Moore’s Meta-Ethics

As part of due diligence for my previous post, I did a quick search to canvas prior uses of the term “meta-ethics” or “metaethics”. The results were somewhat surprising. One source simply called it a branch of analytic philosophy. Another implied that the word was first used by the early analytic philosopher G. E. Moore (1873-1958), but a search of his most famous work Principia Ethica (1903) did not find it there. Before this my closest contact with Moore had been Alasdair Macintyre’s very negative portrayal.

Moore’s work dominated analytic discussions of ethics in the first half of the 20th century. The aspect that later writers have identified as meta-ethical was his strong distinction between the good in itself and things that we merely call good. I cannot help but think of Plato in this context. Moore’s focus on questions of intrinisic worth recalls Aristotle’s discussion of what is sought for its own sake, rather than as a means to some other end. His prime examples of intrinsic worth were beauty and affection between people. He pointed out that in ethical judgements, a whole is not just the sum of its parts.

Moore held that good is undefinable and simple, which again recalls Plato. But contrary to the perspective of the “long detour” associated with Plato’s Republic, he held that good is something we apprehend immediately, in a kind of intuition. I even wonder if this influenced those who claim that Aristotelian “intellect” must be fundamentally intuitive and immediate.

In any case, Moore also held that there is no moral truth, and generally devalued first-order or practical or what some call “normative” ethics. While I do not at all agree with that, I do see philosophical ethics as mainly concerned with broad second-order or “meta” questions.

At the same time, he was principally responsible for highlighting the so-called naturalistic fallacy in utilitarianism and similar doctrines. He also rejected egoism as a moral theory, and identification of the good with will. He held that ethical propositions resemble neither natural laws nor commands. Ethics does not identify absolute duties, but rather makes relative distinctions between alternatives. He held that practical ethical judgements are concerned with means, and therefore involve an element of causal judgment. In general he was much concerned to point out linguistic confusions in ethics, such as the identification of good with a supersensible property. He pointed out the limitations of rule following, and held that the exercise of virtue in the performance of duties is not good in itself.

According to later discussions, Moore laid the ground for the “noncognitive” perspectives on ethics that dominated analytic accounts in the first half of the 20th century. These make practical ethics purely a matter of subjective feeling. That is the basis of Macintyre’s criticism of Moore.

(We saw earlier that Habermas is regarded as working on the “cognitive” side of this divide. I don’t care for this terminology, but on that score my sympathies would have to be with Habermas and his “ideal speech situations”. Habermas acknowledges influence from Gadamer, who saw Platonic dialogue as a model for ethical thought. And Brandom, with his emphasis on Hegelian mutual recognition, is an obvious “cognitivist” who has called Habermas a personal hero.)

Moore speaks of the proper approach to ethics as “scientific”. By science he seems to mean not rational elaboration and interpretation, but a broadly empiricist attitude. I don’t think ethics should strive to be scientific in that sense, but rather “reasonable”, and open and responsive to situations.

Metaphysics or Meta-Ethics?

The work we know as Aristotle’s Metaphysics is at least as deeply interwoven with the Nicomachean Ethics as it is with the Physics.

The title meta ta physika (“after the physics”) is a bit accidental, and definitely not from Aristotle himself. It is attributed to the principal editor of Aristotelian manuscripts, Andronicus of Rhodes (1st century BCE), for whom it very mundanely referred to the placement of those writings sequentially “after” the writings we know as the Physics in his edition, which was apparently the main source of later manuscript traditions of the surviving Greek.

What is at issue in my objections to scholastic, early modern, and Heideggerian notions of “metaphysics” has little or nothing to do with this lexical issue as such, but a common feature of these views is that they neglect the all-important connection of first philosophy to ethics.

In contrast, an implicit view of meta-ethics as second-order ethics, or inquiry into the foundations of ethics, has been seen in historical philosophers as far back as Plato. I would even say that philosophical ethics has always been mostly meta-ethics.

One of the themes I have been developing here is a sort of “general meta-ethics” that would be a legitimate heir of what Aristotle called first philosophy or wisdom, decoupled from speculative astronomy, while offering some lessons of its own. I have also been inspired by Brandom’s idea of “normativity all the way down”, which extends the Kantian thesis of the primacy of “practical” (ethical) reason.

I see Plato and Aristotle as inaugurating a tradition of “rational ethics” that separates ethics from appeals to authority, and emphasizes thoughtful inquiry and dialogue. Although never socially dominant in its purer forms, this philosophical approach to ethics has been historically quite influential.

Even very traditional theologians have often tempered their emphasis on revelation with recognition of at least a relative autonomy of ethics. Some have gone further and explicitly acknowledged that the highest degrees of ethical goodness can arise independent of their own particular faith.

