Logic as Ethics

Since the groundbreaking work of Boole, De Morgan, Pierce, and Frege in the later 19th century, logic has been treated as either the foundation of mathematics — as Russell argued — or as a branch of mathematics, as suggested by contemporary type theory and category theory. This all builds on the “formal” view of logic that has been dominant in the West since the later middle ages.

In fact, the place of formalism in the practice of mathematics is debated by mathematicians. A century after Hilbert and Bourbaki, the complete systematic formalization of mathematics remains an unrealized ideal, although new work in homotopy type theory seems the most promising development yet for this (see New Approaches to Modality).

Plato and Aristotle never thought that reasoning should be “value free”. On the contrary, they treated it as an essential part of ethical life. Aristotle pioneered formal reasoning by composition, but justified the principle of non-contradiction in unmistakably ethical terms. Plato and Aristotle reasoned mainly by examining meanings, whereas in the formal view of logic, all that matters are formal rules for mechanical manipulation of arbitrary symbols. (See also Formal and Informal Language.)

Taking up Kant’s thesis of the primacy of practical (ethical) reason, Hegel took what he called “logic” in a very different direction from that of the modern formalists, focusing like Plato and Aristotle on the development of concrete meanings rather than rules for formal, meaning-agnostic operators.

Within the tradition of modern analytic philosophy, Wilfrid Sellars and Robert Brandom have revived interest in non-formal approaches to logic that are closer to the reasoning we employ in everyday life. Brandom has also written extensively on the ethical content of Hegel’s work and its connections to Hegelian logic. He has always acknowledged that his earlier work on inferential semantics is deeply indebted to Hegel. Brandom’s “inferentialism” puts reason and the interpretation of meaning in relations of reciprocal dependence, in this respect recovering what I think is the perspective of Plato and Aristotle as well as Hegel.

The suggestion here — also supported, I believe, by Harris’ commentary on the Phenomenology — is that “logic” is most fundamentally concerned with what we ought to conclude from what, within the open philosophical perspective of what Hegel somewhat confusingly called “pure negativity”, where our view of the world is “inferential all the way down”. At the level of practical application with real-world meanings that I want to say is most important, logical “laws” are neither tautologies nor some strange kind of abstract facts, but rather a kind of best practices that themselves require interpretation to be applied.

Time and Eternity in Hegel

H. S. Harris in Hegel’s Ladder I points out that Hegel took an unprecedented view of the relation between time and eternity in the Phenomenology. He argues that Hegel’s later advertisement of his logic as characterizing “the mind of God before creation” is extremely misleading with respect to Hegel’s actual views. According to Harris, detailed examination of texts suggests Hegel retained the novel view of time and eternity expressed in the Phenomenology.

Harris notes that from around 1801, Hegel came to agree with Reinhold and Bardili that logic should be “objective” in the sense of being neutral with respect to subject-object distinctions, even though he sharply rejected their formalism.  Logic for Hegel should not be subjective in the sense of Fichte’s Wissenschaftslehre or Schelling’s work before his break with Fichte.

“Hegel was able to make history subordinate in his speculative Logic precisely because he allowed it to be predominant in the lengthy formation of subjective consciousness for truly logical ‘objectivity’, which is the theme of the Phenomenology….  ‘The experience of consciousness’ is necessarily a psychological experience of the singular subject, since only singular subjects are ‘conscious’, but the ‘phenomenology of Spirit’ is the biography of God, the metaphysical substance who becomes ‘as much subject as substance’ when He is comprehended as ‘Spirit’.  The ‘experience of consciousness’ must happen in a single lifetime; the ‘phenomenology of Spirit’ cannot happen so.”

“We might remark that neither can become ‘Science’ except through the recollection in a singular consciousness of a historical process that is necessarily not confined (or confinable) within a single lifetime.  This is a way of saying that God cannot be ‘spirit’ without man being ‘spirit’ likewise — which is, of course, quite correct…. [N]ot the comprehension of ‘self’ but the comprehension of the whole social history of selfhood [is the topic of the Phenomenology]” (p. 11). 

Harris says the Phenomenology was Hegel’s “decisive divergence” (p. 13) from the whole tradition of intellectual intuition and cognitive immediacy.

“The implication is that ‘the eternal essence of God’ is not ‘outside of time’ in the way that God’s thought and action have traditionally been supposed to be.”

