Convention, Novelty, and Truth in Language

We have been exploring the earliest publicly available work of the great contemporary philosopher Robert Brandom, his doctoral dissertation from 1976. He has been concerned to develop the philosophy of language along pragmatist lines, while working hard to point out that a pragmatist approach need not be construed as globally rejecting talk about objectivity, truth, and reality. The pragmatist approach is appealing as a sort of third way that avoids both subjectivist and objectivist excesses. This is the last chapter before his conclusion.

“[W]e saw how the notion of truth and the truth conditions of sentences could arise in a pragmatic investigation into the social practices which are the use of a language by a population. That is, we saw how an account of social practices (which are whatever the linguistic community takes them to be) can require us to consider the sentences uttered in those practices as making claims which are objectively true or false, regardless of what the community takes them to be” (Brandom, Practice and Object, p. 129).

He has argued earlier that understanding the meaning of compound sentences (in which one clause refers to and modifies another) implicitly does after all presuppose a technical concept of truth that goes beyond the warranted assertibility that Dewey recommends as a less pretentious replacement for truth-talk.

Both in ordinary life and in ordinary ethical discourse, warranted assertibility — justification in taking things to be such-and-such — is able to do the work commonly allotted to claims about truth that is what it is independent of us. But insofar as we engage in the meta-level discourse about discourse that is already implied by the understanding of compound sentences, it becomes necessary to introduce a distinction between how things are for us and how they are in themselves. This kind of situation can also be seen as motivation for Kant’s talk about “things in themselves”.

“[W]e will see how that sort of inquiry requires that a sophisticated grammar be attributed to the language being investigated, and in particular requires notions of syntactic deep-structure, meaning, and denotation or reference. We thus extend the method of the previous chapter to consider sub-sentential linguistic components, and see what it is about the practices associated with them in virtue of which it is appropriate to associate them with objective things or features” (pp. 129-130).

He will defend Chomsky’s notion of deep syntactic structure objectively existing in natural language against Quine’s instrumentalist critique.

Only by abstraction from things said do we come to consider individual words in isolation. In common with his later work and at odds with the standard compositional account of meaning in linguistics and analytic philosophy of language, in the understanding of meaning Brandom here gives explanatory priority to sentences over words, and to propositions over terms. This will be more explicitly thematized in his later work.

The compound sentences analyzed by Dummett that Brandom refers to as requiring an auxilary notion of truth beyond epistemic justifiability partake of the character of discourse about discourse, because some parts of them refer to and modify other parts.

He considers what it means to investigate the use of a natural language — what he will later call normative pragmatics. Investigating language use implicitly means investigating proprieties of use, along with their origin and legitimation. We may also collect ordinary empirical facts about the circumstances of concrete “takings” of propriety and legitimacy and their contraries, without prejudice as to whether or not those takings are ultimately to be endorsed by us.

Using the neutral language of “regularities”, he specifies a sort of minimalist, almost behaviorist framework for investigating language use that is designed to be acceptable to empiricists. In later work, he develops a detailed analogy between the deontic moral “necessity” of Kantian duty and a “subjunctively robust” modal necessity of events following events that is inspired by the work of analytic philosopher David Lewis on modality and possible worlds.

“We may divide these regularities of conduct into two basic kinds: Regularities concerning what noises are made, and regularities concerning the occasions on which they are made…. The phonetic descriptions are just supposed to be some rule which tells us what counts as an instance of what utterance-type…. Without attempting to say anything more specific about these regularities, we can express what a speaker, as we say, ‘knows’, when he knows how to use an utterance-type by associating with it a set of assertibility conditions” (p. 130).

“In terms of these notions, we can represent a language by a set of ordered pairs called sentences. The first element of each ordered pair is a phonetic description and the second element is a set of assertibility conditions…. A linguist who has such a representation of the sentences of some alien language ought to be able, subject to various practical constraints, to duplicate the competence of the natives, that is, to converse with them as they converse with each other” (p. 131).

Here he is applying a stipulative re-definition of the ordinary English word “sentence”. “Ordered” pair just means it is always possible, given a member of the pair, to say which member it is. The pair here consists of 1) the sequence of sounds by which a particular sentence is identified, and 2) the conditions under which it is appropriate to use that sentence.

“[A] theory of the use of a language just is some mechanism for generating a list of ordered pairs of phonetic descriptions and assertibility conditions which codifies the social practices which are speaking the language” (p. 132).

