The Unity of Aristotle’s Metaphysics

The anthology that the ancient editors of Aristotle’s manuscripts entitled literally After the Physics is the original paradigm for “meta level” inquiry in general. Medieval writers like Avicenna, Aquinas, and Duns Scotus took it as an authoritative treatise on Being.

The German classical scholar Werner Jaeger greatly influenced early and mid-20th century readings, with claims that apparently inconsistent statements in the Metaphysics reflected different stages in the development of Aristotle’s thought. Earlier, the Marburg neo-Kantian Paul Natorp had proposed that parts of the Metaphysics reflected an immature stage of Aristotle’s thought, and should be removed from the text.

The mid-20th century Catholic scholars Joseph Owens and Giovanni Reale, who both produced valuable major studies of the Metaphysics, were prominent opponents of these developmental approaches, emphasizing instead the dialectical character of Aristotle’s thought. My favorite translator, Joe Sachs, strongly agrees with them. Just because Aristotle says apparently conflicting things on the same topic is no reason to assume that he changed his mind.

That Aristotle’s thought is in general highly coherent ought to be clear to serious students. That it is highly dialectical is easy to establish. Aristotle frequently makes preliminary statements that are easy to grasp, and then substantially corrects them later within the same text. If we are serious about interpretive charity, we ought to try this sort of reading first.

But neither is its dialectical coherence proof that the Metaphysics, despite appearances, was originally written by Aristotle as a single work, structured in the order in which it has come down to us. The coherence of his thought is one question; the composition of the manuscript is another. Owens, Reale, and even Sachs tend to write as if the fact that it is dialectically coherent meant that the surviving text must be basically in the form in which Aristotle wrote it (but see quote below). This is also too strong.

Many different linear orderings of presentation may reflect the same underlying dialectical coherence, so the finding of coherence is not sufficient to establish that the order of the text is Aristotle’s.

Sachs notes that “Its first two books are both numbered one (with upper and lower case alphas)…. But in content, the Metaphysics begins over again much more than twice. Of its fourteen books, only books VIII, IX, and XIV are not new beginnings. The eleven sections of the whole inquiry are not set end-to-end like bricks in a row, but are woven together like threads in a complex design” (p. xv). “And there is no question that the composition of the Metaphysics was not a single act; the work is compiled from a number of separately composed pieces” (p. xii).

I like to imagine that my many blog posts are “woven together like threads in a complex design”, even though they were all written separately, and can be read in many different orders. If I were to turn them into a book, it would not consist of all the posts in chronological order, but would be thematically organized in some way. That is part of the art of editing. I do change my mind from time to time, but the great majority of differences in treatment of related topics have to do with differences in context, or different “places” in a more abstract dialectical development.

I see the various “sections” of the Metaphysics in the same way — as originally separate writings that nonetheless cohere, because the thought in them coheres.

What makes this question important is its relative effect on various points of interpretation. For example, I see Aristotle’s two brief discussions of “being qua being” as relatively isolated responses to what would be an important Platonic question that Aristotle himself decisively moves beyond (especially in books VI through IX), and thus as far from defining the subject of the Metaphysics as a whole. Even if the text were a continuous whole, the claim that the whole is adequately characterized as about being qua being ought to be viewed as at best highly contentious.

I very much like Sach’s top-level summary quoted in Long Detour?, which emphasizes not being qua being, but the dependencies of being on forms and the good.

The Human in Siger of Brabant

Those whom modern scholars called Averroists were supposed to be unoriginal, dogmatic followers of Averroes. This turns out to be as inaccurate as the supposition that the Latin scholastics as a whole were unoriginal, dogmatic followers of Aristotle.

At issue here is what it is to be human, and in particular how the difficult Aristotelian concept of “intellect” relates to human beings. There were not just two but a wide variety of nuanced and well-argued positions on this.

Among the so-called Averroists, Siger of Brabant (1240-1280) is the best known name, but no full book has yet been devoted to his work. According to Alain de Libera, in his later works Siger developed original responses to Thomas Aquinas’ famous critique of Averroes.

Siger argued against Aquinas that the act of thought is not purely immanent but simultaneously immanent and transitive. That is to say, for Siger it is immanent in the human, but transitive in the separate intellect. While affirming a “separate” intellect, Siger emphasized against Aquinas that the total act of thinking is attributable to the whole human, and not just to the human’s intellective soul. Intellect is an “intrinsic operation” in the human that in a way does, and in a way does not, make it the “substantial form” and perfection of a material body. According to Siger, Aquinas’ claim that the intellective soul unequivocally is the substantial form of the body cannot be reconciled with Aquinas’ other claim that intellect as a power of the intellective soul is entirely independent of the body. Siger adopts Albert and Thomas’ term “intellective soul”, but for Siger only the animal and vegetative soul are united with the body in being. Intellective soul is naturally united with the body in operation but not in being, whereas Aquinas says they are united in being.

