Tyranny

Plato diagnosed tyranny as first and foremost an affliction of the soul. Socrates in Plato’s Republic characterizes the tyrannical soul by a malformed desire that strongly resists any kind of balanced consideration of other factors. This kind of desire wants its way immediately and unconditionally.

The tyrannical soul wants a kind of unquestioning recognition from others, without reciprocally recognizing them. This kind of attitude represents the opposite end of the spectrum from what Aristotle called magnanimity or great-souledness; rather, it is characteristic of the attitude of Mastery denounced by Hegel. Unfortunately, modern egoism, with its emphasis on a narrow kind of self, tends to devolve in this direction. (See also Freedom Without Sovereignty.)

While a tyrannical soul may be an Aristotelian cause of particular unjust acts, this does not mean that injustice as a whole is reducible to matters of individual character. Injustice is not just caused by the bad acts of individuals, but also often involves institutions and social structure, which have their persistence in part from a kind of materiality of their own.

Nietzsche, Ethics, Historiography

Nietzsche famously criticized received notions of good and evil, and pointed out the inglorious role of “reactive” and resentful thinking about morals. To negatively frame our notions of goodness and virtue in terms of emotional reactions to bad things done by others is not an auspicious beginning for ethics. It results in a bad order of explanation that puts negative judgments of others before positive consideration of what is right.

Nietzsche pointed out that this occurs more often than we might think. A recurring emphasis on negative, blaming attitudes toward other people over affirmative values is unfortunately all too common not only in ordinary life and actually existing religious practice, but across what passes for the political spectrum. We ought to distance ourselves from this, and develop our values in positive rather than negative terms. We should aim to be good by what we do, not by contrasting ourselves with those other people. As an antidote to resentment, Nietzsche recommended we cultivate forgetfulness of wrongs done by others. I would add that we can have strong concern for justice without focusing on blame or revenge.

Like Aristotle, but without ever mentioning the connection, Nietzsche emphasized a certain sort of character development, and effectively advocated something close to Aristotle’s notion of magnanimity, or “great-souledness” as contrasted with small-mindedness. But in common with some modern interpretations of “virtue ethics”, Nietzsche tended to make whatever a presumably great-souled person might in fact do into a criterion, and consequently downplayed the role of the rational deliberation jointly emphasized by Aristotle and Kant.

Unfortunately, Nietzsche seems to have been so outraged by what he saw as widespread hypocrisy that he sometimes failed to take his own advice to avoid dwelling on the negative. This comes out in his tendency to make sweeping historical generalizations. Thus, he presented all religion in a negative light, and even went so far as to blame the “moralism” of Socrates and Plato for many later historical ills, while failing to note his own partial convergence with Aristotle.

Even at the peak of my youthful enthusiasm for Nietzsche, this negative judgment of Socrates and Plato always seemed wrong to me. Textual evidence just does not support the attribution of primarily “resentful” attitudes to either of them. On the contrary, Socrates and Plato began a completely unprecedented attempt to understand what is good in positive terms, and took great care to avoid prejudice in the process.

Partly as a consequence of his sweeping rejection of Socrates and Plato, Nietzsche looked for alternate heroes among the pre-Socratics, especially favoring Heraclitus. (In the 20th century, with different motivations, Heidegger expanded on Nietzsche’s valorization of the pre-Socratics over Plato and Aristotle, claiming that Heraclitus and Parmenides “had Being in sight” in ways that Plato and Aristotle did not. This seems to me like nonsense. As distinct from poetry and other artistic endeavors (which I value highly, but in a different way), philosophy is not about primordial vision or its recovery; it is about rational understanding and development toward an end, starting from wherever we actually find ourselves. While the pre-Socratics are important in a sort of prehistory of philosophy, the level of rational development they achieved was minimal. Extended rational development first bloomed with Plato, and then was taken to a yet higher level by Aristotle.)

Nietzsche also denied the reality or effective relevance of anything like Aristotelian potentiality, claiming that only what is actual is real. The semantic or expressive category of potentiality underwrites logical and linguistic modality, which among other things in turn underwrites the possibility of expressing objective judgments of “should”, as well as of causality, of which Nietzsche seems to have taken a Humean view. The general role of potentiality and modality is independent of all issues of the correctness or possibly prejudiced character of particular judgments.

Nietzsche’s denial of potentiality is thus related to a denial of any objective good and evil. It is akin to other views that attempt to explain values by facts. He thought mostly in terms of actually occurring valuations, and did distinguish better from worse ones, but mainly in terms of a kind of ad hominem argument from great-souledness or small-mindedness.

In my view, he should have been content to point out that many particular judgments are prejudiced or incorrect, and at any moment we have no sure way of knowing we accurately recognize which these are. Objectivity in ethics cannot be assumed as a starting point, but that does not mean there can never be any. Where it occurs, it is a relative status that is the product of a development. (See also Genealogy.)