Every sentence in every natural language has the two above aspects — a recognizable series of sounds that identifies it, and conditions for its appropriate use.

“Speaking only about the first element of the ordered pairs which we have taken to specify a language, Quine takes the task of a theory of syntax to be the generation of the infinite set of phonetic descriptions. He then argues that if the aim of a theory of syntax is determined by this target description of speaker competence, then many different axiomatizations will generate the same set of phonetic descriptions, and hence be descriptively adequate. Insofar as a theory of syntax is a part of the project of generating the right set of sentences, then, we may choose between alternative theories only on the basis of convenience of their representation (pp. 132-133).”

This is an example of Quine’s instrumentalism that was mentioned earlier. Syntactic constructs in a natural language like English are identifiable by their mapping to distinct series of sounds. I haven’t spent enough time on Quine directly to say much more at this point, but to identify syntax with the phonetics used to pick out syntactic distinctions seems reductionst. Before criticizing it, he elaborates on Quine’s view.

“Representing the conversational capacities as ordered pairs of phonetic descriptions and assertibility conditions, we will see a good translation as associating with each phonetic description in one language a phonetic description in the other which is paired with the same assertibility conditions…. In this way a translation function would enable one to converse in a foreign language. If the goals of translation are regarded as determined in this way by pairs of phonetic descriptions and assertibility conditions, then convenience of representation and arbitrary choice will enter here as much as on the syntactic side” (p. 133).

“Denotational relations are presumably correlations between phonetically distinguishable elements … which appear in the phonetic descriptions of many sentences, and some element which regularly appears in the assertibility conditions of those sentences. A theory of denotation would consist of a relatively small list of such correlations, together with a set of structural rules which would permit the derivation of the full set of ordered pairs which are the sentences of the language, by combination of the various elements…. If one such axiomatization or recipe is possible, many are” (p. 134).

“More generally, given any scheme, we can substitute as the denotation of any phonetically specified expression anything systematically related to it, …and adjust the rest of the scheme to get the same assertibility conditions” (pp. 135-136).

“The point is that we may think of a language as being an abstract object consisting of a set of social practices…. If one now considers the various theoretical notions which have been thought to be crucial to the specification of a language by those who are not primarily concerned with social practices — the syntactic and semantic structure of its sentences, their meaning and the denotation of expressions occurring in them — one finds these notions playing drastically reduced roles” (p. 136).

“It is our purpose in this chapter to show how to circumvent … conventionalism while retaining the pragmatic point of view which renders language as comprised of social practices” (p. 137).

Classic 20th century analytic philosophy has a very thin notion of language use, effectively identifying it with empirically existing conventions. In contrast to this, Brandom sees in Noam Chomsky’s linguistics a crucial recognition of the ubiquity of linguistic novelty. He quotes Hilary Putnam’s critique of conventionalism:

“We see now why conventionalism is not usually recognized as essentialism. It is not usually recognized as essentialism because it is negative essentialism. Essentialism is usually criticized because the essentialist intuits too much. He claims to see that too many properties are part of a concept. The negative essentialist, the conventionalist, intuits not that a great many strong properties are part of a concept, but that only a few could be part of a concept” (ibid).

In contemporary usage, “essentialism” is a bad thing that consists in taking putatively unproblematic essences of things for granted. In contrast, Plato and Aristotle’s preoccupation with questions of what we translate as “essence” reflects a significant problematization.

Brandom now turns to a careful criticism of Quine.

“Quine’s arguments as we have reconstructed them seek to show that, for a particular specification …, the role of a translation function (or of syntactic deep structure, or of denotational scheme) can be played equally well by a number of different notions” (p. 138).

“Such sound conventionalist arguments cannot be refuted. They can be shown not to impugn the usefulness or objectivity of the notions they apply to. To do this one simply has to come up with some other project, with respect to which the various versions of, e.g., translation, do not play equally well the role that notion is invoked to play” (pp.138-139).

“The question I want to consider is, roughly, where the assertibility conditions and phonetic descriptions come from. In virtue of what does a sentence have the assertibility conditions and phonetic description that it does?” (p. 140).

Questions about conventional use are questions of empirical fact. Brandom’s “in virtue of what” question is on the other hand properly philosophical, in a sense that Plato and Aristotle would recognize.

We come to Brandom’s defense of Chomsky against Quine.