According to de Libera, Siger in his Questions on the Book of Causes argues that the form of the human is not simple, but is rather a composite comprising an intellect that “comes from outside” (in Aristotle’s phrase), and a vegetative and sensitive substance that is “educed from the power of matter” (de Libera, Archéologie du sujet vol. 3 part 1, p. 411, my translation). Intellect is said by Siger to be a “form subsistent in itself”. It is not a “substantial form” in the proper sense, which would imply that it was inherent in the human body. It is not in the body “as in a subject”. However, intellect has need of the human body (specifically, the phantasms of the imagination) as an object, and intellect is in turn attributable to the human as a whole, though it is not reducible to the biological organism. Intellect for Siger is neither the inherent form of the human nor a separate, external mover of the human, but a separate form with an operation that is intrinsic to the whole human, in which it participates by composition.

De Libera remarks in passing that the act of thought owes more to intelligible objects than to “intellect”. I would suggest that it is through language and culture and ethical practice that Aristotelian intellect “comes to us from outside”. We talking, encultured animals then acquire a spiritual essence that comes to be intrinsic to us, through our ethical practice, in which acquired intellect and animal imagination cooperate.

According to de Libera, for Siger “The ‘intelligent whole’ is composed of many psychic parts, which are not of the same nature, or of the same origin, or of the same ontological status” (p. 362).

Siger objects that Aquinas’ notion of intellect as united with the body in being “makes the act of thought a perfection of matter” (ibid). This makes the body intellect’s “subject of inherence”. But at the same time, applying Thomas’ own axiom that nothing is accomplished by a power separated from itself, Siger reproaches Thomas for being unable to account for “the integrality of the known” (p. 378), and specifically the knowledge of material things.

For Aquinas, establishing that there is an operation proper to the soul is essential to the possibility of the soul’s existence independent of the body, and thus to his philosophical argument for personal immortality. But Siger argues that in making intellect an operation proper (i.e., uniquely attributable) to the soul, Aquinas implicitly negates its attributability to the whole human. Intellection for Siger is “an operation common to the human composite as an integral whole” (p. 377). In other words, I think with my whole being, not just my “mind”.

De Libera concludes that Siger does preserve the possibility of personal immortality, which was a principal concern of Averroes’ critics. However, he finds that the texts do not support the claims of some recent scholars that Siger in his later works abandoned “Averroism” in favor of Thomism.

The phrase “form subsistent in itself”, according to de Libera, does not have the same meaning for Siger that it does for Thomas. Albert the Great had analyzed three logical possibilities for an “intermediate” kind of form that is neither fully separate nor inseparable from matter. According to de Libera, Siger’s work is consistent with this. Siger aimed at a mean between a Platonist excess of separation between form and matter, and what he perceived as a Thomist excess of union with respect to so-called substantial forms. De Libera does find, however, that Siger, like other authors, is too anxious to simplify the issues at stake, and that he goes too far in identifying the position of Aquinas with that of Alexander of Aphrodisias, who was regarded as having a “materialist” view of the human soul. He also says Siger goes too far in reducing Aquinas’ notion of form to the simple analogy of a stamp in wax.

De Libera meanwhile also raises doubts about Aquinas’ insistence on the absence of any intermediary between the intellective soul and the body. He notes that in a very different context, the Franciscan Augustinian Peter Olivi argued that the intellective soul is united with the body via the intermediary of the sensitive soul. Olivi’s position was rejected by the Council of Vienna in 1312.

De Libera accepts the notion of “substantial form” as genuinely Aristotelian, but appears to endorse the argument of Bernardo Carlos Bazán that Aquinas’ notion of intellective soul gives it a privileged ontological status that makes it more than a substantial form. According to Bazán, Aquinas’ anthropology from the very start goes beyond the Aristotelian hylomorphism that Thomas generally endorses. The form of a human in Aquinas — unlike anything in Aristotle — is such that it could not be the result of any natural generative process, but could only be created by God. Siger comes across as closer to Aristotle.

De Libera notes that in the wake of the English theologian Thomas Wylton (1288-1322), later so-called Averroists “invested massively” in a distinction between an inherent form and an assisting form, and regarded human intellect as an “assisting form”. (See also “This Human Understands”; “This Human”, Again; Averroes as Read by de Libera.)