Medieval discussions on “intellect” reflect various fusions, extensions, and decorations of Aristotelian and neoplatonic notions both of the highest good absolutely, and of the more specific highest good for humans. Spinoza entitled his magnum opus simply Ethics, and spoke of a purely philosophical beatitude, as did Averroes before him. Leibniz advocated a “wise charity” that is both gentler and more generous than law, while also reviving and further sharpening Plato’s critique of one-sided emphasis on God’s will, power, and authority. Kant reversed traditional wisdom and argued that ethical reason is more fundamental than modern notions of theoretical reason. Hegel made a fundamental contribution with his meta-ethical idea of mutual recognition, which Brandom and Pippin have importantly expounded in our own time.

Implication Spaces

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Reason Relations

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

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

This notion of reason relations is already quite fascinating.

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

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

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

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

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

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

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

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

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

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

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

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

Next in this series: Implication Spaces

Quick Note on Proof Theory

I read Aristotelian demonstration as more a making explicit than a proof of truths. The logical expressivism of the author of Making It Explicit (Robert Brandom) does something similar with modern logic. Nonetheless it would be very wrong to conclude that proof theory has no philosophical relevance.

To begin with, proof theory is itself not concerned with proving this or that truth. It is the study of proofs, the beginning of which is to recognize that proofs and proof calculi are themselves mathematical objects. Proofs are functions from premises to conclusions. This has profound consequences.

At an utterly simple level, one small piece of a far larger result is that the notion of an implication A => B is at a certain level formally interchangeable with the notion of a mathematical function A => B. Frege very explicitly treats logical predication as a function as well.

Category theory builds all of mathematics on such morphisms, starting from a single basic operation of composition of arrows. Homotopy type theory suggests that we think of the arrows as paths through spaces. All this is an elaboration and abstraction of the utterly simple but crucial notion of “follows from”, or what Brandom calls subjunctive robustness.

Then an Aristotelian syllogism can be seen on the model of the composition of two predications or functions or morphisms or arrows or paths A => B and B => C around a common type or middle term B that is the output of one and the input of the other. This is not intended to capture a sophisticated result like a mathematical theorem, but rather to express sound reasoning in the simplest, most perspicuous, and most universal way possible.

Next in this series: Reason Relations

An Isomorphism

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Next in this series: Quick Note on Proof Theory

The Role of Reasons

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Next in this series: An Isomorphism

“Intellect” as Culminative Intuition

Once or twice before, I’ve somewhere mentioned the issue of interpreting the remarks Aristotle makes about intellect (nous) in the Posterior Analytics. Some people read this text as attributing to intellect a kind of immediate grasp that they associate with intuition. I have even seen nous translated as intuition.

If intuition is supposed to be immediate in an unqualified way, I don’t think this interpretation can be reconciled with Aristotle’s view that although there is what he calls an inner sense, the soul does not have direct self-knowledge, but only self-knowledge of an indirect sort.

My late father was quite impressed by Kant and Hegel’s critique of the notion that intuition is a source of immediate knowledge, but he also used to distinguish “culminative intuition” from “originary intuition”. This seems very useful to me. Originary intuition is the immediate kind that some people claim to have, but is rejected by Kant and Hegel. Culminative intuition on the other hand arguably resembles what the Arabic philosophers called “acquired intellect”. That is, it is an end result of a long process (see also Long Detour?; First Principles Come Last; Adeptio). One of my very first posts here suggested that Aristotle and Plato would have been sympathetic to the inferentialist account of reason propounded by Robert Brandom. Brandom himself reads Kant and Hegel as inferentialists.

Google returns zero references to culminative intuition on the internet. Now at least there will be one. If a kind of intuition does have a kind of immediacy, I think it must be what Hegel called mediated immediacy, which is like knowing how to ride a bicycle. That is, it depends on a process of learning, but eventually acquires a kind of immediacy.

Averroes vs Ghazali

The Persian al-Ghazali (1055–1111 CE), known to the Latins as Algazel, is regarded as the greatest theologian of the Ash‘arite school of Sunni Islam. According to Wikipedia, the Ash‘arites are one of several schools that advocate the use of reason in expounding the Islamic revelation. In this sense they are definitely to be distinguished from the literalists. The Ash‘arites nonetheless defend a radical version of omnipotence.

