. A new, radically non-Platonic way of thinking language arises: instrument of communication, it ‘takes the place of’ (supponit pro) the thing, and not the idea of the speaker. What is more, it exercises a representative function uniquely defined by its capacity to refer to present and existent things. For Roger Bacon, the name signifies solely the thing on which it has been imposed. It can only refer to things (even if it can signify connotata, by inference). But at the same time, there is a relation between the vox [vocal sound] and the species in the soul. The vocal sound is its proper presentification, but it makes the representation of a thing arise in the mind. It makes the thing be conceived, or makes it arise in the soul. Thus the sign in a single gesture refers to the thing and recalls a representation. The vox is not a concept, but a thing that signifies another; it signifies a singular thing in the present, without involving essence, and no longer passes by way of the intellectus to arrive at the res [thing]. There is a sort of collaterality of the sermo [spoken word] and the intellectus that both refer to the res” (ibid).

Scholastic accounts of language typically focus on proprieties of naming. Implicit in this approach is an account of meaning that begins from individual terms. Broadly speaking, this approach has an affinity to modern bottom-up theories of semantics, which aim to put together a picture of the world in a compositional way from individual terms taken as given.

In the early 20th century, Saussurean linguistics developed an alternative approach that treats the signifier in a relational way, such that each signifier is understood in the first instance as identified by its difference from other signifiers, independent of its nominal reference to a signified. This led to an incipient “deconstructive” analysis of individual terms in the broad current of 20th-century European (especially French) “structuralism”, which then came to be explicitly thematized in developments that Anglophone writers came to refer to as “post” structuralist.

From a completely different starting point in a pragmatist reading of analytic philosophy and German Idealism, in the late 20th century Brandom developed an “inferentialist” semantics that begins from whole sentences as the minimal unit of assertion, and focuses on explaining the “material” inferential properties of propositions in terms of normative assessments of proprieties of concrete assertion, rather than in terms of universal formal rules. Brandom understands the meaning of concepts inferentially, in terms of their use or functional role in assertions, and emphasizes the non-psychological character of meaning understood in this way. From this point of view, concepts are not to be identified with individual terms, and instead have a holistic character, such that each concept involves other concepts.

In sharp contrast to both of these as well as to Aristotle and Augustine, Scotus develops his triangular model of signification in a way that aims to be consistent with a primacy of individual things, and with a direct association of words to things.

“[I]n his first commentary on [Aristotle’s] treatise On Interpretation, [Scotus] maintains, like Boethius and Thomas Aquinas, that the vocal sound signifies the concept, which resembles the thing or ‘represents’ it. The vox immediately signifies the species, the representation of the thing in the intellect, but it mediately signifies that which it represents, which is to say the thing itself. But in the second commentary, closer to Bacon, he holds that the vocal sound directly signifies not the conceptions of the intellect, but the thing itself. When Aristotle and Boethius say that the name directly signifies the passions of the soul, it is necessary to understand by this not the concept, or the resemblance in the soul, but the thing that is conceived. This second version is evidently a radical revision of Scotist semantics. It is also the definitive position of the theological works” (pp. 36-37).

“Following Bacon and [Peter] Olivi, Duns Scotus breaks with the Boethian interpretation of signification, but he does so with a nuance, integrating the Aristotelian semantics; the verbal sign (verbum) is directly the sign of both the thing and the concept, but it is in the first instance the sign of the thing, and then the sign of the concept. The sign comes from a direct causality of the thing and signifies it directly. Nonetheless there is a logical anteriority of the concept, for it is on it that the linguistic sign depends. Scotus formulates his response in the vocabulary of his own theory of causality. The concept, the written sign, and the phoneme are all three ordered effects of the same cause: the thing itself…. Writing, the vocal sound, and the concept are signs, situated on the same plane, none of them exercising any causality over the others, and they signify the same signified” (p. 37).

If the sign is in the first instance the sign of the thing, it is difficult to see how the concept can be logically anterior to the relation of sign to thing. But Scotus apparently wants to assert both, and also that the concept is a kind of sign, and that the sign is a kind of thing.

“[T]he word, the concept, and the thing no longer form a series, but a triangle…. The play of natural causes, the weight of institution, and the semantic relation are articulated with one another, but remain autonomous…. The concept is the first, natural effect of the thing itself. It is it that is first of all a sign of the thing, and not the vocal sound or writing. It constitutes the object of logic, an anterior object, more fundamental than vocal sounds, and supposed by them…. If there is a science of things, metaphysics, and a science of words, grammar, logic occupies an intermediary and central place, as the science of concepts” (p. 39).

Scotus wants to give metaphysics a new status as a rational science, in a strong sense that is independent of Aristotle. Meanwhile, he also explicitly rejects Aristotle’s thesis that logic is a tool for clearly expressing meaning and not a science with its own subject matter, which Brandom has recently revived under the name of logical expressivism.

“Noetics studies the concept insofar as it constitutes an aspect of the mind (mens), where it is found as an accident in a subject. Logic, on the contrary, considers the concept as sign, insofar as it refers to a signified. This is the ambiguity of representation: we consider in it either the thing that represents, or the thing that it represents, the being of the representing or the being represented…. Logic is distinct from psychology…. The aim of thought is not reducible to its psychic reality” (pp. 39-40).

Boulnois does not point it out here, but Scotus’s assumption that the concept is in the mind “as an accident in a subject” is directly opposed to Augustine’s strong contention that the mind should not be seen as a subject in which knowledge and love inhere as accidents.

“In this triangle of word, concept, and thing, the concept is described as a sign, and reciprocally the cognitive act is itself a semiosis. Duns Scotus breaks with Augustine and Boethius, who reserve signification to vocal sounds and writing. He participates in what C. Panaccio has called a general movement of ‘semantization’ of thought. Logic, conceived as a rational science, a theory of signs or of ‘signifying reasoning’ (ratio significandi), is no longer a subalternate discipline, concerned with the expression of thought. Because thought is signifying, logic becomes a theory of thought itself. Nevertheless, it does not fall to it to resolve the problem of the place of thought. Concepts are natural signs, not conventional ones: they are combined in propositions according to logical rules, the structure of which subtends all possible oral or written propositions, even if they are not proffered. They constitute the elements of a universal mental language, of a general grammar and of a pure theory of communication. This language is for Duns Scotus a subjacent condition of all oral enunciations and effective writings” (pp. 40-41).

Thus apparently the treatment of concepts as a kind of sign is closely related to the non-Aristotelian idea that logic is a science with its own subject matter.