“Chomsky has argued on statistical grounds that most sentences used by adult native speakers have never been heard or used by that speaker before, and indeed that the majority of these have never been uttered by anyone in the history of the language. This is a striking empirical observation of far-reaching theoretical significance. Let us consider the sentences of English which have never yet been used. Not just any phonetic description is the phonetic description of some sentence of this set…. But a native speaker can not only discriminate between the phonetic descriptions which are on this list and conform to them in his own utterances, he has exactly the same acquaintance with the assertibility conditions of such a sentence that he does with the assertibility conditions of some familiar sentence like ‘Please pass the salt’. That is, a native speaker can discriminate between occasions on which it might be appropriately used and those on which it would be inappropriate. Granting, as we must, that there is a community of dispositions concerning these novel sentences which is sufficient to determine a social practice regarding their use, a notion of correct or incorrect utterance, surely this fact is remarkable. Why should the community agree as much about how to use sentences no one has ever heard before as about how to use common ones?” (pp. 140-141).

“For human beings, training in the use of the relatively few sentences we have actually been exposed to determines how we will use (or would use) the vast majority of sentences which we have not been exposed to” (p. 142).

“The question ‘In virtue of what is there a correct usage for a sentence no one has ever used before’ is distinct from, but not independent of the question ‘How do individual members of the linguistic community come to acquire dispositions which conform to the standard of correct usage for novel sentences?’ The questions are distinct because no individual’s dispositions, however acquired, establish a standard of correct usage. The questions are not independent since using a sentence is a social practice…. The question of how such agreement is achieved, its source and circumstance, is clearly related to the question of how individuals come to behave in ultimately agreeable ways…. The explanation of projection by populations must ultimately rest on facts about individual projective capacities…, although that explanation need not resemble the explanation of any such individual capacity” (pp. 143-144).

He clarifies what he means by projection.

“I want to argue that a theory of grammar is properly a part of the attempt to explain and predict the projective capacities of language-using populations. A theory of syntactic structure, of meaning, and of denotation and truth are to provide a framework for accounting for the empirical fact that the practices of a population which are the use of [a] relatively small number of sentences of a natural language determines, for that population, the use of a potentially infinite remainder they have never been exposed to” (p. 144).

“The notion of ‘grammar’ which I am addressing here is that of an interpreted categorial-transformational grammar. Such a grammar is an account of the generation of surface sentences of a language … from an underlying set of deep structures” (p. 144).

This is grammar in a Chomskyan rationalist, antibehaviorist sense.

“The projective capacities which are to be explained are obviously not entailed by the practices and dispositions codified in a set of those phonetic descriptions and assertibility conditions…. An account of projection is thus an explanation of how people, being the sorts or organisms that we are, can engage in the complex social practices we do engage in. It is just this sort of inquiry which we considered … as the sort of inquiry within which the objects involved in a practice become important” (p. 145).

This puts new light on how individual words and phrases come to mean what they do.

“Consideration of projective facts of this sort can lead us, further, to attribute structural classes of sub-sentential components to some speaker” (ibid).

“We are interested in seeing how, by looking at facts about the acquisition of vocabulary and compounding forms by a subject, we can in principle explain his open-ended competence to use novel utterances, by exhibiting that competence as the product of projective capacities associated with classes of sub-sentential components” (p. 147).

“Projective classes for an individual were pictured as attributed on the basis of two sorts of acquisition, roughly the acquisition of some projective form, and the acquisition of vocabulary” (pp. 147-148).

“Indeed, it is only in terms of such projective dispositions that we can explain the notion of correctness for novel utterances. We can only explain how there should be such an agreement in terms of shared structural classes induced by familiar expressions, which determine the projection to novel utterances” (p. 148).

Linguistic structure is a theoretical object of just the kind whose status is a matter of dispute between the realists and the instrumentalists.

“This picture of linguistic structure as postulated to account for a speaker’s ability to use novel utterances correctly, on the basis of facts about the acquisition of capacities to project sub-sentential expressions, leads immediately to a change in the criteria of adequacy we impose upon translation functions, and accordingly to a change in the notion of the ‘meaning’ of a sentence which is preserved by translation” (p. 150).