Ghazali wrote a work that circulated in the Latin world, which summarized the views of the Islamic philosophers accurately enough that the Latins mistakenly regarded him as one of them. “Philosophy” in this context principally refers to the thought of al-Farabi and Ibn Sina (Avicenna). But Ghazali is best known to historians of philosophy for his sharp attack The Incoherence of the Philosophers, which treated Ibn Sina as representative. Ghazali was a very strong creationist who insisted that creation must be understood as having occurred in time. Like Duns Scotus and William of Ockham a bit later in the West, he defended a radically voluntarist theology.

In a short work called the Decisive Treatise that was never translated to Latin, Ibn Rushd (Averroes) argues as an Islamic jurist that the Koran commands those capable of doing so to study philosophy. Though his philosophy had very little influence in the Islamic world, he was the leading Maliki jurist in al-Andalus and the Maghreb in his day. He wrote the authoritative textbook of Maliki jurisprudence. I learned that Maliki law is still practiced in many Islamic countries.

Ibn Rushd wrote a refutation of Ghazali called The Incoherence of the Incoherence, which interspersedly contains the full text of Ghazali’s work. It circulated in Latin under the title Destructio Destructionum (destruction of the destruction). I’ve transcribed some small excerpts of this historically fascinating book.

The dispute is basically about Aristotle versus creationism. The particular focus of the first part I have excerpted addresses this from the angle of views about the relation between what is eternal and what is in time. The other part I’ve excerpted has to do with Aristotle versus theological voluntarism.

[Ghazali] “The philosophers say: It is impossible that the temporal should proceed from the absolutely Eternal…. When the world begins in time, a new determinant either does or does not arise…. If it does not, the world will stay in the same state of pure possibility as before; if a new determinant does arise… either we shall have an infinite regress or we shall arrive at a principle determining eternally” (Averroes’ Tahafut al-Tahafut (The Incoherence of the Incoherence), tr. Van Den Bergh (1954), p. 1).

[Averroes] “This argument is in the highest degree dialectical and does not reach the pitch of demonstrative proof. For its premises are common notions, and common notions approach the equivocal, whereas demonstrative premises are concerned with things proper to the same genus” (ibid).

Averroes retains Farabi’s exaggerated emphasis on strict demonstration in the sense of the Prior Analytics in Aristotle. Reading Aristotle partly through a Farabian lens, Averroes does not recognize the large place and positive role that Aristotle implicitly gives to dialectic in the sense of the Topics throughout his works. Averroes sees “dialectic” as an intellectually loose approach that easily falls into sophistry.

[Averroes] “For the term ‘possible’ is used in an equivocal way of the possible that happens more often than not, of the possible that happens less often than not, and of the possible with equal chances of happening, and these three types of the possible do not seem to have the same need for a new determining principle” (ibid).

“All these are multifarious and difficult questions which need, each of them, a special examination, both in themselves and in regard to the opinions the ancients held about them. To treat what is in reality a plurality of questions as one problem is one of the well-known seven sophisms, and a mistake in one of these principles becomes a great error by the end of the examination of reality” (pp. 1-2).

[Ghazali] “[The world’s] existence was not willed before and therefore did not happen… at the exact moment it began it was willed by an eternal will and therefore began” (p. 3).

[Averroes] “The act of the agent necessarily implies a change and … each change has a principle which causes it…. [T]he Eternal cannot change in any way. But all this is difficult to prove” (ibid).

“[O]ur expressions ‘eternal will’ and ‘temporal will’ are equivocal, indeed contrary…. [W]hen one says: ‘There is a Willer who wills eternally one of two contraries in Himself’, the definition of the will is abandoned” (p. 4).

[Ghazali summarizing the philosophers] “The effect only takes place when a new event, i.e. entering the house or the arrival of tomorrow, has actually happened…. A delay in the object willed is imaginable only in decision, for decision is not sufficient for the existence of the act” (p. 5). “If, however, the eternal Will is analogous to our decision, it does not suffice to produce the thing decided upon, but the act of creation must be accompanied by a new act of volition, and this brings us again to the idea of a change” (ibid). “[W]ithout the realization of any new condition, this effect comes into existence and is produced. And this is absurd” (p. 6).

[Averroes] “[Ghazali’s] example of divorce based on convention seems to strengthen the argument of the philosophers, but in reality it weakens it. For it enables the Ash’arites to say: In the same way as the actual divorce is delayed after the formula of divorce till the moment when the condition of someone’s entering the house, or any other, is fulfilled, so the realization of the world can be delayed after God’s act of creation until the condition is fulfilled on which this realization depends, i.e. the moment when God willed it. But conventional things do not behave like rational” (ibid).

[Ghazali] “[T]he party which believes in the creation of the world in time through an eternal Will includes so many persons that no country can contain them and no number enumerate them, and they certainly do not contradict the logically minded out of obstinacy, while knowing better in their hearts” (p. 7).