“But above all, this ideal possibility is real: it is accomplished par excellence in the domain of angelic communication. Angels communicate with the aid of intelligible signs, which is to say pure concepts, without phonetic or graphical support. Each angel directly causes a concept in another, by an immediate communication. It is on this occasion that Duns Scotus formulates a formal theory of pure thought” (p. 41).

If concepts are natural signs and signs are real things, then concepts are real things.

“The sign establishes a double relation. On the one hand, it is the image of the thing that caused it; on the other hand, what is more important, it signifies it: the concept is a real object, which has a natural existence, belonging to a causal chain; but it bears a resemblance to the object it represents. This resemblance is produced by the concurrent double causality of the thing itself and the intelligible species conserved in memory. — Is it necessary to say that the concept preserves the transparency of representation, while the conventional sign loses it? For a concept, does representare signify a ‘resemblance to’, or simply: ‘taking the place of the presence’ of an object, which was already the sense of the word in Peter of Spain? Does the representivity of the concept for the intellect come from its resemblance to real objects, or from its dependence on a cause?” (pp. 41-42).

Given Scotus’s insistence that the sign refers directly to the thing, it is surprising to read that “We cannot pass directly from the representation to the thing” (p. 43). But our act is different from the reference of the sign, so technically there is no contradiction.

“But even in maintaining that the relation of cause to effect is first, Scotus does not go to the point of abandoning resemblance: both are real aspects of intellection. Even if it supposes the causality of the object, semiosis is a complex process that is not reduced to it, since it supposes a play of resemblances. The sign is recognized more than it is produced” (ibid).

In a way, the play of resemblances resembles the mutual dependence of signifiers in the Saussurean tradition.

That the sign is recognized more than it is produced is a nice injection of good sense that stands in obvious tension with the foundation myth of signs as imposed and instituted “at will”. But the user of a sign is usually not its institutor.

“The phoneme homo no longer signifies the concept of the human: like the concept, it signifies the real human, even if it depends on the concept for this. The three forms of signification (formal sign, oral sign, written sign) are parallel, even if their terms are ordered according to a serial dependency. The signification of the concept is a natural relation between the intellect and things. The signified of phonemes and graphemes remains the thing itself, but it depends on a conventional relation.”

“In this Scotus directly opposes Aristotle, for whom the vox is a sound emitted by the mouth of a human being, accompanied by an imaginative representation. Words are not the tools of knowledge, but of communication” (p. 43).

I think that knowledge in Plato and Aristotle (and Hegel and Gadamer and Habermas and Brandom, among others) implicitly has a dialogical (and therefore in part communicative) character. Gadamer has highlighted the dialogical element in Plato and Aristotle. The “communicative reason” elaborated by Habermas involves a dialogical view of knowledge. It is only “monological” conceptions of knowledge that do not involve an element of communication.

“In itself, the written or oral sign is only an ensemble of sounds or letters, which causes nothing more than the knowledge of itself. The imposition of the sign describes the passage from concept to sign, and reciprocally interpretation allows a reascent from the sign to the intelligible concept that subtends it. The process of interpretation follows a trajectory inverse to that of imposition. It is thus a contingent process of association” (p. 45).

“In the moment of imposition, the imposer associates sense and intellect, in relating a perceived name to a conceived thing. In the moment of interpretation, the hearer recalls the relation between the name perceived in the present, and the past thing that she knew more or less distinctly” (p. 46).

I don’t think of interpretation as happening in a moment. It is not only dialogical, but also involves mediation, concepts, and an extension in time. In the same way, only in a very improper sense is jumping to a conclusion a kind of judgment. But Boulnois is summarizing Scotus here, not necessarily asserting this in his own name.

“Signification cannot take the place of knowledge. There is no transparency between the sign and thought” (ibid).

Knowledge implies a knower in a way that formal signification does not. But the dialogical expression and elaboration of knowledge is closely interwoven with the dialogical elaboration of signification and meaning.

“But what is it that is signified? The thing, yes, but in what sense of the word ‘thing’? According to [Scotus’s] Questions on On Interpretation, not the thing in its singularity and its existence, but the thing as quiddity [what Aristotle calls the “what it is”], indifferent to singularity and universality, to existence and nonexistence: the thing as it is seen by the mediation of a concept…. According to this semantic, signification is no longer an intelligible correlation between the signifying and the concept” (pp. 46-47).

Indeed, “thing” is said in many ways. Thing as quiddity and thing as object are almost mutually exclusive. I use “object” in a deflationary way as a relative term, as in “the object of”, not as naming something that is assumed to be a free-standing thing in its own right. I don’t actively use the term “quiddity”, but I think of it as a more static and self-contained projection of essence, which in its more proper usages is not something self-contained. Brandom says that a concept is not the kind of thing we could have just one of. I think of essence in a similar way. All articulation is inter-articulation, involving more than one term.

“From now on, signification can be thought independent of the scope of the concept.”

“Linguistic signs signify directly, without passing through the concept. They can signify a thing more precisely than intellect can conceive it. The circulus vini, a sign that indicates the presence of new wine in the inn, causes nothing new in the intellect of the one who perceives it. It is an arbitrary sign, constituted by a convention…. Convention is limited to establishing a relation of reason between two things, two physical realities: the sonorous matter of the phoneme (the vox) and the reality signified (the res). To be valid, this relation-convention supposes the knowledge of the two terms…. A weak and confused knowledge of the thing suffices for us to be able to use a sign, and to signify in a suitable way. We can signify in a way that is more precise than we conceive” (pp. 47-48).

Signification is a “formal” concept, in what seems to be Scotus’s distinctive sense of the term “formal”, which is neither Platonic nor Kantian, and also not to be understood in terms of modern logical or mathematical formalism. The formal status of signification is what allows it to be “more precise” than the knowledge we actually have. But as Hegel reminds us, formal precision (in any of these senses) is not always a virtue when applied to real things.

“Duns Scotus is inspired by the analyses of Olivi to establish a relation between semantic representation and juridical representation, the sign and the law.”

Peter Olivi was another important 13th-century Franciscan, and another strong voluntarist.

“A sign can be speculative or practical. The speculative sign leads to knowledge; it allows a concept of the signified to be formed in the intellect, but its characteristic tells us nothing of its real existence; for example, homo is the sign of a concept, and allows the knowledge of an essence, of a nature in general, whether or not a human exists. The practical sign implies the existence of its signified; it is the sign of an existence, and not of a simple possibility…. Since the practical sign signifies the advent of an effect, and this effect depends on the ordered power (that is to say on the free voluntary disposition) of someone who can cause it, only the author of this effect can give this practical sign certain being. It suffices that the institutor is disposed to regularly produce the signified of the sign she institutes…. Contracts, pacts, and promises are examples. The practical sign pertains to a juridical order instituted by humans. It depends on a law…. The sign belongs to the domain of the will of a free agent, who is self-determining in limiting herself to the order she institutes. This one, in proportion to her political power, can engage in rendering real what she has disposed in the order of signs” (pp. 48-49).