Nietzsche’s poetic notion of the Eternal Return does in a way partly make up for his overly strong denial of any objective good or evil. The Eternal Return works especially as an ethical, selective thought that distinguishes purely affirmative valuations from others. I used to want to think this was enough to recover something objective that acts like a notion of good as affirmativeness, but that is contrary to what he says explicitly.

Meno

Plato’s short dialogue Meno — concerned with virtue and knowledge — is among the most famous of what are referred to as his “Socratic” dialogues, which dwell on Socratic method, and on the character of Socrates as a kind of role model. Meno wants Socrates to provide an easy answer to how virtue is to be acquired. Socrates, ever distrustful of easy answers, shifts the discussion toward the more basic question of what virtue is. Meno first responds with examples, but Socrates points out that examples do not answer the “what is” question.

Meno eventually suggests that virtue is the desire of honorable things, combined with the power of attaining them. Socrates then points out that some people desire evil, and that a person may have power, yet still fail to properly recognize good as good and evil as evil. Meno complains that Socrates is always doubting himself and making others doubt, and says he feels bewitched.

Socrates introduces a poetic myth that learning is a kind of recollection of knowledge that we already had. He then walks a young boy through a simple geometrical construction. At the beginning, the boy seems to have no idea how to solve the problem. Then he thinks he does, but he is wrong. At a later point, he recognizes the mistake. Socrates points out that it is always better to know that we do not know, than to think that we know when we do not. But still later, after following the steps of the construction, it seems like the boy does understand how to find the solution, though he is never told. As Brandom might remind us, this shows the value of making what was implicit into something explicit.

Eventually, Socrates leads Meno to the conclusion that virtue is “either wholly or partly wisdom”. But then he introduces a further doubt, whether virtue can be reduced to knowledge. True opinion is said to be as good a guide to action as knowledge, and this is said to be how most good people function.

But then finally, true opinion is said not to be of very great value after all, because it is not “fastened by the tie of the cause”, and therefore tends to “run away” from us. That is to say, when we do not really know — i.e., cannot articulate — the why of a conclusion that is right in one context, it is easy to misapply it in a different context. (See also Dialogue; Platonic Truth; What and Why; Reasons.)

Form as a Unique Thing

Ever since Plato talked about Forms, philosophers have debated the status of so-called abstract entities. To my mind, referring to them as “entities” is already prejudicial. I like to read Plato himself in a way that minimizes existence claims, and instead focuses on what I think of as claims about importance. Importance as a criterion is practical in a Kantian sense — i.e., ultimately concerned with what we should do. As Aristotle might remind us, what really matters is getting the specific content of our abstractions right for each case, not the generic ontological status of those abstractions.

One of Plato’s main messages, still very relevant today, is that what he called Form is important. A big part of what makes Form important is that it is good to think with, and a key aspect of what makes Plato’s version good to think with is what logically follows from its characterization as something unique in a given case. (Aristotle’s version of form has different, more mixed strengths, including both a place for uniqueness and a place for polyvocality or multiple perspectives, making it simultaneously more supple and more difficult to formalize.) In principle, such uniqueness of things that nonetheless also have generality makes it possible to reason to conditionally necessary outcomes in a constructive way, i.e., without extra assumptions, as a geometer might. Necessity here just means that in the context of some given construction, only one result of a given type is possible. (This is actually already stronger than the sense Aristotle gave to “necessity”. Aristotle pragmatically allowed for defeasible empirical judgments that something “necessarily” follows from something else, whenever there is no known counter-example.)

In the early 20th century, Bertrand Russell developed a very influential theory of definite descriptions, which sparked another century-long debate. Among other things (here embracing an old principle of interpretation common in Latin scholastic logic), he analyzed definite descriptions as always implying existence claims.

British philosopher David Corfield argues for a new approach to formalizing definite descriptions that does not require existence claims or other assumptions, but only a kind of logical uniqueness of the types of the identity criteria of things. His book Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy, to which I recently devoted a very preliminary article, has significant new things to say about this sort of issue. Corfield argues inter alia that many and perhaps even all perceived limits of formalization are actually due to limits of the particular formalisms of first-order classical logic and set theory, which dominated in the 20th century. He thinks homotopy type theory (HoTT) has much to offer for a more adequate formal analysis of natural language, as well as in many other areas. Corfield also notes that most linguists already use some variant of lambda calculus (closer to HoTT), rather than first-order logic.

Using first-order logic to formalize natural language requires adding many explicit assumptions — including assumptions that various things “exist”. Corfield notes that ordinary language philosophers have questioned whether it is reasonable to suppose that so many extra assumptions are routinely involved in natural language use, and from there reached pessimistic conclusions about formalization. The vastly more expressive HoTT, on the other hand, allows formal representations to be built without additional assumptions in the representation. All context relevant to an inference can be expressed in terms of types. (This does not mean no assumptions are involved in the use of a representation, but rather only that the formal representation does not contain any explicit assumptions, as by contrast it necessarily would with first-order logic.)