[Averroes] “[T]his argument is mistaken, for it is not a condition of objective truth that it should be known to all” (ibid).

[Ghazali] “[T]o suppose the Creator of the world ignorant of His own work is necessarily absurd” (ibid).

[Averroes] “This assertion belongs to the class of assertions whose contrary is equally false. For there exists no proof which refutes anything that is evidently true, and universally acknowledged. Anything that can be refuted by a demonstrative proof is only supposed to be true, not really true…. Equally, if it is absolutely true that the effect of a cause cannot be delayed after the causation and the Ash’arites claim that they can advance a proof to deny it, then we can be absolutely sure that they cannot have such a proof. If there is a controversy about questions like this, the final criterion rests with the sound understanding which does not base itself on prejudice and passion, when it probes according to the signs and rules by which truth and mere opinion are logically distinguished” (p. 8).

[Ghazaili] “[E]ternity of the world is impossible, for it implies an infinite number and an infinity of unities for the spherical revolutions, although they can be divided by six, by four, and by two” (p. 9).

[Averroes] “This too is a sophistical argument. It amounts to saying: In the same way as you are unable to refute our demonstrative argument for the creation of the world in time, that if it were eternal, its revolutions would be neither even nor uneven, so we cannot refute your theory that the effect of an agent whose conditions to act are always fulfilled cannot be delayed. This argument aims only at creating and establishing a doubt, which is one of the sophist’s objectives…. But when the existence of an eternal prime mover had been proved, whose act cannot be posterior to his being, it followed that there could as little be a beginning for his act as for his being; otherwise his act would be possible, not necessary, and he would not be a first principle…. The agent who has no beginning either for his existence or for those acts of his which he performs without an instrument, has no first instrument either to perform those acts of his without beginning which by their nature need an instrument.”

“But since the theologians mistook the accidental for the essential, they denied this eternal agent” (pp. 10-11).

“It will be clear to you that neither the arguments of the theologians for the temporal creation of the world of which Ghazali speaks, nor the arguments of the philosophers which he includes and describes in his book, suffice to reach absolute evidence or afford stringent proof” (p. 12).

Like Aquinas, Averroes holds that arguments on neither side of the debate for and against creationism reach demonstrative certainty. Averroes defends a theory of eternal “creation” that is far removed from what creationists mean by creation. It has been argued that Albert the Great also had a notion of eternal creation.

[Averroes] “No motion possesses totality or forms an aggregate, i.e. is provided with a beginning or an end, except in so far as it is in the soul, as is the case with time. And it follows from the nature of circular movement that it is neither even nor uneven except as represented in the soul” (p. 13).

“[T]he impossibility of an actual infinite is an acknowledged axiom in philosophical theory, equally valid for material and immaterial things…. Perhaps Avicenna wanted only to satisfy the masses, telling them what they were accustomed to hear about the soul. But this theory is far from satisfactory” (p. 14).

[Ghazali] “We seek to show by all this that the philosophers cannot shake the conviction of their adversaries that the eternal Will is connected with temporal creation, except by claiming its absurdity by the necessity of thought, and that therefore they are in no way different from the theologians who make the same claim against the philosophical doctrines opposed to theirs. And out of this there is no issue” (p. 15).

“[W]e say that the soul of Zaid is either identical with the soul of Amr or different from it; but their identity would mean something absurd, for everyone is conscious of his own identity and knows that he is not another” (ibid).

[Averroes] ” ‘[D]ifferent’ is an equivocal term, and ‘identity’ too is predicated of a number of things which are also called ‘different’…. The souls of Zaid and Amr are one in one sense and many in another; we might say, one in relation to their form, many in relation to their substratum” (pp. 15-16).

“When someone denies a truth of which it is absolutely certain that it is such-and-such, there exists no argument by which we can come to an understanding with him; for every argument is based on known premises about which both adversaries agree. When each point advanced is denied by the adversary, discussion with him becomes impossible, but such people stand outside the pale of humanity and have to be educated” (p. 16, emphasis added).

In emphasizing argument from agreed-upon premises, Averroes treats something like Platonic dialogue as a norm.

[Ghazali] “God before the creation of the world was able to create it, say, one year or two years before He did, and there is no limit to His power; but He seemed to have patience and did not create. Then He created” (p. 17).

[Averroes] “[W]hat has no beginning does not finish or end.” (ibid).

[Ghazali for the philosophers] “[W]e philosophers know by the necessity of thought that one thing does not distinguish itself from a similar except by a differentiating principle…. [I]f you answer that the Will of God is the differentiating principle, then one has to inquire what differentiates the Will, i.e. the reason why it has been differentiated in such or such way (p. 18).”