To me it seems preposterous to say that the sign belongs to the domain of the will of a free agent. A sign belongs to a field of reciprocal determination that is independent of anyone’s will. (See also Hegel on Willing.)

“The practical sign is an ordination of power. In this sense, it belongs to the theology of absolute power and ordained power. In Duns Scotus, these two concepts apply to every free agent: absolute power includes all that a free being can effectively do, de facto. Ordained power includes all she can do in conformity to a law, de jure. The institutor is an absolutely free agent, who self-determines freely in choosing this or that order” (p. 49).

An earlier book by Boulnois develops the history of the theology of absolute power and ordained power in detail. A later book treats the history of theological voluntarism in the Latin tradition.

For Scotus “It is will that founds the truth of the practical sign, and not the inverse” (p. 52).

But “there are signs of which we are not the institutors, and that we receive as fully established by an alien will…. We are under the law of signs, and they do not always depend on us” (ibid).

Scotist Semiotics?

Still slowly working on a re-reading and partial translation of Olivier Boulnois’s L’Être et représentation (1999), we have already gotten a hint that Latin scholastics such as Roger Bacon and John Duns Scotus used some of the very same key terminology as the 20th-century Saussurean structuralists, but seem to have held a diametrically opposed view on the specific matter of the relation of signifier and signified. Boulnois does not explicitly mention the more recent French context. The last post was in part about what is called “signification”.

As a university student in the late 70s, I was tremendously excited to learn about French so-called “structuralism”, which seemed to support my own primitive insight that “relations are prior to things”. In this context there was a lot of talk about signifier and signified, growing out of the structural linguistics of Ferdinand de Saussure. Together with the American pragmatist Charles Pierce, Saussure is considered to have originated modern semiotics, or the study of signs. For a while, semiotics was high on my horizon.

A key point in the Saussurean tradition, which grew very big in postwar France, was that there is no direct relation of the signifier to the signified. Instead, it was said in effect that we are signifying animals who live and thrive in a sea of signifiers, and build meaning out of differentiation.

For Saussure, the signified is not the referent but the concept. What the concept really is was not discussed in detail. Saussure himself seems to have seen it as falling under what he called psychology and social psychology, which was a rather conventional view when he was writing in the early 20th century, but this plays no real role in his theory.

What is essential is the detachment of signification from reference. For Saussure, the sign is a two-leveled thing that consists of (sensible) signifier and (conceptual) signified. But in relation to its referents in the world, the sign is “arbitrary”. The sound or word “tree” has no inherent relation to a tree. I am not concerned to argue for or against Saussure here, just setting the stage.

For Roger Bacon, signs refer directly to things. For Scotus, “The sign leads immediately to the signified. Between them, we must not ask about any intermediary. It attaches only to a single signified: the present thing itself. It represents it” (p. 26, my translation throughout, emphasis in original throughout)

Here we see an explicit strong positive valuation both on presence and immediacy, and at the same time on representation. Representability will be Scotus’s minimal criterion of being. I see all three of these claims as deeply problematic, but that does not mean they can be simply and categorically rejected.

“This theory is unfolded in four theses:

“1) Every sign is a thing, and reciprocally every thing can be a sign; it is thus that the father is a sign in relation to his son. ‘The sign is said relative to a signified, as “father” relative to a “son”; and it is also necessarily the sign of something, which is its foundation.’ A sign is at the same time the manifestation of something, and refers to an other. It is necessarily a real foundation, even if it also implies a relation of signifying/signified. On the one hand, it brings an information to the sense, the sensible species (visible, audible, etc.), or to the cognitive power (the intelligible species); on the other, it produces a knowledge of something else” (ibid).

The sign thus brings a (participial or ongoing) “information” or informing form to sense or intellect.

The notion of forms being somehow transmitted, and of their being a kind of thing that can be transmitted, has an interesting ambiguity. The image of species as discrete things flying through the air seems hard to sustain. And yet, there is a sense in which form is not locked up in one thing, but can be “communicated”. And what we call the thing — not merely stuff or an object, but participial “information”, or some form as a happening — is grounded in the becoming or manifestation associated with a present participle.

This manifestation is the mark of reality, which is not just a collection of ready-made objects or truths but a process of being manifested. This goes beyond mere presence as a snapshot or image capable of being mastered, and beyond mere representation as referentially standing for something. This is the sense in which objectivity as a happening involving essentiality goes far beyond the mere being of objects mastered or possessed.

I have always thought it was a happening or unfolding (or happening-as-unfolding, as distinct from happening as a mere punctual event — procession or “emanation”) like this that the neoplatonic talk about something beyond being aimed at — not mere being-there or a necessary support for it, but a nonpunctual unfolding of unmastered essence that is precisely not to be identified with “Being”, or with the putative object of “ontology”. And on the other hand, I want to think that ordinary being is already nonpunctual or outside of itself, and thus strictly transcends both representation and event, at very the same time that it is susceptible to genuine understanding and criteria of reasonableness.

“2) Every sign supposes an inference. Here Scotus recollects the Aristotelian heritage, in line with the unification aimed at since Albert the Great. Taking the theology of sacraments as a point of departure, and trinitarian theology as an example, it is not limited to the model of the linguistic sign. The sign permits an inference, which starts from the posterior to go back to the inferior [sic]: if b, then a. A thing signifies another if its existence entails that of another, be it anterior or posterior. Indeed it becomes the element of a reasoning by inference or likelihood (enthymeme). One same theory of the sign is to provide an account of signification and of inference. It allows a unified theory of semiotics as cognitive science to be constructed. The linguistic sign is only a particular case, thought on the model of inference. It functions not as a code (according to a biunivocal correspondence), but according to relations that are more numerous and more complex” (p. 27).

Quite unexpectedly, we have here not only an emphasis on inference in the context of signification, but it is contrasted with a mechanical code or biunivocal correspondence in a way that makes it sound like what Sellars and Brandom call material inference. But for Brandom this grounds a non-representationalist account, whereas Scotus, as we will see over the course of a number of upcoming posts, is arguably the arch-representationalist of the whole Western tradition.