From an empiricist point of view, questions about norms are questions of fact about what is usually the case. Empirical norms are “norms” in a non-normative, statistical sense of “normal” that has nothing to do with what should be the case, except accidentally. The projection of grammar to novel cases on the other hand is possible because grammar has a properly normative sense of “right” usage that is independent of whatever we conclude are the facts about statistically “usual” usage.

“[I]f translation is really to transform the capacity to speak one language into the capacity to speak another, it must transform an individual’s capacity to project novel sentences…. In order to learn to speak the new language, to form novel sentences and use them appropriately, an individual must have a translation-scheme which does more than match assertibility conditions. It must generate the matched assertibility conditions of an infinite number of sentences on the basis of a familiarity with the elements out of which they are constructed, as exhibited in fairly small samples” (p. 150).

Speaking is not merely the utterance of sounds, and it is not just an imitation of other speaking. Concrete meanings presuppose learned notions of rightness or goodness of fit that are furthermore always in principle disputable. This also requires a non-behaviorist account of learning.

“Our account of this fact must show how what the subject learned to do before enables him to use this expression in just this way now, even though he has never been exposed to a correct use of it” (p. 151).

“Projection is not just a matter of using novel utterances, but also of using familiar ones under novel circumstances” (ibid).

“We can conclude that competence involved, not just in using … a free-standing utterance, but in projecting it as a genuine component of compound utterances, cannot be expressed merely by assertibility conditions, but requires some additional element” (p. 153).

“We should notice that the argument we have just considered is formally analogous to two arguments we have seen before. In the first place, it is just the same style of argument which we employed … in order to show that truth conditions were required to account for the contribution by component sentences to the assertibility conditions of compound sentences containing them…. All we have done here is to extend the earlier argument to sub-sentential compounding, an extension made possible by the more detailed consideration of why compounding is important. Second, this argument … is analogous to the ‘syntactic’ arguments of Chomsky…. In each case similar surface forms (phonetic descriptions and assertibility conditions respectively) are assigned different deep structures on the basis of their different projective roles…. So it is clear that these expressions would have to be associated with something besides assertibility conditions in our theory of their projection anyway” (pp. 154-155).

“Our explanation of the fact that there are correct phonetic descriptions and assertibility conditions for sentences no one has ever used before will be that the use of those sentences is determined by the grammar, … and that any individual’s learning to use the language is his learning to conform to the regularities of projection codified in that grammar” (p. 156).

“We have found that explaining the actual, empirical generation of the sentences of the language, shown by the sorts of projection of one corpus of utterances onto another which actually occur, requires that structural elements underlying phonetic structure be assigned to parallel structural elements underlying the assertibility conditions…. Just as the structure underlying the phonetic descriptions is plausibly identified as syntactic structure, so the corresponding structure underlying assertibility conditions is plausibly identified with semantic structure” (ibid).

“The same argument which gave us objective truth conditions … may thus be extended, within the context of our more detailed account of the empirical project which produces a grammar, to yield a parallel account of the function and origin of objective denotations” (p. 158).

“The case of the brown rabbit with a white foot shows that the denotations associated with the expressions ‘rabbit’ and ‘undetached rabbit-part’ must determine in some way the boundaries which white patches must exhibit in order to be grounds for reporting white rabbits or white undetached rabbit-parts” (ibid).

“But the boundaries which determine what objects or objective features are denoted by the expressions are not apparent boundaries…. Explaining the different patterns of projection of the elements of these pairs requires an objective difference in boundaries around white patches” (p. 159).

“It is important to realize that our grammar does not just seek to account for individual linguistic competence. It seeks to account for the shared projective practices in virtue of which there is a distinction between correct and incorrect uses of sentences no one has ever used before…. The grammar must account for the correct and incorrect potential uses of even quite complicated sentences which the ordinary man would never use” (ibid).

“[D]enotational schemes are part of an empirical explanation of certain social practices. Such explanations must cohere with the empirical explanations we are prepared to offer for other sorts of human conduct…. It is a prime virtue of the account we have offered of the question to which a grammar would be an answer that it shows us we can pick the objects in terms of which we explain projective practices in the same way we pick the objects in terms of which we explain color vision, indigestion, and quasars” (p. 162).

Here he is appealing to empirical explanation, and to something like the positivist notion of the unity of science. I am inclined to go to the opposite extreme, and to argue that genuine explanation is never merely empirical. There are empirical things, and we do want to explain them. There also is an empirical field of experience, but it too belongs to what is to be explained. In themselves empirical things do not explain anything. I think, though, that coherence does not apply only to explanation. There is also an implicit coherence on the level of what is to be explained. That is the sounder basis of the ideal of the unity of science.

