Free Will in Aristotle?

A recent large book by Olivier Boulnois, Généalogie de la liberté [Genealogy of Freedom] (2021), provides great detail on the emergence of the notion of free will (liberum arbitrium in Latin). I have previously mentioned his Être et représentation (1999), which gives fascinating documentation of the role of Duns Scotus in the formation of modern notions of representation, and metaphysics as ontology. Boulnois has written extensively on medieval philosophy. Like Alain de Libera, he turns a broadly Foucaultian “archaeological” method in the direction of showing the large and largely unknown role of medieval philosophy in the development of common Western philosophical concepts. This post will focus on a part of his discussion of how Aristotle stands largely apart from later views.

Early on in the present work, Boulnois cites the first sentence of G. E. Moore’s Principia Ethica:

“It appears to me that in Ethics, as in all other philosophical studies, the difficulties and disagreements, of which its history is full, are mainly due to a very simple cause: namely to the attempt to answer questions, without first discovering precisely what question it is which you desire to answer” (quoted in Boulnois, p. 34).

Boulnois notes how Latin translations extensively transformed the meanings of Aristotelian concepts.

“Is free will proper to the human? All of medieval and modern reflection on action rests on this thesis…. The concept of proairesis is analyzed for the first time in book III of the Nicomachean Ethics” (Boulnois, p. 133, my translation throughout). “To begin with, must we follow the [12th century Latin] translation of Burgundio? Does proairesis really mean free will?” (p. 134).

“With the translation of proairesis by ‘choice’, the key concept of Aristotelian ethics is integrated into the semantic field of will. The Burgundian node, which connects Aristotle and [the Church Fathers] Nemesius and Damascene in the same bundle of translations, constitutes a second origin of proairesis as free will in the 12th century” (p. 137). “Aristotle defines proairesis as a kind of desire joined with deliberation (with discourse)” (p. 139). “With Aristotle, we are indeed far from the medieval and modern interpretation, which speaks of choice (electio)” (p. 141).

Until now I have followed Joe Sachs’s translation in using “choice” myself. Sachs uses the English word with the same root as the French that Boulnois is questioning, but he explains it in terms of Aristotle’s definition just mentioned. But as we will see in an upcoming post, the Latin tradition gave it a voluntaristic coloring that is foreign to Aristotle.

“The most rigorous translation seems to be ‘resolution’…. Resolution introduces logos and time” (p. 140). “The object of our resolution is first of all the object of our desire, insofar as this results from a deliberation” (pp. 140-141). “Our moral character depends not on our theoretical attitude but on the ensemble of our resolutions, the repetition of which constitutes our disposition to act, indeed our aptitude for beautiful actions” (p. 142).

This ensemble of our resolutions sounds like the commitments of which Brandom and other contemporary writers speak.

“Since Cicero, the boulesis of the Stoics has been translated to Latin by voluntas [will]. But the Stoics affirm that such a mastery of impulse is found only in the sage…. It is only later, with Augustine, that this prerogative of the sage becomes a faculty accessible to all. Our concept of will, as capacity to consent or not to our representations, carries all this history. But in Aristotle, boulesis always designates the desire that pertains to that part of the soul that is capable of speech. It is a form of desire that is enunciable, intelligible…. Boulesis indeed is a wish: a wish does not require the existence of a will; like all desire, it is moved by its object” (p. 143).

“Among our desires, resolution results from a deliberation, which deploys itself in language…. The true principle of our resolution is of the order of language and of thought. Like all living beings, the human is necessarily moved by what appears to her as desirable; but in distinction from the other living beings, it is through speech that the desirable appears to her…. Resolution bears on action that can be accomplished by us…. There is only a place for deliberation when several lines of action are possible…. We deliberate on that which no one can do in our place” (p. 145, emphasis in original).

Here the resolution of deliberation is explicitly grounded in language and thought, and not in an anachronistic non-Aristotelian notion of a faculty of will.

“It is necessary to underline: Aristotle does not exactly say that the resolution depends on us. What depends on us is the action that is the object of that resolution…. Aristotle does propose a theory of decision, or of resolution, but not a theory of freedom of choice, or of free will” (pp. 145-146, emphasis in original).

Unlike Boulnois here, some 20th century writers have used “decision” in the sense that Boulnois gives to “choice”.

“Such actions are ontologically contingent: they could [also] not be. The metaphysical tradition deduced from this the existence of a power of choice, of a will or a free will” (pp. 146-147).

The important point here is that this “metaphysical tradition” does not include Aristotle.