“We cannot mediate the problem of how logic is in time, unless we shift our attention from the ‘real philosophy’ that comes after logic (in every sense) to the ‘real philosophy’ that goes before ‘logic’, as a comprehension of the time in which it was shown finally that logic itself is as much in time as out of it and that it must come to be self-consciously ‘in’ time in order to be properly ‘out’ of it….  [F]rom Heraclitus and Parmenides to Kant and Fichte, no one has managed to formulate a consistent theory of human experience as a rational whole on any intuitive basis.  Instead of simply taking it for granted that eternity comprehends time, just as ‘possibility’ comprehends ‘actuality’, we must start from the other end and ask how time comprehends eternity.”

“There is no intuitive answer to this question” (p. 14).  The project of the Phenomenology “involves a total inversion of the intuitive assumption of all the ‘philosophers of experience’ before Hegel….  But the history of religion is more important to the argument than is the history of philosophy, in any case, because it is in religion that the natural assumption is inverted for the natural consciousness itself.  It is Hegel’s predominant concern with the actual experience of the natural (i.e., nonspeculative) consciousness that makes it hard for us to see and understand what happens to Descartes, and to the ‘philosophers of experience’ proper, in Hegel’s argument” (pp. 15-16).

Harris speaks of an “explicitly Fichtean self…. But his self makes no Fichtean assumptions, and has no absolute ‘intuitions’.  It merely observes; and what it learns, in the end, is precisely what the standpoint of philosophical ‘observation’ is and means. This observing consciousness leaves Fichte behind decisively when it leaves moral judgment to the valets and aligns itself with the Weltgeist [world Spirit] in its evaluation of all the experience it recollects.”

“This all-accepting and all-forgiving alignment with the Weltgeist is the logical standpoint, the eternal standpoint concretely established in time and now, at last, comprehensively understood” (p. 17).  What is shown is “Spirit’s eternity in time” (p. 18), but “The ‘hero’ is the finite consciousness — Jacob wrestling with the angel” (ibid).

Harris is here using the word “consciousness” in an equivocal way to refer to something that is far beyond what Hegel described as the standpoint of Consciousness.  It is already Spirit.  The standpoint of Consciousness is inseparable from assumptions of immediacy and of what philosophers from Locke to Schelling have called “intuition”, as some sort of immediate grasping.  Emphasizing some underlying continuity where something underwent a transformation is a common way of speaking, but I would rather identify the continuity with “us” rather than an abstracted property like consciousness.

Harris properly distinguishes between “natural consciousness” and “the philosophers of experience” who purport to speak on its behalf.  Hegel sharply rejects the philosophers of experience as propounding a bad notion of experience focused on immediacy, but he wants to entice common sense to become philosophical. 

The Fichtean self is already a difficult topic.  Fichte, in his better known early writings at least, propounded a very extreme “subject-centered” point of view, but he was a brilliant writer and serious philosopher who cannot be simply reduced to that.  His “self” is certainly not an empirical matter of fact, and seems constitutionally incompatible with petty egocentrism or self-seeking (certainly a far cry from the acute vulgarization of Max Stirner in The Ego and His Own), even though it seems like he had some bad ideas about German cultural superiority.  I think the Fichtean self not so much “has” intuitions as Harris suggests, but rather is itself an “absolute intuition” (the only one) for Fichte.  But Fichte also in his later writings formulated a notion of ethical mutual recognition.

Harris alludes to Hegel at a certain early point turning back from Schelling’s mystical intuitionism toward Fichtes’s practical philosophy.  Although I think this is historically accurate, if taken out of context or connected with stereotypes of Fichte, it could lead to serious misunderstanding. 

Harris himself does not make this mistake.  He clearly indicates that Hegel cannot be reduced to Fichtean subjectivism, as the young Marx and some others have done or precipitously claimed others had done. He goes on to discuss the fundamental role of “otherness” in Hegel’s thought, particularly in regard to constitution of self.  This is as far from an “absolute intuition” of self as could be.  But Fichte’s practical-ethical orientation and sharp mind tower above not only the woolly-minded forgotten Schellingian epigones who so irritated Hegel, but also the superficial dazzle of Schelling himself.  I would also note that to ground the social in concrete relations rather than abstract collectivity is in no way to reduce the social to actions of individuals.