“3) Scotus aims to provide a general and unique theory of the sign. To be a sign, it suffices to be a thing. But what is a ‘thing’? Not always a sensible, physical, material reality: for him it suffices to have a formal being, a reality sufficiently unified and positive to be able to be opposed to the term with which it is in relation, to become the foundation of this relation. The sign is the real term of a real knowledge. Unlike a sensible thing, a sign is first of all a formal object, a possible object of knowledge. ‘This is true not only of the sensible sign, taking “sense” [in Augustine’s definition] strictly, for the corporeal sense, but again it is true for the incorporeal sense, taking sense generally, for any cognitive power.’ The senses are not only sensibility (here, in the organic sense), but knowledge in the broad sense — intellection. The sign is not always sensible; it can be immaterial, and consist in a concept or an intelligible species. Like Bacon, Duns Scotus integrates in the theory of the sign the intelligible signs that are the concepts of the soul. But he envisions also the case of the angels, who communicate and transmit species or purely intelligible representations. By a philosophical decision, Scotus generalizes the status of the sign. The subtle Doctor gives an indifferent definition that is neutral and transcends genres. He conceives a transcendental semiotic” (pp. 27-28, brackets in original).

The idea of “formal distinction” — roughly, that there can be a “real” difference in definition where there is no difference in “being”, whatever that is — seems both plausible, and by no means inherently tied to the objectionable claims that will is superior to reason.

I’m still grappling with the suggestion that a concept could be a sign. That concepts are inferences, or at least are closely associated with inferences, seems plausible enough, and certainly better than the idea that a concept is a mental image. Brandom identifies concepts with rules we adopt to govern inference. That signification is closely related to inference also makes sense. But while it makes sense that a concept would be immaterial, I find it hard to affirm that the same would be true of a sign.

“4) The sign concerns the category of relation. Bacon had already remarked that ‘the sign pertains to the category of relation’. By itself, the sign brings about the knowledge of something else. It is constituted by a relation of inference to the thing signified. Does it go the same for signification as for knowledge? For Bacon, the sign represents something to someone: it implies two relations, in the accusative and in the dative, toward the signified and toward the interpreter, and it is the second that is essential. But Aristotle himself describes knowledge as a relation, and remarks that the destruction of the thing known entails that of the corresponding knowledge. Does the sign still signify when its signified disappears? The first, traditional, position consists in dissociating the truth of enunciation from the truth of the sign, and says, like Anselm, that there is a ‘true sign’ even when it does not signify something. Quite the contrary, for Bacon the sign loses its value as a sign. ‘If we cannot conceive anything by a sign, it is void (cassum) and vain, it cannot be a true sign; but it is only a sign according to the substance of the sign, and it does not have the status of a sign: it is thus that the substance of the father remains when his son is dead, but not the relation of paternity. And whatever vocal sound, the circle of wine or an other [sign], imposed in act in relation to a thing and instituted for it, can represent it and signify it, if what it signifies does not exist in act, it is not a sign in act.’ If the thing that it represents is absent, the sign represents nothing, it is indeed not a sign. It must receive a new institution” (pp. 28-29).

This use of Latin substantia seems very far indeed from Aristotle’s ousia.

Earlier, Boulnois had contrasted the radicality of Bacon’s direct realism with traditional views. He said that Bacon’s notion of the sign — in contrast with either that of Augustine or that of Aristotle — involves only two elements, omitting the mediating role of concepts or of the soul. Here it sounds like Bacon on another level does still leave a role for an interpreter. But perhaps an implicit distinction is being made between interpretation as immanent to the level of content (which a direct realist would presumably reject), and a transcendent dimension of something like the person of an interpreter standing over and above any content, which may be related to the voluntarism we will be hearing about shortly.

“The distinction between the kinds of sign is at the center of the semiotic theory: it brings out the principal articulations, and in particular allows the relation of signs in general to linguistic signs, of semiotics to semantics, to be thought. In Scotus, the relation signifier/signified is organized along three divisions” (p. 30).

Much more than a simple division of the subject matter is going on here.

“1) The relation signifier/signified can be natural or conventional. The natural sign manifests a real relation that is found in nature, while the conventional sign translates a relation of reason, which only exists for the intellect that establishes it. This opposition recovers the division between two kinds of inferential signs. The non-linguistic natural signs imply a causality and a real relation; the instituted signs, of which linguistic signs are a part, imply an intellectual decision, and indeed a relation of reason. The conventional (ad placitum) sign has only a relation of reason with its object; it is a second intention, a simple perspective of the mind with no objective correlate. Scotus gives as an example ‘the voice and the gestures of the monks’ who have taken a vow of silence. These signs ‘could signify other things, if it pleased the institutors’, for what has been instituted at will can be revoked at will. — But the natural sign better reveals the essence of the sign: ‘The natural sign signifies more truly than the conventional sign’. In effect, the natural relation of the thing to its sign is a real relation, implying a first intention: an aspect of the thing has exercised a direct causality on what signifies it. For example, the relation of smoke to fire and that of the thing to the concept are real” (pp. 30-31).

The vocabulary of first and second intentions comes from Avicenna. Roughly, first intentions are supposed to refer directly to concrete real things and genera like “horse”, whereas second intentions refer to abstract concepts like “subject” or “genus”. For Avicenna, Scotus, and others in the scholastic tradition, second intentions generally have a second-class status and valuation in comparison to first intentions.

Whether there really are such things as natural signs is a question that will have to be considered. Of course insofar as there are natural things, or phenomena that we agree to call natural things, there “are” such natural things as smoke and fire. We can probably agree too that smoke is in some sense “caused” by fire. But that that inference from smoke to fire is truly naturally given, and not in any way due to us, is quite debatable.

Scotus’s talk about the will of the institutors of a language is also problematic. It can be fairly said that the state of a natural language at a given time is not the product of anyone’s will, individual or collective. Even more generally, real history is not based on a foundational moment. It is the cumulative compound of many accidents.

“Duns Scotus nonetheless does not relate signification to knowledge, but to will. Speech is an ordered communication, which makes manifest certain signs of a mutual will…. Language does not express a knowledge, but rather indicates a will…. What we understand, what is said, manifests what the speaker wants to say. It is inscribed in the space of reciprocity (mutuae voluntatis), and not that of monologue or meditation. Finally, it has communication in this space of interlocution as its aim. Language agrees with the human as a being who is not limited to reason, but who is given a will” (p. 31).

The invocation of mutuality and reciprocity and a “space of interlocution” here is an important surprise that makes this more interesting. This overlaps with the concerns of Hegel, Gadamer, Habermas, and Brandom.

I use the locution “I want to say that x” from time to time myself. Right now “I want to say” that while to speak of a definite will in the sense of intending this and not that is a perfectly good distinction, claims that there even is a power of pure arbitrary choice — let alone that it is superior to intellect — ought to be rejected. What the speaker according to herself wants to say is indeed a part of the story of meaning, but it is only a part.