[Ghazali] “[W]ill is a quality which has the faculty of differentiating one thing from another, and if it had not this faculty, power in itself would suffice…. And to ask why will differentiates one of two similars is like asking why knowledge must comprehend the knowable” (ibid).

[Averroes] “As the theologians were unable to give a satisfactory answer, they took refuge in the theory that the eternal Will is a quality the nature of which is to differentiate between two similar things, without there being for God a differentiating principle which inclines Him to one of two similar acts” (p. 20).

This is the originally Stoic idea of a “freedom of indifference”. The Ash‘arites defend both predestination and theological and anthropological voluntarism.

[Ghazali] “Everyone, therefore, who studies, in the human and the divine, the real working of the act of choice, must necessarily admit a quality the nature of which is to differentiate between two similar things…. Suppose two similar dates in front of a man who has a strong desire for them, but who is unable to take them both. Surely he will take one of them through a quality in him the nature of which is to differentiate between two similar things” (p. 21).

[Averroes] “[I]t is by no means a matter of distinguishing between two similar things when, in this condition, he takes one of the two dates. It is nothing but the admission of an equivalence of two similar things. His will attaches itself therefore merely to the distinction between the fact of taking one of them and the fact of leaving them altogether” (p. 23).

“A definite moment cannot be assigned for the creation of the world, for either time did not exist before it, or there was an infinite time” (p. 32).

“[T]he temporal proceeds from the First Eternal, not in so far as it is temporal but in so far as it is eternal, i.e. through being eternal generically, though temporal in its parts…. for its arising anew is not a new fact, but is an eternal act, i.e. an act without beginning or end. Therefore its agent must be an eternal agent, for an eternal act has an eternal agent, and a temporal act a temporal agent. Only through the eternal element in it can it be understood that movement has neither beginning nor end, and this is meant by its permanence, for movement itself is not permanent, but changing” (p. 36).

[Ghazali on the philosophers] “They assert that he who affirms that the world is posterior to God and God prior to the world cannot mean anything but that He is prior not temporally but essentially” (p. 37).

[Averroes] “[T]he posteriority of the world to the Creator, since He does not precede the world in time, can only be understood as the posteriority of effect to cause” (p. 39).

[Ghazali] “How will you refute the man who claims that creation and annihilation take place through the will of God: if God wills, He creates, and if He wills, He annihilates, and this is the meaning of His being absolutely powerful, and notwithstanding this He does not alter in Himself, but it is only His act that alters?” (p. 83). “[T]he agent must be willing, choosing, and knowing what he wills to be the agent of what he wills, but according to [the philosophers] God does not will, He has no attribute whatever, and what proceeds from Him proceeds by the compulsion of necessity” (p. 87).

[Averroes] “Ghazali’s words ‘The agent must be willing, choosing, and knowing what he wills to be the agent of what he wills’ are by no means self-evident and cannot be accepted as a definition of the maker of the world without a proof, unless one is justified in inferring from the empirical to the divine” (pp. 87-88).

“[H]e who chooses and wills lacks the things which he wills, and God cannot lack anything He wills. And he who chooses makes a choice for himself of the better of two things, but God is in no need of a better condition. Further, when the willer has reached his object, his will ceases and, generally speaking, will is a passive quality and a change, but God is exempt from passivity and change. God is still farther distant from natural action, for the act of the natural thing is a necessity in its substance, but is not a necessity in the substance of the willer and belongs to its entelechy. In addition, natural action does not proceed from knowledge: it has, however, been proved that God’s act does proceed from knowledge. The way in which God becomes an agent and a willer has not become clear in this place, since there is no counterpart to His will in the empirical world. How is it therefore possible to assert that an agent can only be understood as acting through deliberation and choice? For then this definition is indifferently applied to the empirical and the divine” (p. 88).

The argument that the One cannot lack anything is a good example of a neoplatonic argument that was widely adopted and applied to the monotheistic God in later theistic traditions. Although it is speculative in the pre-Hegelian sense, the logic seems unassailable.

Ghazali uses the Aristotelian term “deliberation”, but gives it a different sense. In Aristotle, deliberation determines choice, and there is no separate faculty of will. The idea of a faculty of will separate from reason is a later development that was designed to support the notion of a freedom of indifference. This has the disastrous effect of subordinating reason to arbitrariness.

Aristotle never says that the First cause deliberates, only that it contemplates. The idea of a freedom of indifference is Stoic and only emerged later. Aristotle would not have regarded his notion of deliberation as compatible with the alleged freedom of indifference, because deliberation is concerned with identification of differences or distinctions that have practical import.