Fichte was accused of atheism and drummed out of Jena for identifying God with the moral order. Now I can’t find the passage, but I think Harris somewhere says Hegel put God as the moral order historically in between God as law and God as love.

The explicit idea that the eternal is constituted in time that Harris highlights is, I think, original to Hegel. Others had denied the eternal, but I don’t recall anyone arguing that a genuine eternal originates in time. Harris relates this novel aspect of Hegel’s thought to his inversion of the Kantian priority of possibility over actuality. Aristotle of course also maintained that actuality comes first, but never explicitly suggested a temporal origin of the eternal.

I think a temporal constitution of the eternal — especially when connected with logic, as Harris suggests it was for Hegel — actually makes a lot of sense. After a temporal process of experience and learning that may involve reversals and twists and turns, it is possible to construct a static logical theory (not logical in Hegel’s sense, but in the formal sense) of all the lessons learned, but not before. What Hegel calls logic is a lot closer to the twists and turns of experience. Formal logic obviously has no temporal element, but the “logic” of experience and learning does. Formal logic comes “after” Hegelian logic. Hegelian logic can be read as an account of the constitution of formal logic, through the constitution of meaning.

Brandom and Hermeneutics

It’s been a while since I said much about Robert Brandom, though his work — along with my own nonstandard reading of Aristotle — continues to be one of the main inspirations behind everything I write here.

Lately I’ve been devoting a lot of energy to belatedly catching up on the hermeneutics of Paul Ricoeur. To my knowledge, Ricoeur never commented on Brandom during his lifetime, and Brandom has not specifically commented on Ricoeur.

Brandom has, however, in Tales of the Mighty Dead explicitly endorsed some of the broad perspectives of Hans-Georg Gadamer’s hermeneutics, and he has devoted much attention to a “hermeneutics of magnanimity” in Hegel’s Phenomenology. Brandom’s mentor Richard Rorty concluded his famous work Philosophy and the Mirror of Nature by recommending a general turn from foundational epistemology to nonfoundationalist hermeneutics, and I have previously suggested that Brandom’s work as a whole could be viewed as a novel sort of hermeneutics developed within the analytic tradition.

Brandom’s fundamental concept of the priority of material inference over formal inference puts meaning — and therefore the interpretation of meaning — in the driver’s seat for reasoning, so to speak. This allows for the recovery of a more historic concept of Reason, which ever since Descartes has been mostly replaced by a mathematically based kind of rationality that is more precise and invaluable in technical realms, but also much more rigid, and in fact far more limited in its applicability to general human concerns (see Kinds of Reason).

Even prior to Descartes, Latin medieval logic already moved increasingly toward formalism. Since Frege and Russell, the rigorous mathematization of logic has yielded such impressive technical results that most philosophers seem to have forgotten there is any other way to view logic.

In the 1950s Wilfrid Sellars took the first steps toward initiating a counter-trend, reaching back to the pre-Cartesian tradition to formulate the notion of material inference later taken up by Brandom.

Modern complaints against Reason strongly and wrongly presuppose that it inevitably follows or approximates a formal path. Material inference provides the basis for a fundamentally hermeneutic view not only of Reason but also of logic and logical truth.

I have further stressed the fundamentally ethical or meta-ethical character of material inference, leading to a concept of ethical reason as the most fundamental form of Reason overall in a view that puts material inference before formal logic. As I put it not too long ago, ethical reason may optionally use the more technical forms of reason as tools. Ethical reason, I want to say, has a genuinely active character, but technical reason does not. Ethical reason is fundamentally oriented toward the concrete, like Aristotle’s practical judgment.

I want to say that there is such a thing as logical or semantic reference — saying something about something is not in vain — but a prior hermeneutic inquiry is necessary to ground and explain reference. Moreover, both Aristotle and Kant recognized something like this. Such a perspective is compatible with science, while putting ethical and meta-ethical inquiry first.

A hermeneutic concept of Reason saves us from a false dilemma between formalism on the one hand and question-begging appeals to intuition, authority, or irrational “decision” on the other. (See also Dialogue.)

Split Subject, Contradiction

The Žižekians, referencing Lacan, like to talk about a “split subject” that is noncoincident with itself. In broad terms, I think this is useful. What we call subjectivity is divided, and lacking in strong unity. (See also Pure Negativity?; Acts in Brandom and Žižek.) But it seems to me that if we try to speak carefully about this, we should not then go on using singular articles like “the” or “a”.