“Nothing obliges us to understand contingency in an absolute manner, and as subject to our power. Aristotle refers to the ensemble of actions that depend on us (eph’ hemin) in general (in the sense of a collectivity: the humans, the agents, the citizens), but not to those that depend on me (here and now)…. But Aristotle never claims that an agent has, other things being equal, at a given instant, the capacity to do one thing or its contrary, to act and not to act. ‘What depends on us’ is a generic capacity, proper to humankind, and not to some particular individual, here and now. Reciprocally, in insisting on the idea that deliberation is the cause of our resolution, Aristotle holds that at the interior of this bivalence, we more often see what the logos presents as desirable” (p. 147, emphasis in original).

“In this context, what is the principle of action?” (p. 150). He quotes Aristotle, “and the principle of resolution is desire and reason…. What affirmation and negation are in thought, pursuit and flight are to desire…. For resolution to be good, it is necessary at the same time that the discourse be true and the desire just” (p. 150).

Boulnois summarizes, “Thus the properly human principle of action is resolution, that is to say the conjunction of desire and of logos in the pursuit of an end” (p. 151).

He turns to the background that Aristotle is responding to.

“The sophists affirm that every desire is good; Plato, that we can only truly will the true or absolute good” (ibid). “While the sophists identify freedom with the capacity to do what we want, and Plato with sole adherence to the Good, Aristotle proposes a third way: ethical freedom is the art of deciding well, of arriving at the resolution the circumstances require…. The resolution taken by the serious human [substituting Sachs’s “serious” for spudaios in the homme de bien or man of the good in Boulnois] is indeed a point of coincidence between the apparent good (which all seek) and the true good (that she discerns). In leaving behind the confrontation between sophists and Platonists, Aristotle has recourse neither to a relativism of appearances nor to an objective norm; in the element of virtue (and of desire), he aims at a coincidence between the phenomenon of good and its truth” (p. 152).

This Aristotelian idea of a point of coincidence between appearance and truth was later taken up by Hegel.

“Is it necessary to say that resolution is free? Does it consist in a choice?… Aristotle never makes the concept of freedom intervene in relation to the question of choice, nor even that of willingness” (p. 153). “Nevertheless, Aristotle knows and uses a concept of freedom (eleutheria). But this pertains to politics and not to the theory of action” (ibid, emphasis in original).

“The Latin translation not withstanding, [the adjective] ‘hekousion’ (willing) does not mean ‘voluntary’ (voluntarium); it is rather the mode of our action, except in cases of constraint or ignorance. Proairesis does not mean ‘free will’ (liberum arbitrium), but decision, resolution… Freedom is the ethical horizon of our action, and not the metaphysical attribute of a will that Aristotle did not envisage” (p. 154).

“It is indeed possible to analyze human action without postulating in the agent a central instance of arbitration, and without inscribing her in a physical determinism…. Ethics is indeed thinkable without a theory of will” (p. 155).

As I have noted many times, Plato and Aristotle founded ethics without the later notion of a faculty of will.

“Ethical action does not necessarily require a freedom of choice. It depends on a resolution (proairesis), which mainly refers to a dimension of anticipation, and does not always imply a choice. Ethics is indeed thinkable without the doctrine of free will” (ibid).

Here again the emphasis is on something like commitment.

“Resolution presupposes a process of deliberation in the agent: she at least implicitly evaluates the reasons to do x rather than nothing; that which she does is not imposed on her from the outset. That is to say that for her, there are a multitude of options and reasons to act” (ibid, emphasis in original).

Deliberation is concerned with the goodness of reasons.

“A stranger to the metaphysical problem of free will, freedom is ethical in essence; it consists in the ability to act well; it is only acquired at the completion of an education in virtue” (ibid).

“All thought about action situates itself in the horizon of the good, and freedom is nothing other than liberation from the bad” (p. 156).

“It is ethics that founds freedom, and not freedom that founds ethics.” (ibid, emphasis in original).

“On the plane of finite existence, no one knows if they have absolutely accomplished the best action. In the same way in their reflections on our moral lack of power, Aristotle and Ovid speak of that which is ‘better’ (comparative) and not of that which is ‘best’ (superlative)” (ibid).

Thoughts on Meta-Ethics

When I first set up a category of “general meta-ethics”, it did not reflect a programmatic intent. It was a convenient heading for the broadest and sketchiest of my broad and sketchy notes. I see the whole development here as a sort of expanding spiral. The typical writing has evolved from extremely informal, minimalist fragments to somewhat more substantial pieces responding to some text or other.

At this point, “meta-ethics” very much has acquired a programmatic significance, particularly inspired first by Brandom’s idea of “normativity all the way down”, and then by Gwenaëlle Aubry’s detailed “axiological” reading of Aristotelian first philosophy, but encompassing all the concerns raised here. This now gives a more particular, more coherent form to my original goal of exploring possible connections between Aristotle and Brandom. It draws important support from the work of Paul Ricoeur, and from readings of Hegel developed by Robert Pippin and H. S. Harris, as well as my own work and that of numerous others on both the first-order history of philosophy and the second-order “historiography” of that history.

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.