[Ghazali] “We say: ‘Agent’ means someone from whom there proceeds an act with the will to act according to choice and with the knowledge of the object willed. But according to the philosophers the world stands in relation to God as the effect to the cause, in a necessary connexion which God cannot be imagined to sever, and which is like the connexion between the shadow and the man, light and the sun, but this is not an act at all” (p. 89).

[Averroes] “The agent is what causes some other thing to pass from potency to actuality and from nonexistence to existence; this actualization occurs sometimes from deliberation and choice, sometimes by nature, and the philosophers do not call a person who throws a shadow an agent, except metaphorically, because the shadow cannot be separated from the man” (ibid).

[Averroes] “His assertion that not every cause is called an agent is true, but his argument that the inanimate is not called an agent is false, for the denial that the inanimate exhibits acts excludes only the rational and voluntary act, not act absolutely, for we find that certain inanimate things have powers to actualize things like themselves; e.g. fire, which changes anything warm and dry into another fire like itself, through converting it from what it has in potency into actuality” (p. 92).

[Ghazali] “If the inanimate is called an agent, it is by metaphor, in the same way as it is spoken of metaphorically as tending and willing” (ibid).

[Averroes] “[W]hen by these expressions is meant that it actualizes another’s potency, it is really an agent in the full meaning of the word” (ibid).

[Ghazali] “This is wrong, because will necessarily implies knowledge, and likewise act necessarily implies will” (ibid).

[Averroes] “But in the definition of ‘act’ knowledge is not included, because actualization of another thing is possible without knowing it” (p. 93).

[Ghazali] “[T]here is as a matter of fact a contradiction when ‘natural act’ is taken in a real sense, only this contradiction is not at once evident to the understanding nor is the incompatibility of nature and act felt acutely, because this expression is employed metaphorically; for since nature is in a certain way a cause and the agent is also a cause, nature is called an agent metaphorically. The expression ‘voluntary act’ is as much redundant as the expression ‘he wills and knows what he wills’ ” (ibid).

[Averroes] “This statement is undoubtedly wrong, for what actualizes another thing, i.e. acts on it, is not called agent simply by a metaphor, but in reality, for the definition of ‘agent’ is appropriate to it. The division of ‘agent’ into ‘natural’ and ‘voluntary agent’ is not the division of an equivocal term, but the division of a genus” (ibid).

“But as a matter of fact the natural agent has an act much more stable than the voluntary agent, for the natural agent’s act is constant — which is not the case with the act of the voluntary agent” (p. 94).

[Ghazali] “[I]f a man were to throw another into a fire and kill him, it is the man who would be called his killer, not the fire…. This proves that the word ‘agent’ is used of one whose act proceeds from his will, and, behold, the philosophers do not regard God as endowed with will and choice” (p. 95).

[Averroes] “This is an answer of the wicked who heap fallacy on fallacy. Ghazali is above this, but perhaps the people of his time obliged him to write this book to safeguard himself against the suspicion of sharing the philosophers’ view. Certainly nobody attributes the act to its instrument, but only to its first mover. He who killed a man by fire is in the proper sense the agent and the fire is the instrument of the killing, but when a man is burned by a fire, without this fact’s depending on someone’s choice, nobody would say that the fire burned him metaphorically” (ibid).

[Ghazali] “Our aim is to show that such is not the meaning of ‘act’ and ‘work’. These words can mean only that which really proceeds from the will. But you reject the real meaning of ‘act’, although you use this word, which is honoured amongst Muslims. But one’s religion is not perfect when one uses words deprived of their sense” (p. 96).

[Averroes] “This would indeed be a correct conclusion against the philosophers, if they should really say what Ghazali makes them say…. He does not unmask their imposture by his words, but he himself deceives by ascribing to them theories which they do not hold” (ibid).

[Ghazali] ” ‘Act’ applies to temporal production, but for [the philosophers] the world is eternal and is not produced in time. The meaning of ‘act’ is ‘to convert from not-being into being by producing it’ and this cannot be imagined in the eternal, as what exists already cannot be brought into existence. Therefore ‘act’ implies a temporal product, but according to them the world is eternal; how then could it be God’s act?” (ibid).

[Averroes] “If the world were by itself eternal and existent (not in so far as it is moved, for each movement is composed of parts which are produced), then, indeed, the world would not have an agent at all. But if the meaning of ‘eternal’ is that it is in everlasting production and that this production has neither beginning nor end, certainly the term ‘production’ is more truly applied to him who brings about an everlasting production than to him who procures a limited production” (pp. 96-97).