I tend to think subjectivity is not just fractured or un-whole, but also actually consists of a complex overlay of different things that we tend to blur together. In particular, it seems clear to me that a common-sense, biographical “self” whose relative unity over time is trackable by relation to the “same” physical body — or by Lockean continuity of memory — is not the same as what we might in a given moment view from a distance as an individualized ethos, or up close as a unity of apperception. This is, I believe, the same distinction that Brandom discusses in terms of sentience and sapience.

Ethos and unity of apperception, and their constituent values and conceptions — the very things that most properly say “I”, and play the functional role of an ethical “subject”, or of a subject of knowledge — are profoundly involved with language, social relations, and what Lacan in his earlier work called the Symbolic and the “Other”. These instances of sapience are pure forms whose identity can only be expressed in terms of sameness of form — nonempirical, but inseparable from a larger ethical world — and simultaneously intimate to us, but by no means strictly “ours”. (See also Self, Subject.)

Where I am still a bit torn is that I also feel that emotions — which I’ve been locating on the former, “self” side — are fundamental to subjectivity as a whole, but I have theoretically separated them from the main locus of transcendental ethical and epistemic subjectivity, even though they play an essential role in making it possible. One logical solution would be to say this just means subjectivity as a whole is more than just ethical and epistemic. Another would be to say that there is a separate kind of emotional subjectivity. I’m not entirely satisfied yet, because I think feeling combines these, but the noncoincidence of our factual selves with our ethical and epistemic being seems very important in understanding how we overcome empirical limitations.

The Žižekians will perhaps remind us that they were not talking about a split between self and subject, but about a split within the subject. I think we habitually overstate the degree of unity and identity we attribute to selves, subjects, and things in general, so I’m fine with that, too. They also want to expand this into a general “ontological” point, which I see as a semantic point.

Perhaps the Žižekians are more comfortable talking about “a” or “the” subject in part due to their doctrine of the ubiquity of contradiction. Todd McGowan in Emancipation After Hegel (2019) nicely distinguishes the Žižekian notion from the old confusion between contradiction and conflict or polarity — and from immediate self-contradiction — but still wants to maintain that the standard logical law of noncontradiction ultimately “refutes itself”, and that Hegel thought this as well. This argument combines a laudable awareness of some of the practical issues with identity, with a logically invalid use of the distinction between explicit and implicit self-contradiction.

Hegel meditated profoundly on the difficulties of applying logic to meaningful content and to real life. He strained language to the breaking point trying to express his conclusions.

On the frontiers of mathematical logic today, the so-called law of identity has been replaced by a requirement to specify identity criteria for each formally defined type, and identity in general has been weakened to isomorphism. (See also Form as a Unique Thing.)

Real-world applications of strong identity typically involve loose “extensional” reference to things assumed to be the same, and a lot of forgetting. The linchpin of old “identity thinking” was inattention to difficulties of formalization from ordinary language — basically an illegitimate moving back and forth between formal and informal domains, resulting in lots of homogenizing confusion of things that ought to be distinct. Weaker, “intensional” assertions about identity as specifiable sameness of form make it the exception rather than the rule. What come first conceptually are distinctions within the manifold, not pre-synthesized things already possessed of identity. Where things are not the same to begin with, contradiction — far from being omnipresent — is not even potentially at issue. (See also Self-Evidence?)

Meanwhile, Sellars and Brandom have revived material inference about meant realities in contrast to formal logic, which deals with purely syntactic relations between presumed extensional “things” with presumed identity. Things Kant and Hegel said about Understanding and Reason can be nicely understood in terms of the relation between syntactic inference about symbolic terms standing for formless extensional “things” and substantive, material inference about the actual form of meant realities. Especially in the reading of Hegel, not having the resource of this distinction available now seems positively crippling.

Finally, Aristotle, who originated the law of noncontradiction as a kind of ethical imperative, and stands in the background to all of Hegel’s discussions of logic, was himself rather cautious and tentative about applying identity to real things, and in his logic was also mainly concerned with (composition of) material inferences, which have more to do with the actual form of things .