“Signs suppose an institution on our part. They follow from a voluntary decision, and in no way from a nature of signs. The order of signs is not in the nature of things. Established, stopped, they found a status, a state, or an order among the participants in discourse. But the instituted sign can efficaciously represent an invisible reality: a will. It thus represents an intellection, but under its highest form, as will, and allows the willed effect to be produced. The sign thus instituted has a double function: it guarantees the certitude of recognition, it allows the efficacy of its operation. The model is thus that of a pact (pactio), whether it is a matter of a firm engagement (sponsio), a guarantee (fideiussio), or an oath (juramentum). The efficacy of signs comes from a pact between the liberties they represent” (pp. 31-32).

We can see that there is a high-level analogy between this notion of the “institution” of a regime of signs and the common early modern foundation myth of a social contract. Like the social contract, which is supposed to ground strong claims of political sovereignty — and unlike Hegelian mutual recognition, which is always in process and open to another chapter — the institution of signs for Scotus putatively has an “always already founded” status.

As is common in the scholastic tradition, efficacy here is also unequivocally associated with efficient causation, which is treated as the most primary kind of cause, whereas in a purely Aristotelian context efficient causes are subordinate, which implies that efficacy cannot be simply identified with efficient causality. Moreover, for Aristotle himself, something like the art of building is more truly an efficient cause than the architect or the carpenter or the hammer or the hammer’s blow.

“2) The signified can be permanent or intermittent. The sign that always has its signified is a ‘true sign’ in the sense of saint Anselm. It is also called ‘efficacious’ because it implies an efficient causality between the event and its sign. Reciprocally, for the one who depends on it, it always leads to a knowledge. It has no need of an interpreter, and always does what is expected of it: it always realizes its proper operation. The necessary sign can only appear accompanied by its signified: the eclipse is the true sign and efficacity of the interposition of the earth, since it is always the effect. This signification, which rests on a necessary inference, is necessary and always true. Thus all the natural signs are efficacious signs” (p. 32).

From an Aristotelian point of view, I have already expressed some skepticism about the claim that there are natural signs, but in the Catholic tradition it is commonly held that the sacraments, unlike linguistic signs, are efficacious in themselves, and Scotus is giving voice to this.

“But among the conventional signs, certain are efficacious (the sacraments), while others are not. The latter do not always imply their signifieds, but are sometimes true, sometimes false, that is to say neutral. This kind of sign is falsifiable, it is enunciated in variable propositions, and its signification is contingent. It is not efficacious, not having the power to realize its signified: in a proposition, it is not in the power of the speaker to make it so that the sign is accompanied by the thing it signifies. The sign is thus not true by itself, but is an exterior adequation to its signified. The ambivalence between the truth of the sign and truth of adequation mark the division between the conventional sign in general and the efficacious sign” (ibid).

The notion of efficacy here also seems be an all-or-nothing proposition — either total or inapplicable. I think there is a kind of efficacy of signs, but it is never total.

“3) Again we can distinguish signs according to their relation to a temporal signified. Some refer to the past (commemorative signs), others to the future (predictive signs: prognosticum), and others finally to the present (deictic signs: demonstrativum). For Scotus language is a commemorative sign, while the sacrament is a demonstrative sign” (pp. 32-33).

The “commemorative” status of linguistic signs is presumably supposed to be a kind of reference back to a founding event or will. Again I think of social contract theories.

Husserl also speaks of “deictic” expressions, but gives the term the nearly opposite meaning of indexical or occasional, as contrasted with ideal. Something like Husserlian deictic expressions are called “floating” signifiers in the Saussurean tradition, because they have no fixed reference.

“According to Thomas Aquinas, every sacrament has an omnitemporal signification. It is the sign of the past, of the present, and of what is to come (it recalls respectively the Passion of Christ, source of all grace, the present which is the gift of grace, and the glory to which every grace destines the human). Its signification contains an essential presence, present to all the dimensions of time. For Scotus, on the contrary, the sacrament is a demonstrative sign. Like every sign, it has an intentionality pro praesenti. It refers to the present and to it alone. It is in this sense that it is a representative sign: the representational function of the sacrament as sign implies the realization of the signified at the instant of its utterance, and indeed the temporal presence of the object represented. It has a deictic dimension that is demonstrative, in contrast to memory and the promise. Representation is first of all a form of presence.”

Aquinas and Scotus are both doing things with presence, but it seems as though presence in Scotus is contracted to a punctual status that is connected with a punctual or all-at-once view of representation. The strong association of representation with presence is also important.

“Duns Scotus cannot accept the thesis according to which the verb in present tense signifies the instant at which the utterance of every enunciation is completed, or all the conclusions that depend on it. ‘When it is uttered, the verb cosignifies time in the same way that it signifies [the signified]’: as a consequence, when it cosignifies the present, it only refers to the instant of its utterance. When no indication comes to specify a proposition, the time of the enunciated in the present is that of its enunciation. The intention of the speaker comes to coincide with the rhythm of the phrase. Expressed temporality follows lived temporality. In the same way, by the force of discourse, the demonstrative pronoun hoc [this] signifies what it shows the instant it is proffered” (pp. 32-34).

For Brandom, pronouns like “this”, far from being indissociable from immediacy, are anaphoric back-references to something said before.

“Three metaphysical principles are interlaced in the Scotist semantics: the primacy of the will for justifying the institution of signs, that of univocity for establishing their ideal state, and that of presence for explicating their temporal reference” (p. 34).

Signification, Representation

The next section of Boulnois’s L’Être et représentation, barely over a page in length, begins to develop the relation between signification and representation.

“What is a sign? What is signification?”

“If, according to Bacon, the sign and the concept represent, we cannot directly identify signification and representation. Signification is not a special case of representation. But by another detour, we will come to concentrate representation in intellection. If the sign is a thing that, as Augustine says, presents itself to sense, it also presents an other to the spirit — it presents and it represents. The Baconian analysis opens the way for the formula of Scotus: ‘Signifying is representing something to the intellect’. Signification is a representation. In every proposition, the term represents in act all the signifieds. The sign is a substitute for the thing, which allows it to be rendered present to thought so that the latter can conceive it. It implies two distinct relations, to exterior things and to the concepts of the intellect.”