In later work he explicitly criticizes empiricism in the philosophy of science, but he continues to be interested in empirical things, as evinced by many of his examples and by the theme of “semantic descent” in A Spirit of Trust.

Grammatical Prejudice?

In several of his works, Nietzsche attacks the “grammatical prejudice” or “superstition of logicians” in positing a doer behind the deed. For example:

“‘[T]he doer’ is merely a fiction added to the deed — the deed is everything. The popular mind in fact doubles the deed; when it sees the lightning flash, it is the deed of a deed: it posits the same event first as cause and then a second time as its effect. Scientists do no better when they say ‘force moves’, ‘force causes’, and the like” (Genealogy of Morals, 1st essay, section 13, Kaufman tr., p. 45).

One of the more obvious targets of this polemic would seem to be a certain stereotypical Aristotelianism. Such a view would take Aristotle’s more superficial characterization of “substance” [ousia] as the “underlying thing” as a final truth. As Nietzsche points out, this view has very wide diffusion, and has come to be regarded as common sense.

We have seen in some detail, however, that in his more advanced thought in the Metaphysics, Aristotle explicitly inverts this popular prejudice, and makes act [energeia] the criterion of what is a substance most of all [ousia malista]. As Goethe said, “In the beginning was the deed”.

Contrary to Nietzsche though, this does not make of substance a mere fiction. For Aristotle, substance is ultimately a result rather than a starting point. It turns out to be a derived concept, rather than an elementary one as may first appear. But as a result and as a derived concept, it has legitimate use.

Even the great 20th century Thomist Etienne Gilson suggests in his Being and Some Philosophers that we should think of being as a verb rather than as a noun. I too keep harping on the fact that all the many “senses of being” Aristotle enumerates in book Delta of the Metaphysics are senses of the connective “is”. But this is not the end of the story either.

The next thing we should notice is that what Aristotle principally enumerates and emphasizes in book Delta and elsewhere are the senses of being in which we say something “is” something (else) in accordance with one of the categories. These are transitive (connective) senses of “is”, associable with the formation of propositions that could be evaluated as true or false. Behind Aristotle’s talk about being is a guiding concern with normative saying and intelligible explanation of what properly speaking “is” the case. With his Thomistic roots, Gilson on the other hand emphasizes an intransitive sense of being as “existing”.

In numerous passages in the Metaphysics, Aristotle does indeed use “being” in an intransitive way, but my contention is that this is by way of summary or a kind of shorthand, which should be understood as presupposing and referring back to something like the enumeration of senses of being that we actually find in book Delta, all of which I would contend are transitive.

The only apparent exception in Delta is none other than being in the sense of in-act and in-potentiality. This occurs at the very end of the enumeration, and can reasonably be interpreted as shorthand for the longer expressions used earlier. Moreover, the detailed discussion of being in-act and in-potentiality in book Theta is about something (transitively) being something definite in-act or in-potentiality. In Delta, I think the brief mention of being in-act and in-potentiality is to be understood as wrapping a modal dimension around the more basic saying of “is” in the senses of the Categories. (Here I have passed over other senses of being that Aristotle himself says are less important, but none of these corresponds to what the scholastics and the moderns call existence either.)

Perhaps Gilson is right that Aquinas can be read as a sort of “existentialist”. But relatively speaking, I think Aristotle himself is closer to the analytic and continental philosophers who have emphasized the importance of language, meaning, and discourse. (See also Being as Such?.)

On a Philosophical Grammar

It seems like a good time to get back to a bit more detail on Alain de Libera’s “archaeology of the subject”, which I introduced a while back. Volume 1 is subtitled Naissance du sujet or “Birth of the Subject”. He begins with a series of questions asked by Vincent Descombes in a review of Paul Ricoeur’s Oneself as Another:

“1) What remarkable differences are there, from the point of view of use, between these words which we place too lazily in a single category of personal pronouns (and particularly here I, he, me, him, her, oneself)?

“2) What is the status of intentions to act? Are they first properties of the agent?

“3) Should we distinguish, as Ricoeur proposes, two concepts of identity, identity as sameness (idem) and identity as ipseity [“selfness”] (ipse)?

“4) What is this self that figures in the expression self-awareness?” (Archéologie du sujet vol. 1, p. 31).