Hegel never violated Aristotle’s imperative not to say opposite things about the same thing said in the same way. What he did was to constantly point out the gap between reality and traditional semi-formal logic applied to ordinary language — not to encourage us to reject logic, but rather to refine and sublimate it. (See also Aristotelian and Hegelian Dialectic.)

Logic as Semantics

I think of logic in general as mainly concerned with the perspicuous rendering of distinctions for use in reasoning, rather than with the arbitration of truth based on some other presumed truth as a starting point.

An emphasis on this expressive or semantic role was, I think, what led Aristotle to insist that what modern people call logic should be viewed as a tool (organon) and not a “science”.

The great scholar of Latin medieval logic L. M. De Rijk, in his major study Aristotle: Semantics and Ontology (2002), recommended replacing references to Aristotle’s own “logic” with references to semantics, or investigation of meaning.

Hegel contended that traditional metaphysics should be replaced by a kind of “logic” that addresses meaningful content.

Brandom has given us an unprecedentedly thorough and clear account of the conditions that make meaningful content possible in the first place.

On the formal side, type theory and category theory provide a new, unified view of logic, mathematics, and formal languages that fits very well with this “meaning before truth” perspective.

Syllogism

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

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

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

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

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

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

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

Three Logical Moments

The “Logic Defined & Divided” chapter of Hegel’s Encyclopedia Logic contains some brilliant, relatively popular aphorisms from his lectures, and provides a nice introduction to his views. Having recently treated with approval Kant’s denunciation of speculation in the usual sense, I’m turning to this now because among other riches, it contains Hegel’s recovery of an alternative, much more positive sense for “speculation”. As Aristotle would remind us, things are said in many ways, and it is wise to give heed to the differences.

Hegel says that every notion and truth involves three moments that are all essential and cannot really be separated from one another: Understanding, Dialectic, and Speculation.

In other places, Hegel frequently polemicizes against the narrowness and rigidity of mere Understanding. Here, he rounds out the picture, noting that “apart from Understanding there is no fixity or accuracy in the region of theory or of practice” and that knowledge begins “by apprehending existing objects in their specific differences”. He cites examples of how Understanding contributes to science, mathematics, law, practical life, art, religion, and philosophy.

Preparing the transition to dialectic, he notes “It is the fashion of youth to dash about in abstractions — but the man who has learnt to know life steers clear of the abstract ‘either-or’, and keeps to the concrete”. Dialectic for Hegel if viewed separately is the moment of “negative” Reason or criticism. He says that dialectic subordinated to Understanding’s mode of thought leads to skepticism, but dialectic freed from this subordination builds on distinctions developed by the Understanding, even while “the one-sidedness and limitation of the predicates of understanding is seen in its true light”. Dialectic studies things “in their own being and movement”. He goes on to expound Plato’s use of dialectic, and its difference from sophistry. (See also Contradiction vs Polarity; Aristotelian and Hegelian Dialectic.)

Speculation in Hegel’s special sense is the “positive” moment of Reason, which if considered separately begins from a kind of faith in reasonableness in the world. He implicitly connects it with a charitable reading of the long religious tradition of faith seeking understanding, construed in such a way as to be not incompatible with a charitable version of Enlightenment criticism. He notes that “the true reason-world, so far from being the exclusive property of philosophy, is the right of every human being [of] whatever grade of culture or mental growth”, adding that “experience first makes us aware of the reasonable order of things… by accepted and unreasoned belief”. Once this rational order becomes an object of thought rather than mere belief, we have speculative Reason proper.

Speculative Reason builds on both Understanding and dialectic. “A one-sided proposition… can never even give expression to a speculative truth.” He notes a connection between this and basic intuitive fairness. Starting from a simple faith in the reasonableness of the world and advancing through various stages of criticism, speculative Reason ultimately realizes substance as subject, and overcomes the dichotomy of subject and object.

Dialectic undid the abstract, atomistic, foundationalist, “either-or” tendencies of isolated Understanding. Speculative Reason in Hegel’s sense turns this into a new affirmation. In many places, Hegel talks about Reason or dialectic in ways that subsume both the dialectical and the speculative moment described here.