Searching for a Middle Term

“But nothing, I think, prevents one from in a sense understanding and in a sense being ignorant of what one is learning” (Aristotle, Posterior Analytics; Complete Works revised Oxford edition vol. 1, p. 115). The kind of understanding spoken of here involves awareness “both that the explanation because of which the object is is its explanation, and that it is not possible for this to be otherwise” (ibid). To speak of the “explanation because of which” something is suggests that the concern is with states of affairs being some way, and the “not… otherwise” language further confirms this.

Following this is the famous criterion that demonstrative understanding depends on “things that are true and primitive and immediate and more familiar than and prior to and explanatory of the conclusion…. [T]here will be deduction even without these conditions, but there will not be demonstration, for it will not produce understanding” (ibid). The “more familiar than” part has sometimes been mistranslated as “better known than”, confusing what Aristotle carefully distinguishes as gnosis (personal acquaintance) and episteme (knowledge in a strong sense). I think this phrase is the key to the whole larger clause, giving it a pragmatic rather than foundationalist meaning. (Foundationalist claims only emerged later, with the Stoics and Descartes.) The pedagogical aim of demonstration is to use things that are more familiar to us — which for practical purposes we take to be true and primitive and immediate and prior and explanatory — to showcase reasons for things that are slightly less obvious.

Independent of these criteria for demonstration, the whole point of the syllogistic form is that the conclusion very “obviously” and necessarily follows, by a simple operation of composition on the premises (A => B and B => C, so A=> C). Once we have accepted both premises of a syllogism, the conclusion is already implicit, and that in an especially clear way. We will not reach any novel or unexpected conclusions by syllogism. It is a kind of canonical minimal inferential step, intended not to be profound but to be as simple and clear as possible.

(Contemporary category theory grounds all of mathematics on the notion of composable abstract dependencies, expressing complex dependencies as compositions of simpler ones. Its power depends on the fact that under a few carefully specified conditions expressing the properties of good composition, the composition of higher-order functions with internal conditional logic — and other even more general constructions — works in exactly the same way as composition of simple predications like “A is B“.)

Since a syllogism is designed to be a minimal inferential step, there is never a question of “searching” for the right conclusion. Rather, Aristotle speaks of searching for a “middle term” before an appropriate pair of premises is identified for syllogistic use. A middle term like B in the example above is the key ingredient in a syllogism, appearing both in the syntactically dependent position in one premise, and in the syntactically depended-upon position in the other premise, thus allowing the two to be composed together. This is a very simple example of mediation. Existence of a middle term B is what makes composition of the premises possible, and is therefore what makes pairings of premises appropriate for syllogistic use.

In many contexts, searching for a middle term can be understood as inventing an appropriate intermediate abstraction from available materials. If an existing abstraction is too broad to fit the case, we can add specifications until it does, and then optionally give the result a new name. All Aristotelian terms essentially are implied specifications; the names are just for convenience. Aristotle sometimes uses pure specifications as “nameless terms”.

Named abstractions function as shorthand for the potential inferences that they embody, enabling simple common-sense reasoning in ordinary language. We can become more clear about our thinking by using dialectic to unpack the implications of the abstractions embodied in our use of words. (See also Free Play; Practical Judgment.)

New Approaches to Modality

I periodically peek at the groundbreaking work on formal systems that is going on in homotopy type theory (HoTT), and in doing so just stumbled on an intriguing treatment of modal HoTT that seems much more philosophically promising to me than standard 20th century modal logic.

Types can be taken as formalizing major aspects of the Aristotelian notions of substance and form. Type theory — developed by Swedish philosopher Per Martin-Löf from early 20th century work by the British philosopher Bertrand Russell and the American mathematician Alonzo Church — is the most important thing in the theory of programming languages these days. It is both a higher-order constructive logic and an abstract functional programming language, and was originally developed as a foundation for constructive mathematics. Several variants of type theory have also been used in linguistics to analyze meaning in natural language.

Homotopy type theory combines this with category theory and the categorical logic pioneered by American mathematician William Lawvere, who was also first suggested a category-theory interpretation of Hegelian logic. HoTT interprets types as paths between topological spaces, higher-order paths between paths, and so on, in a hierarchy of levels that also subsumes classical logic and set theory. It is a leading alternative “foundation” or framework for mathematics, in the less epistemologically “foundationalist” spirit of previous proposals for categorical foundations. It is also a useful tool for higher mathematics and physics that includes an ultra-expressive logic, and has a fully computational interpretation.

There is a pretty readable new book on modal HoTT by British philosopher David Corfield, which also gives a nice introductory prose account of HoTT in general and type theory in general. (I confess I prefer pages of mostly prose — of which Corfield has a lot — to forests of symbolic notation.) Corfield offers modal HoTT as a better logic for philosophy and natural language analysis than standard 20th century first-order classical logic, because its greater expressiveness allows for much richer distinctions. He mentions Brandom several times, and says he thinks type theory can formally capture many of Brandom’s concerns, as I previously suggested. Based on admittedly elementary acquaintance with standard modal logic, I’ve had a degree of worry about Brandom’s use of modal constructs, and this may also help with that.