The birth of the subject in the modern sense is what de Libera will investigate. He aims to show how “the Aristotelian ‘subject’ [hypokeimenon, or thing standing under] became the subject-agent of the moderns in becoming a kind of substrate for acts and operations” (p. 39). He quotes a famous passage from Nietzsche denouncing the “grammatical superstition” of the logicians who assume that wherever there is a predicate for an activity such as thinking, there must be something corresponding to a grammatical subject that performs it. Nietzsche says that a thought comes when it wants, not when I want.

De Libera asks, “How did the thinking subject, or if one prefers, man as subject and agent of thought, first enter into philosophy? And why?” (pp. 45-46). He points out the simple fact that a grammatical subject need not be an agent, as when we say “the boy’s timidity made him afraid”. He quotes Frédéric Nef to the effect that action is not a grammatical category. How then did “the subject” become bound up with agency?

He notes that something like this is already at play in Aquinas’ Disputed Questions on the Soul, when Aquinas develops the notion of a “subject of operation” related to sensibility, associating the subject of an action or passion with a power of the soul. How, de Libera asks, did we come to assume that every action requires “an agent that is a subject” and “a subject that is its agent” (p. 58)? (See also Not Power and Action.)

He will be looking for medieval roots of notions that most people, following Heidegger, consider to be innovations of Descartes. Meanwhile, de Libera recalls that Augustine had gone so far as to label it blasphemy to call the soul a “subject”. Knowledge and love, Augustine said, are not in the mind as in a subject.

Predication

It is extremely common to see references to “predication” as if it were a central concept of Aristotelian logic. We are so used to a grammatical interpretation in terms of relations between subjects and predicates that it is hard to disengage from that. However, historically it was Aristotelian logic that influenced ancient Greek accounts of grammar, not vice versa.

Modern logicians distinguish between a neutral proposition — which might be merely mentioned, rather than asserted — and the assertion of the proposition. Grammatical predication in itself does not imply any logical assertion, only a normatively neutral syntactic relation between sentence components. But “said of” in Aristotle always refers to some kind of meaningful assertion that has a normative character, not to grammatical predication.

Aristotle talks about what we might call kinds of “sayables” (“categories”). He famously says that we can only have truth or falsity when one kind of sayable is “said of” another. Mere words or phrases by themselves don’t assert anything, and hence cannot be true or false; for that we need what modern writers have referred to as a “complete thought”.

The ordinary meaning of “to categorize” in ancient Greek was “to accuse in a court of law”. Aristotle used it to talk about assertions. It didn’t originally connote a classification. The modern connotation of classification seems to stem from the accident that independent of what “category” meant in his usage, Aristotle famously developed a classification of “categories”.

Aristotle also talks about logical “judgment” (apophansis, a different word from practical judgment or phronesis). Husserl for instance transliterated this to German, and followed the traditional association of logical judgment with “predication”. But the ordinary Greek verb apophainein just means to show or make known. Aristotle’s usage suggests a kind of definite assertion or expressive clarification related to demonstration, which makes sense, because demonstrations work by interrelating logical judgments.

All of Aristotle’s words and phrases that get translated with connotations of “predication” actually have to do with normative logical assertion, not any connecting of a grammatical subject with a grammatical predicate. Nietzsche and others have complained about the metaphysical status foisted on grammatical subjects, implicitly blaming Aristotle, but all these connotations are of later date.

The great 20th century scholar of ancient and medieval logic and semantics L. M. de Rijk in his Aristotle: Semantics and Ontology (2002) argued at length that Aristotle’s logical “is” and “is not” should be understood as not as binary operators connecting subjects and predicates, but as unary operators of assertion and negation on whole propositions formed from pairs of terms. (See also Aristotelian Propositions.)

As in similar cases, by no means do I wish to suggest that all the work done on the basis of the common translation of “predication” is valueless; far from it. But I think we can get additional clarity by carefully distinguishing the views and modes of expression of Aristotle himself from those of later commentators and logicians, and I think Aristotle’s own more unique perspectives are far fresher and more interesting than even good traditional readings would allow.

Ideas Are Not Inert

In the British empiricist tradition, “ideas” are supposed to be inert contents of an active “mind”, and to be either identical with sensible contents or derived from sensory experience. They are supposed to have content that just “is what it is”, but is nonetheless sufficient to serve as a basis for our conclusions and motivations.