“This distinction recalls the distinction between reference and the semantic field, or, in medieval terms, between supposition and signification. In simple supposition, a term supposes for what it signifies: it recalls all the supports designated by its signification. On this point two interpretations confront one another. For one tradition of logic (called ‘Parisian’), supposition is the act of taking the place of the referent, of being an intentional and semantic back-reference (supponere pro). For another tradition (called ‘Oxonian’), supposing is being the subject of a predicate in a proposition, according to an extensional and syntagmatic presentation (supponere sub). This delimitation seems insufficient, for it obliges us to consider Scotus as Parisian more than Oxonian! He declares in effect ‘The common term supposes for all the supports’ that it recalls. Thus, the common term, ‘when it is not specified by some added [term], supposes absolutely [for] its [common] signified’. Supposition reveals itself as strictly indifferent, with neither priority nor pre-eminence of one support over the others: the term supposes ‘equally for all the [individual supports] that are equally related to its signified’. This indifference is also an indifference to their existence or nonexistence: the term ‘supposes for all the supports, existent or nonexistent’. It refers equally to each one of them. Every universal is distributed in its inferiors, since all the supports are of the same kind and of the same degree supports which the common term recalls. The theory of representation recovers the concept of supposition and takes over the whole weight of the reference of a term in a proposition” (pp. 24-25, my translation, brackets in original).

Realism, Nominalism, Modality

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

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

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

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

Anaphora and 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

One, Many, Same, Different

Book Iota (X) of Aristotle’s Metaphysics extends the discussion in book Delta (V) of things said in many ways, going into detail on what makes things one, many, the same, or different. These are extremely important matters for any sound reasoning, though somewhat technical in nature. It also contains Aristotle’s sharp critique of the saying of Protagoras, “Man is the measure of all things”.

“[T]here are four senses in which something is said to be one primarily and in its own right, rather than incidentally” (ch.1, p. 185).

As to the first, “oneness belongs to what is continuous, either simply or, especially, by nature, and not by contact or a binding cord (and of these that is more so one and is more primary of which the motion is more indivisible and simple)” (ibid).

Continuity in a material is the lowest degree of something being one in its own right. That which is materially united by contact or by any artificial means would not be one in its own right.

As to the second, “[oneness] belongs still more to what is whole and has some form and look, especially if something is of that sort by nature and not by force, as those things are that are so by means of glue or bolts or being tied with a cord, but rather has in itself that which is responsible for its being continuous. And something is of this sort if its motion is one and indivisible in place and time; and so it is clear that, if something that has a source of motion that moves it in the primary kind of the primary class of motions (by which I mean a circular type of change of place), this is one magnitude in the primary sense” (ibid).

Being a whole is a higher degree of unity than being materially continuous. The association of circular motion with a strong unity is relevant to the upcoming argument in book Lambda (XII) about the first cause.

“So some things are one in this way, insofar as they are continuous or whole, but others are one because the articulation of them is one, and of this sort are those things of which the thinking is one, and this in turn is of this sort if it is indivisible, and an act of thinking is indivisible if it is of something indivisible in form or in number” (ibid, emphasis added).

As to the third, “a particular thing is one by being indivisible in number” (ibid, emphasis added).

These would include all the independent and non-independent things that were extensively discussed in book Zeta (VII).

He continues, “but that which is one by means of intelligibility and knowledge is indivisible in form, so [fourth] what is responsible for the oneness of independent things would be one in the primary sense” (ibid, emphasis added).

I expect that this last kind will turn out to be the first cause.

“But it is necessary to notice that one must not take the sorts of things that are spoken of as one as being meant in the same way as what it is to be one, or what the articulation of it is” (p. 186).

This is analogous to the distinction between saying something about something in general, and saying what something is, also discussed in book Zeta. He illustrates this below, with the example of fire.

“The same thing would also be the case with ‘element’ and ’cause’, if one had to speak about them, distinguishing the things to which the words are applied, and giving a definition of the words. For there is a sense in which fire is an element… and a sense in which it is not; for being fire is not the same thing as being an element…. And it is that way also with ’cause’ and ‘one’ and all such things, and this is why being one is being indivisible, just exactly what it is to be a this, separate on its own in either place or form or thinking, or to be both whole and indivisible, but especially to be the primary measure of each class of things, and, in the most governing sense, of the class of things with quantity, for it has come from there to apply to other things” (ibid).

Being one in the third sense above (being a particular thing) is now said to be “just exactly what it is to be a this“. This foreshadows an extensive one-to-one mapping he will develop below, between all the ways of the saying of being he elaborates in book Delta (V), and the ways of the saying of oneness.

He goes on to speak at some length about measures, which we would call units of measurement.

The most important point is that “a measure is always the same kind of thing as what it measures, for the measure of magnitudes is a magnitude, and in particular, that of length is a length, of breadth a breadth, of spoken sounds a spoken sound, of weight a weight, and of numerical units a numerical unit” (p. 188, emphasis added).

The distinction he makes here tracks perfectly with the way that different types, dimensions, and variables are handled separately in the operations defined by modern mathematics.

“And we speak of knowledge or sense perception as a measure of things for the same reason, because we recognize something by means of them, although they are measured more than they measure” (ibid).

The simultaneously humorous and serious caveat that “they are measured more than they measure” means that knowledge and perception are constrained by reality. More precisely, they are involved in mutual dependencies with the realities of things that they at once measure and are measured by.

“And Protagoras says a human being is the measure of all things, as if he were saying that a knower or perceiver were the measure, and these because the one has knowledge and the other perception, which we say are the measures of their objects. So while saying nothing, these people appear to be saying something extraordinary” (ibid).

Aristotle, at the end of his discussion of measure (longer and more detailed than included here), refers to Protagoras’ famous saying, commonly quoted as “Man is the measure of all things”. With uncharacteristic sharpness, he calls this “saying nothing”. Why? This seems worthy of a short digression.

Protagoras was a prominent Sophist, who appears in Plato’s dialogue of the same name. He wrote a controversial treatise entitled Truth, which began with the sentence, “Of all things the measure is man: of those that are, that they are; and of those that are not, that they are not”. Plato and Aristotle both took Protagoras to be asserting a kind of individualist relativism. Reportedly, the skeptic Sextus Empiricus also read him this way. Plato took him to deny any objective reality. Aristotle in book Gamma (IV) shows rare outrage at his other reported claim that “it is not possible to contradict”. I didn’t mention him by name in my account, but Aristotle names him there as well.

Aristotle implies it is a bit more plausible to much more specifically say that knowledge and perception are measures of things, but even that only with the caveat that really “they are measured more than they measure”.

But why go on to add with such sharpness that Protagoras is “saying nothing”? I suspect the answer may lie with the other part of Aristotle’s interpretation: “as if he were saying that a knower or perceiver were the measure, and these because the one has knowledge and the other perception”.

I’m inclined to think Aristotle would regard it as outrageous to transfer what may (ambiguously) be said of specific knowledge and perception, to an unqualified saying about one who is said to possess knowledge and perception in general.