“And therefore, just as the eternal existent is more truly existent than the temporal, similarly that which is eternally in becoming is more truly coming to be than that which comes to be only during a definite time” (p. 100).

[Ghazali] “We do not say that the simultaneity of agent and act is impossible, granted that the act is temporal…. It is only an eternal act that we consider impossible, for to call an act that which does not come into being out of not-being is pure metaphor and does not conform to reality…. Our answer is that our aim in this question is to show that you philosophers use those venerable names without justification, and that God according to you is not a true agent, nor the world truly His act, and that you apply this word metaphorically — not in its real sense. This has now been shown” (p. 102).

In Aristotle there is a very important distinction between ordinary “action” as understood by everyone and his own completely original notion of “act”, which, as Gwenaëlle Aubry has very thoroughly documented, is most properly said of entelechy as a self-referential, purely internal determination, and is therefore not an “action” in the ordinary sense at all. In particular, Aristotelian act in its proper sense has nothing to do with efficient causality, especially as that latter notion was transformed by Latin writers such as Aquinas and Suárez. Efficient cause in Aristotle is the instrumental means by which some end is achieved. As such, it is the least primary of Aristotle’s four causes, not the most primary as it is for Aquinas and Suárez. This is a really big difference between them and Aristotle.

[Averroes] “In this argument he supposes that the philosophers concede to him that they only mean by God’s agency that He is the cause of the world, and nothing else, and that cause and effect are simultaneous. But this would mean that the philosophers had abandoned their original statement, for the effect follows only from its cause, in so far as it is a formal or final cause, but does not necessarily follow from its efficient cause, for the efficient cause frequently exists without the effect’s existing” (p. 103).

“[T]he term ‘eternal becoming’ is more appropriate to the world than the term ‘eternity’ ” (p. 104).

“When, however, after a close examination, it was discovered that all things tend to one end, and this end is the order which exists in the world, as it exists in an army through its leader, and as it exists in cities through their government, they came to the conclusion that the world must have one highest principle…. They believed therefore, because of the good which is present in everything, that evil occurs only in an accidental way…. [F]or the existence of much good with a little evil is preferable to the non-existence of much good because of a little evil” (p. 106). “Nowadays, however, … that out of the one all things proceed by one first emanation, is generally accepted, and with our contemporaries we need discuss only this latter statement” (p. 107).

The military metaphor does briefly appear in book Lambda of the Metaphysics. To me though, it has always seemed incongruous with Aristotle’s main idea of the First cause as a pure entelechy.

[Averroes] “But when the philosophers of our religion, like Farabi and Avicenna, had once conceded to their opponents that the agent in the divine world is like the agent in the empirical, and that from the one agent there can arise but one object (and according to all the First was an absolutely simple unity), it became difficult for them to explain how plurality could arise from it” (ibid).

This notion of the First as an absolutely simple One sounds to me more like Plotinus than Aristotle. “According to all” in this context would presumably be a reference to the neoplatonizing Farabian tradition. Of all medieval philosophers, Averroes is probably the closest to being a pure Aristotelian, but that is a relative distinction, not an absolute one. The only completely pure Aristotelian I know of is Aristotle himself. (Though I try to distinguish a genuinely historical Aristotle from the many Aristotles of the commentary tradition, I am certainly no pure Aristotelian either.)

[Averroes] “[T]hey declared that from the First, who is a simple existent, the mover of the highest sphere proceeds, and from this mover, since he is of a composite nature, as he is both conscious of himself and conscious of the First, a duality, the highest sphere, and the mover of the second sphere, the sphere under the highest can arise. This, however, is a mistake, according to philosophical teaching, for thinker and thought are one identical thing in human intellect and this is still more true in the case of the abstract intellects. This does not affect Aristotle’s theory, for the individual agent in the empirical world, from which there can only proceed one single act, can only in an equivocal way be compared to the first agent…. And thereby Aristotle proves that the agent of the human intelligibles is an intellect free from matter, since this agent thinks all things, and in the same way he proves that the passive [sic] intellect is ingenerable and incorruptible, because this intellect also thinks all things” (p. 108).

“They” in this case is clearly a reference to the Farabian tradition. The translator’s choice of “passive” intellect above for the potential intellect reflects the near total absence of specific scholarship on the texts of Averroes that still prevailed in the mid-20th century. In Averroes, the difference between the potential or “material” intellect on the one hand, and the passive “intellect” or the soul’s faculty of cogitation on the other, is huge. (See Cogitation, Intention; Imagination, Cogitation).