I read Hegelian speculative Reason — or dialectic incorporating the speculative moment — as just ordinary reason moving forward without the crutches of foundationalism and dogmatic claims of certainty. Reason without foundationalism is concerned with the very same open-ended work of interpretation I have attributed to Aristotle. Ultimately, Hegelian Reason is defeasible rational interpretation of experience, optimistically doing the best we can with the resources we have, and always on the lookout for something better. Thus, it too can be reconciled with Kantian discipline. (See also “Absolute” Knowledge?)

Italian Aristotelianism

From the middle ages through the Renaissance, Italy was host to a flourishing development of relatively naturalistic Aristotelianism. Especially in northern Italy and unlike most of the rest of Europe, universities there tended to be dominated by medical rather than theological faculties. Albert the Great and Averroes were among the strongest influences on this tradition, and many of the Italians did not shy away from the controversial aspects of Averroes. Contemporary scholars debate how “Averroist” particular figures were, but it is no accident that the first printed editions of the collected works of Aristotle (16th century) included the commentaries of Averroes, and were published in northern Italy.

The long list of people who taught in Italy and have been described by scholars as broadly Averroist (with different caveats for each) includes John of Jandun (1285 – 1328), Marsilius of Padua (1275 – 1342), Taddeo da Parma (early 14th century), Gaetano da Thiene (1387 – 1465), Nicoletto Vernia (1442 – 1499), Agostino Nifo (1473 – 1545), and Marcantonio Zimara (1460 – 1532).

An important freethinking non-Averroist Aristotelian in the Renaissance was Pietro Pomponazzi (1462 – 1525). Other Italian scholastics who were largely naturalistic in their approach included Pietro D’Abano (1257 – 1313) and Biagio da Parma (1350 – 1416).

Leading Italian Aristotelian logicians included Paul of Venice (1369 – 1429), who wrote a giant summa of logic. Giacomo Zabarella (1533 – 1589) wrote extensively on logical methodology and natural philosophy, and also influenced German Protestant scholars..

Aquinas was Italian, and Italy was also home to the important Thomist, Thomas Cajetan (1469 – 1534).

In the 15th century, older Greek commentaries on Aristotle were rediscovered by Italian scholars. Some were misled into thinking that the heavily neoplatonizing readings of a commentator like Simplicius (490 – 560) must be closer to the original Aristotle than those of the much later Arab, Averroes.

Categorical Hegel?

I just discovered a book-length nLab web draft with extremely detailed interpretation of Hegel’s Science of Logic into higher category theory and homotopy type theory. (Reading category theory into Hegel was originally suggested by William Lawvere in the 1960s.) A lot of it is way beyond me, but there is much of interest. nLab in general hosts world-class work in math and logic, as well as applications of it to physics and philosophy. Remarks there about historical philosophers are uneven in quality, but a number of them are interesting, and the more mathematical or logical they are, the better the quality gets. The aforementioned draft does reference old, inadequate generalizations about Hegel as “mystical”, but the detail and scope of the interpretation into state-of-the-art mathematics are awe-inspiring. It also includes a nice formalization of Aristotelian logic, which is mathematically much simpler and relatively easy to understand. I previously found a much shorter page there that explicitly mentions Brandom, and connects with his interest in modal logic. (See also Identity, Isomorphism; Categorical “Evil”; Higher Order.)

Ontology

Ontology as a supposed science of being acquired its basic shape in the middle ages, as a sort of reification of Aristotelian semantics. Duns Scotus was very proud of his ontological “improvement” of Aristotle. Aristotle himself preferred to shift clumsy, sterile discussions of sheer being onto more subtle and fruitful registers of form and meaning at the earliest opportunity.

Kant pointed out that existence is not a property, and Hegel pointed out the equivalence of Being to Nothing. When Hegel talks about “logic” as the form of future metaphysics, this means a return to the original meaning of “metaphysics” as Aristotelian dialectical semantics, not an ontologization of dialectic. Broadly Aristotelian dialectical semantics give us all the “ontology” we will ever need.

For the historical back story of how Scotus invented ontology as we know it today, if you read French, see Olivier Boulnois, Être et représentation: Une généalogie de la métaphysique moderne à l’époque de Duns Scot (XIIIe–XIVe siècle). As suggested by the title, this work also has extremely important things to say about the premodern history of strongly representationalist views. The famous univocal “being” invented by Scotus was defined in terms of representability. (See also Being, Existence; Aristotelian Dialectic; Objectivity of Objects; Form; Repraesentatio.)