Aristotle has just given an account of what a measure is, that it must be of the same kind as the things that it measures. How could one thing (“man”) possibly be the measure of countless things that have no common measure? That does sound like nonsense. Any measure has to be of one kind or another. Modern mathematics agrees that kinds, dimensions, variables can only be collapsed together if very specific criteria are met.

What Aristotle emphasizes here about knowledge and perception — that they have a remarkable involvement with things that also measure them — seems very consistent with his general views. But the way Protagoras implicitly presents “man” as their possessor makes the possessor stand apart from the mutual involvement with things that Aristotle emphasizes, in which knowledge and perception and things measure one another. In splendid isolation from all constraints of real measure, the possessor seems to have arbitrary freedom to claim whatever she wishes.

I intuitively associate Protagoras with the attitude that what’s true for you is true for you, but what’s true for me is true for me, so don’t tell me I’m wrong, and I won’t tell you you’re wrong! Then and now, such sentiments had and have a superficial appeal, because they seem to express a live-and-let-live attitude, which seems to be a good thing. But the way it is expressed, in fact it completely undermines any possibility of meaningful dialogue, which undermines reason itself, which undermines the very thing that makes us human.

Back to the text, Aristotle turns to illustrating the one-to-one mapping I mentioned between sayings about being and sayings about oneness.

“[S]ince not even being itself is an independent thing as though it were some one thing capable of having being apart from the many beings (since it is common to them), other than solely as a thing attributed to them, it is clear that oneness is not a universal either” (ch. 2, p. 189).

For Aristotle, neither Being nor the One is an independent thing in its own right. He will nonetheless argue in book Lambda (XII) that there is a first cause for all things.

“What’s more, what is true about oneness must hold true in a similar way for all things; and being and oneness are meant in equally many ways” (ibid).

“And the same account applies also to the other classes of things, … and [if] in all instances it is the case both that the number is a number of something and that oneness is some particular one thing, and oneness itself is not the thinghood of it, then it must also be the same way with independent things” (p. 190).

“[S]o too in thinghood, one independent thing is oneness itself; and that oneness in a certain way means the same thing as being, is clear from the fact that it follows along equally through the ways being is attributed, and is not any one of them (for instance, it is not what anything is, nor of-what-sort anything is, but stands similarly toward them just as being does), and from the fact that no other thing is predicated in ‘one human being’ over and above what is predicated in ‘human being’ (just as being is not something over and above what and of-what-sort and how-much a thing is), or in ‘being one’ over and above being any particular thing” (ibid).

Saying something is one human being is the same as saying it is a human being. In book Zeta, he analogously said that “good” and “being good” are the same.

Things are often one in one respect, but many in another. The one and the many are “contraries, and not opposed as contradictories or as what are called relative terms” (ch. 3, p. 190). Next he turns to the meanings of same, other, and different.

“Since the same is meant in more than one way, in one way we sometimes speak of what is the same in number, but we say it in another sense if things are one in meaning as well as in number, as you are one with yourself in both form and material, and in another again if the articulation of the primary thinghood of things is one, for instance in the way equal straight lines are the same, … but in these equality is oneness” (p. 191).

In Fregean terms, things are what Aristotle calls one in number when they have the same reference. They are what Aristotle calls one in meaning when they have the same sense. Frege illustrates how they differ by saying that the morning star and the evening star have the same reference, but different sense.

“Things are alike if, not being simply the same, nor without difference in their composite thinghood, they are the same in form, just as a larger square is like a smaller one…. Other things are alike if they have the same form, and have it in them to be more and less, but are neither more nor less than one another. Other things, if they are the same attribute, and one in form, say white, more and less intensely, people say are alike because their form is one. Other things are alike if they have more things the same than different, either simply or superficially, as tin is like silver insofar as it is white, and gold is like fire insofar as it is yellow and fiery-red” (ibid).

“So it is clear also that other and unlike are meant in more than one way” (ibid).

“[B]ut difference is something other than otherness…. [W]hat is different from something is different in some particular respect, so it must necessarily be the same in some respect as that with which it differs” (p. 192).

For Aristotle, calling two things different presupposes that they can be meaningfully compared in the first place. This is not the case for things that are just “other” than one another. Black is different from white; they are both colors. But an apostrophe is just other than an aardvark.

This is followed by a ten-page discussion of technical details of contrariety, which I will mostly skip. Contrariety supports a definitive ruling out of some things based on other things. This has great importance for reasoning.

Incidentally, Aristotle explains why there is no essential difference between human beings with different colorings.

“And since one sort of thing is articulation while another is material, those contrarieties that are in the articulation make a difference in species, but those that are in what is conceived together with the material do not make such a difference. This is the reason that whiteness of a human being, and blackness, do not make such a difference…. For there is a difference between a white human being and a black horse, but that is not insofar as the one is white and the other is black” (ch. 9, pp. 201-202).

Finally, he argues that destructibility and indestructibility inhere in things by necessity. Whether a thing is destructible or not depends strictly on what genus of things its species belongs to.

“[A] destructible thing and an indestructible thing must be different in genus…. Therefore it is necessary that destructibility either be the thinghood or be present in the thinghood of each destructible thing; and the same argument also concerns the indestructible, since both are among things present by necessity” (ch. 10, p. 202).

Next in this series: Toward a First Cause

Ockham on Reference

William of Ockham (1285-1347) is the most famous so-called “nominalist” in Latin medieval philosophy. He sought to explain our practical and theoretical uses of universals entirely in terms of our relations to existing singular things.

Without losing sight of Plato’s emphasis on the value of pure thought, Aristotle had adopted a broader perspective, starting from the generality of human life. In this context, in contrast to Plato he had emphasized the genuine importance, positive role, and irreducibility of singular beings or things that we encounter in life. “For us” singular beings and things come first, even if they do not come first in the order of the cosmos.

Singular beings and things are more concretely “real” than any generalizations about them. But Aristotle simultaneously upheld the “Platonic” view that knowledge in the strong sense can apply only to generalizations of necessary consequences between things, and not to our experiences of singulars. There can be no necessity in our experience of something purely singular. What I would call the extraordinarily productive tension between Aristotle’s fundamental views of reality (putting singulars first) and of knowledge (putting universals first) created an appearance of paradox that later commentators sought to resolve, often by favoring one side at the expense of the other.

Ockham wanted to explain universals entirely in terms of singulars. In the Cambridge Companion to Ockham, Claude Panaccio summarizes that “Ockham’s project is to explicate all semantical and epistemological features — truth values, for instance — in terms of relations between sign-tokens and singular objects in the world” (p. 58).

Ockham built on the work of many less well-known figures. The Latin world had seen lively inquiries about logic and semantics since the 12th century, when Arabic learning first began to be disseminated across Europe. Within this tradition, there is more than one approach to meaning.