The worry has to do with a concept of necessity that occasionally sounds overly strong to my ear, and is related to my issues with necessity in Kant. I don’t like any universal quantification on untyped variables, let alone applied to all possible worlds, which is the signature move of standard modal logic. But it seems that adding types into the picture changes everything.

Before Corfield brought it to my attention, I was only dimly aware of the existence of modal type theory (nicely summarized in nLab). This apparently associates modality with the monads (little related to Leibnizian ones) that I use to encapsulate so-called effects in functional programming for my day job. Apparently William Lawvere already wrote about geometric modalities, in which the modal operator means something like “it is locally the case that”. This turns modality into a way of formalizing talk about context, which seems far more interesting than super-strong generalization. (See also Modality and Variation; Deontic Modality; Redding on Morals and Modality).

It also turns out Corfield is a principal contributor to the nLab page I previously reported finding, on Hegel’s logic as a modal type theory.

Independent of his discussion of modality, Corfield nicely builds on American programming language theorist Robert Harper’s notion of “computational trinitarianism”, which stresses a three-way isomorphism between constructive logic, programming languages, and mathematical category theory. The thesis is that any sound statement in any one of these fields should have a reasonable interpretation in both of the other two.

In working life, my own practical approach to software engineering puts a high value on a kind of reasoning inspired by a view of fancy type theory and category theory as extensions or enrichments of simple Aristotelian logic, which on its formal side was grounded in the composition of pairs of informally generated judgments of material consequence or material incompatibility. I find the history of these matters fascinating, and view category theory and type theory as a kind of vindication of Aristotle’s emphasis on composition (or what could be viewed as chained function application, or transitivity of implicit implication, since canonical Aristotelian propositions actually codify material inferences) as the single most important kind of formal operation in reasoning.

Aristotelian Propositions

Every canonical Aristotelian proposition can be interpreted as expressing a judgment of material consequence or material incompatibility. This may seem surprising. First, a bit of background…

At the beginning of On Interpretation, Aristotle says that “falsity and truth have to do with combination and separation” (Ch. 1). On its face, the combination or separation at issue has to do not with propositions but with terms. But it is not quite so simple. The terms in question are canonically “universals” or types or higher-order terms, each of which is therefore convertible with a mentioned proposition that the higher-order term is or is not instantiated or does or does not apply. (We can read, e.g., “human” as the mentioned proposition “x human”.) Thus a canonical Aristotelian proposition is formed by “combining” or “separating” a pair of things that are each interpretable as an implicit proposition in the modern sense.

Propositions in the modern sense are treated as atomic. They are often associated with merely stipulated truth values, and in any case it makes no sense to ask for internal criteria that would help validate or invalidate a modern proposition. But we can always ask whether the combination or separation in a canonical Aristotelian proposition is reasonable for the arguments to which it is applied. Therefore, unlike a proposition in the modern sense, an Aristotelian proposition always implicitly carries with it a suggestion of criteria for its validation.

The only available criteria for critically assessing correctness of such elementary proposition-forming combination or separation are material in the sense that Sellars and Brandom have discussed. A judgment of “combination” in effect just is a judgment of material consequence; a judgment of “separation” in effect just is a judgment of material incompatibility. (This also helps clarify why it is essential to mention both combination and separation affirmatively, since, e.g., “human combines with mortal” canonically means not just that human and mortal are not incompatible, but that if one is said to be human, one is thereby also said to be mortal.)

This means that Aristotle’s concept of the elementary truth and falsity of propositions can be understood as grounded in criteria for goodness of material inference, not some kind of correspondence with naively conceived facts. It also means that every Aristotelian proposition can be understood as expressing a judgment of material consequence or incompatibility, and that truth for Aristotle can therefore be understood as primarily said of good judgments of material consequence or incompatibility. Aristotle thus would seem to anticipate Brandom on truth.

This is the deeper meaning of Aristotle’s statement that a proposition in his sense does not just “say something” but “says something about something”. Such aboutness is not just grammatical, but material-inferential. This is in accordance with Aristotle’s logical uses of “said of”, which would be well explained by giving that a material-inferential interpretation as well.

The principle behind Aristotelian syllogism is a form of composition, formally interpretable as an instance of the composition of mathematical functions, where composition operates on the combination or separation of pairs of terms in each proposition. Aristotelian logic thus combines a kind of material inference in proposition formation and its validation with a kind of formal inference by composition. This is what Kant and Hegel meant by “logic”, apart from their own innovations.