I want to argue instead that the only possible basis for our conclusions and motivations is other conclusions and motivations. As individuals we always start in the middle, with some already existing conclusions and motivations that were not necessarily individually ours to begin with. Language and culture and upbringing provide us with a stock of pre-existing conclusions and particularly shaped motivations.

Further, I don’t see ideas as inert. The notion that ideas are completely inert comes from an extreme polarization between active mind and passive idea that results from entirely subordinating this relation to the grammatical model of subject and predicate. Aristotle’s rather minimalist account of these matters effectively treats objects and ideas as having some activity of their own. For Aristotle, “we” do not hold a monopoly on activity. There is also activity in the world that is independent of us, and much of our activity is our particular reflection of the world’s activity. Indeed for Aristotle I take it to be thought rather than an assumed “thinker” that is primarily active.

Hegel has often been criticized for speaking as if “the Idea” had life of its own, independent of us humans. If one holds an empiricist view of ideas, this can only sound like nonsense, or some kind of animism. But with an Aristotelian view of thoughts as a kind of intrinsically active “contents”, that is not the case. If thoughts are intrinsically active, we need not posit a separate mental “subject” distinct from any actual thought or perception or content as the source of all activity, behind thought.

Plato compared the human soul to a city — a kind of unity to be sure, but a weak one consisting of a federated community and relatively specific “culture” of thoughts and perceptions, subject to varying degrees of coherence. Only under the influence of later theology did it come to be assumed that the soul must necessarily have the far stronger unity of a simple substance. A looser unity of the soul is very compatible with a view of thoughts and perceptions as multiple fibers of activity, from which the overall activity we attribute to the soul or mind is constituted.

Syllogism

Aristotle invented logic as a discipline, and in Prior Analytics developed a detailed theory of so-called syllogisms to codify deductive reasoning, which also marks the beginning of formalization in logic. Although there actually were interesting developments in the European middle ages with the theory of so-called supposition as a kind of semi-formal semantics, Kant famously said Aristotle had said all there was to say about logic, and this went undisputed until the time of Boole and De Morgan in the mid-19th century. Boole himself said he was only extending Aristotle’s theory.

The fundamental principle of syllogistic reasoning is best understood as a kind of function composition. Aristotle himself did not have the concept of a mathematical function, which we owe mainly to Leibniz, but he clearly used a concept of composition of things we can recognize as function-like. In the late 19th century, Frege pointed out that the logical meaning of grammatical predication in ordinary language can be considered as a kind of function application.

Aristotle’s syllogisms were expressed in natural language, but in order to focus attention on their form, he often substituted letters for concrete terms. The fundamental pattern is

(quantifier A) op B
(quantifier B) op C
Therefore, A op C

where each instance of “quantifier” is either “some” or “all”; each instance of “op” is either what Aristotle called “combination” or “separation”, conventionally represented in natural language by “is” or “is not”; and each letter is a type aka “universal” aka higher-order term. (In the middle ages and later, individuals were treated as a kind of singleton types with implicit universal quantification, so it is common to see examples like “Socrates is a human”, but Aristotle’s own concrete examples never included references to individuals.) Not all combinations of substitutions correspond to valid inferences, but Prior Analytics systematically described all the valid ones.

In traditional interpretations, Aristotle’s use of conventionalized natural language representations sometimes led to analyses of the “op” emphasizing grammatical relations between subjects and predicates. However, Aristotle did not concern himself with grammar, but with the more substantive meaning of (possibly negated) “said of” relations, which actually codify normative material inferences. His logic is thus a fascinating hybrid, in which each canonical proposition represents a normative judgment of a material-inferential relation between types, and then the representations are formally composed together.

The conclusion B of the first material inference, which is also the premise of the second, was traditionally called the “middle term”, the role of which in reasoning through its licensing of composition lies behind all of Hegel’s talk about mediation. The 20th century saw the development of category theory, which explains all mathematical reasoning and formal logic in terms of the composition of “morphisms” or “arrows” corresponding to primitive function- or inference-like things. Aside from many applications in computer science and physics, category theory has also been used to analyze grammar. The historical relation of Aristotle to the Greek grammarians goes in the same direction — Aristotle influenced the grammarians, not the other way around. (See also Searching for a Middle Term; Aristotelian Demonstration; Demonstrative “Science”?)