[Averroes] “Aristotle connects sensible existence with intelligible, saying that the world is one and proceeds from one, and that this Monad is partly the cause of unity, partly the cause of plurality. And since Aristotle was the first to find this solution, and because of its difficulty, many of the later philosophers did not understand it, as we have shown” (pp. 108-109). “But what we said of this connexion of every existent with the One is something different from what is meant by ‘agent’ and ‘object’, ‘maker’ and ‘product’ in this sublunary world” (p. 112).

Aristotle and Averroes

Out of general interest, long before my “Aristotelian turn”, I first read Simon Van Den Bergh’s translation Averroes’ Tahafut al-Tahafut (The Incoherence of the Incoherence) (1954) in the early 1980s. This was a deliberately less technical work that Averroes addressed to a non-specialist public, as a defense of philosophy and Aristotle against the attacks of the conservative Sunni theologian al-Ghazali. The most prominent of many disputed points concerned Aristotle’s thesis of the eternity of the world, which was understood to be incompatible with creationism. At the time, Averroes was only a name to me. But I was quite impressed with his overall defense of reason against Ghazali’s theological voluntarism and appeals to authority.

A bit later, I happened upon a translation of the Errors of the Philosophers attributed to Giles of Rome, and then the condemnations of 1270 and 1277. As a young contrarian, I became interested in the miscellany of propositions that were condemned. Later scholarship has pointed out the rather haphazard character of these lists. But conservative officials in the Latin Church were alarmed at the unbounded enthusiasm of some of their contemporaries for the influx of new, emancipating ideas from Greek and Arabic philosophy, the formulation of ethics independent of revelation, and the questioning of authority that accompanied it. The only kind of “authority” I accept is that based on actual merit that can be independently established. That rules out the possibility that any authority could be unconditional. In any case, I found that enthusiasm — even filtered through hostile representations — to be quite contagious.

It took many years before I was able to be more discriminating about all the many more or less sympathetic readings of Aristotle. I had first read Aristotle in 1977, in Richard McKeon’s Basic Works edition (1941). Even then I found many of the texts quite fascinating, but at the time I was more interested in Plato and Plotinus. Then in the 80s it was Foucault and Derrida and Deleuze and Nietzsche, and in the 90s Spinoza, then Leibniz. It was actually Deleuze who first put me onto Spinoza and Leibniz, but more and more I gravitated toward Spinoza and Leibniz themselves. I read more of and on Averroes during my Spinozist phase in the 1990s.

If you had told me in the 1990s that I would end up thinking of myself as an Aristotelian of sorts, in spite of my earlier moderate interest I would have thought you were crazy. At that point I was actually more interested in Averroes than in Aristotle himself.

It’s hard for me to say just when Aristotle became central for me, but it was some time in the early 2000s. Oddly enough, at this stage my first attraction was to the Categories. In my employment as a software engineer, I used to say to myself that Plato and Aristotle taught me more that I used on a daily basis than all my computer science courses and voluminous reading. Around the same time my father, who had been a philosophy professor, became very interested the work of Robert Brandom. It took a while for me to come to share that, but I read Brandom at first because I enjoyed the opportunities it provided for discussions with my dad. Eventually, Brandom taught me to appreciate Kant and Hegel, so I owe him a big debt.

I first read Brenet’s Transferts du Sujet shortly after it was published in 2003. Many of the distinctions Brenet makes went over my head at the time, but I was very impressed. I started collecting the Ancient Commentators on Aristotle series. In the early 2010s a friend and I embarked on reading my former St. John’s tutor Joe Sachs’s marvelous Aristotle translations out loud.

I started this blog in 2019 after my father died, as a way of continuing the conversation. My first posts were very informal and brief notes on Aristotle; on what was then Brandom’s brand new book on Hegel, A Spirit of Trust; and some personal reflections on ethics and life in general.

Among other things I already wanted to work on Brenet’s book from the start, but I felt that a lot of preparation was needed. I envisioned the blog as a sort of expanding spiral, and said to myself that it might be five years before I had enough context assembled to do justice to it.

Now it has come full circle, and that forecast turned out to be about right. In no way did I engineer this; it has been very spontaneous at each moment. But this writing has taught me a great deal. Initially, it replaced my very informal handwritten journal, but I have come to use a lot of literal reproduction and commentary.

Averroes in his four surviving Long Commentaries reproduced the entire text of Aristotle that he discussed in each. H. S. Harris in his monumental Hegel’s Ladder — also a literal, paragraph-by-paragraph commentary that I greatly admire — mentions Averroes’ use of this literary style as a precedent.

My own habit of frequent heavy quotation may raise a few eyebrows, but ever since the 70s I have particularly found that manual transcription or doing my own translations really helped consolidate my relationship to a text. I fondly hope that others will find similar value in this endeavor.