The technical notion of “signification” was a development inspired largely by Augustine’s theory of “signs”. Unlike more recent usages (e.g., in Saussurean linguistics), this kind of signification involves a simple relation of correspondence between a thing taken as a “sign” and some other thing.

Ockham and many of his predecessors held that there is such a thing as natural signification, independent of any language. In this sense, smoke is taken to be a “sign” of a fire. This relation of smoke signifying fire is called “natural”, because in our experience smoke only exists where there is fire, and this has to do with how the world is, rather than with us. This is very different from the conventional imposition of the word “fire” to refer to a fire.

At the same time, this notion of signification also seems to have an irreducible “psychological” component. It has something to do with how the world is, but in a more direct sense, it has to do with something like what the British empiricists later called the association of ideas. Our “natural” association of smoke with fire is not arbitrary. As the empiricists would say, it is grounded in experience. As the Latin scholastics would say, the soul “naturally” tends to associate smoke with fire, and this is as much a truth about the soul — or about the soul existing in the world — as it is a truth about the world.

For Ockham, natural signification applies to concepts, which constitute the core of a sort of “mental language” that is in many ways analogous to spoken or written language, but is more original and does not depend on convention. Concepts on this understanding are subject to all the same kinds of syntactical relationships as individual words in speech.

In this tradition, the meaning of concepts is analyzed by analogy with the role of individual words in speech. This presupposes a view that linguistic meaning overall is founded on the meanings of individual words. The individual concepts of “mental language” that apply to individual real-world things are analogously supposed to have pre-given, natural meanings. Logic and semantics are then a sort of mental hygiene with respect to their proper use.

Ockham offers a rich analysis of connotative terms that modify the concepts corresponding to things.

Again building on the work of many authors in the Latin tradition, he develops the theory of logical “supposition”, which contemporary scholars associate with semantic discussions of reference to real-world objects. This has nothing to do with supposition in the sense of hypothesis; rather, it relates etymologically to a notion of something “standing under” something else.

Notably, Ockham and this whole tradition insist that while individual words independently have signification, only in the context of propositions or assertions expressed by whole sentences do words have the kind of reference associated with supposition. I suspect this is ultimately grounded in Aristotle’s thesis that truth and falsity apply only to whole propositions or assertions; “supposition” is to explain not just meaning, but also truth and falsity. This tradition develops a much more explicit theory of reference than Aristotle did, and the kind of reference it develops is tied to contexts of assertion, or true assertion.

The idea that reference to real-world things should be approached at the level of propositions rather than individual words or concepts has much to recommend it. But for Ockham and the tradition he continued, supposition is still fundamentally governed by signification, and signification begins with individual words or concepts. Individual words or concepts are thought to have pre-given meanings, and Ockham attempts to give this a theoretical grounding with his notion of “mental language”.

As Ockham suggests, there is a way in which notions of syntactic relations apply to pure concepts. But I take this to be an abstraction from actual usage in spoken or written language, and I don’t believe in any pre-given meanings.

Ockham’s general strong privileging of individual things over universals has a deep relation to his voluntarist and fideist theology, which owes much to his fellow Franciscan Duns Scotus. In logic, Scotus is considered a defender of “realism” about universals as opposed to nominalism, but in his theology he developed a strong notion of individuation, tied to a very radical notion of divine omnipotence that refused to subordinate it in any way, even to divine goodness (see Aquinas and Scotus on Power; Being and Representation). Essentially, from this point of view, every single thing that happens is a miracle coming directly from God, and all observed regularity in the world pertains only to a sort of divine “habit” that could be contravened at any moment.

Aquinas aimed at a sort of diplomatic compromise between this extreme theistic view that makes everything solely dependent on God, and Aristotle’s unequivocal assertion of the reality of “secondary” causes. Scotus and Ockham applied high levels of logical sophistication in defense of the extreme view.

Ockham also denied the reality of mathematical objects. Together with his extreme view on divine power, this makes very unlikely the view promoted by some scholars that Ockham in particular represented the strand of medieval thought that most helped promote the emergence of modern science. Ockham’s undeniable logical acumen was dedicated to downplaying rather than elaborating the practical importance of order in nature.

It does seem, though, that views like Ockham’s contributed to the shaping of British empiricist philosophy. Here is another chapter in the complex history of notions of reference and representation. Ockham’s very strong notion of reference as directly grounded in singular real-world objects — combined with that of the natural signification or pre-given meaning of concepts in “mental language” — helped lay the ground for what modern empiricism would treat as common sense.

For most of the 20th century, the mainstream of analytic philosophy seemed to be inseparable from a strongly empiricist direction. But Wittgenstein, Quine, Sellars, Brandom, and others have initiated a new questioning of the assumptions of empiricism from within contemporary analytic philosophy. Analytic philosophy is no longer nearly so opposed to the history of philosophy or to continental philosophy as it was once assumed to be. It is in this context that we can begin to look at a sort of Foucaultian or de Libera-esque “archaeology” of empiricism, in which Ockham certainly deserves an important place.

Normative “Force”

Frege’s notion of the “force” of an assertion plays a large role in the discussions of analytic philosophers about speech acts. In his usage, it has nothing to do with coercion or Newtonian physics. Rather, it concerns what I might call the “substance” of what is said, and what Brandom calls conceptual content, which for Brandom would be made explicit first of all through being interpreted as a kind of doing. The question of force seems to be, what are we doing in asserting this rather than that? This also brings in the larger real-world context of that doing.

Although Brandom subordinates reference to Fregean sense or intensional meaning, he also complements and interweaves his account of material-inferential sense with an account of real-world normative-pragmatic “force”, and suggests that this is the ultimate driver of meaning. How things come to have or lose normative-pragmatic force — i.e., how the appearance of such force is legitimized or de-legitimized — he very persuasively argues is best explained by the Hegelian theory of mutual recognition.

At a programmatic level, a deep and wide historical and critical genealogy of the specific forms emerging from mutual recognition is the more particular shape that something like Ricoeur’s “long detour” of mediating interpretation takes for Brandom. Brandom’s monumental work pulling all the pieces of his general account together has left him little time to dwell on details of interpretation for particular cases, but I see it as an open invitation. My own “historiography” and “history of philosophy” notes tentatively sketch some key details in the broad panorama of the history of values. (See also Normativity; Autonomy, Normativity; Space of Reasons; Ethics.)

One important result of Brandom’s comprehensive development is that cases where reality figuratively “pushes back” against us are subsumed under the figure of normative force. (See also Rethinking Responsibility; Expansive Agency; Brandomian Forgiveness.)