A main reason for the major difference between first-order logic and HoTT with respect to assumptions is that first-order logic applies universal quantifications unconditionally (i.e., for all x, with x free or completely undefined), and then has to explicitly add assumptions to recover specificity and context. By contrast, type theories like HoTT apply quantifications only to delimited types, and thus build in specificity and context from the ground up. Using HoTT requires closer attention to criteria for identities of things and kinds of things.

Frege already had the idea that logical predicates are a kind of mathematical function. Mathematical functions are distinguished by invariantly returning a unique value for each given input. The truth functions used in classical logic are also a kind of mathematical function, but provide only minimal distinction into “true” and “false”. From a purely truth-functional point of view, all true propositions are equivalent, because we are only concerned with reference, and their only reference (as distinguished from Fregean sense) is to “true” as distinct from “false”. By contrast, contemporary type theories are grounded in inference rules, which are kinds of primitive function-like things that preserve many more distinctions.

In one section, Corfield discusses an HoTT-based inference rule for introduction of the definite article “the” in ordinary language, based on a property of many types called “contractibility” in HoTT. A contractible type is one that can be optionally taken as referring to a formally unique object that can be constructed in HoTT, and whose existence therefore does not need to be assumed. This should also apply at least to Platonic Forms, since for Plato one should always try to pick out the Form of something.

In HoTT, every variable has a type, and every type carries with it definite identity criteria, but the identity criteria for a given type may themselves have a type from anywhere in the HoTT hierarchy of type levels. In a given case, the type of the identity criteria for another type may be above the level of truth-functional propositions, like a set, groupoid, or higher groupoid; or below it, i.e., contractible to a unique object. This sort of contractibility into a single object might be taken as a contemporary formal criterion for a specification to behave like a Platonic Form, which seems to be an especially simple, bottom-level case, even simpler than a truth-valued “mere” proposition.

The HoTT hierarchy of type levels is synthetic and top-down rather than analytic and bottom-up, so everything that can be expressed on a lower level is also expressible on a higher level, but not necessarily vice versa. The lower levels represent technically “degenerate” — i.e., less general — cases, to which one cannot “compile down” in some instances. This might also be taken to anachronistically explain why Aristotle and others were ultimately not satisfied with Platonic Forms as a general basis for explanation. Importantly, this bottom, “object identity” level does seem to be adequate to account for the identity criteria of mathematical objects as instances of mathematical structures, but not everything is explainable in terms of object identities, which are even less expressive than mere truth values.

Traditionally, mathematicians have used the definite article “the” to refer to things that have multiple characterizations that are invariantly equivalent, such as “the” structure of something, when the structure can be equivalently characterized in different ways. From a first-order point of view, this has been traditionally apologized for as an “abuse of language” that is not formally justified. HoTT provides formal justification for the implicit mathematical intuition underpinning this generally accepted practice, by providing the capability to construct a unique object that is the contractible type of the equivalent characterizations.

With this in hand, it seems we won’t need to make any claims about the existence of structures, because from this point of view — unlike, e.g., that of set theory — mathematical talk is always already about structures.

This has important consequences for talk about structuralism, at least in the mathematical case, and perhaps by analogy beyond that. Corfield argues that anything that has contractible identity criteria (including all mathematical objects) just is some structure. He quotes major HoTT contributor Steve Awodey as concluding “mathematical objects simply are structures. Could there be a stronger formulation of structuralism?”

Thus no ontology or theory of being in the traditional (historically Scotist and Wolffian) sense is required in order to support talk about structures (or, I would argue, Forms in Plato’s sense). (In computer science, “ontology” has been redefined as an articulation of some world or domain into particular kinds, sorts, or types, where what is important is the particular classification scheme practically employed, rather than theoretical claims of real existence that go beyond experience. At least at a very high level, this actually comes closer than traditional “metaphysical” ontology did to Aristotle’s original practice of higher-order interpretation of experience.)

Corfield does not discuss Brandom at length, but his book’s index has more references to Brandom than to any other named individual, including the leaders in the HoTT field. All references in the text are positive. Corfield strongly identifies with the inferentialist aspect of Brandom’s thought. He expresses optimism about HoTT representation of Brandomian material inferences, and about the richness of Brandom’s work for type-theoretic development.

Corfield is manifestly more formally oriented than Brandom, and his work thus takes a different direction that does not include Brandom’s strong emphasis on normativity, or on the fundamental role of what I would call reasonable value judgments within material inference. From what I take to be an Aristotelian point of view, I greatly value both the inferentialist part of Brandom that Corfield wants to build on, and the normative pragmatic part that he passes by. I think Brandom’s idea about the priority of normative pragmatics is extremely important; but with that proviso, I still find Corfield’s work on the formal side very exciting.

In a footnote, Corfield also directs attention to Paul Redding’s recommendation that analytic readers of Hegel take seriously Hegel’s use of Aristotelian “term logic”. This is not incompatible with a Kantian and Brandomian emphasis on the priority of integral judgments. As I have pointed out before, the individual terms combined or separated in canonical Aristotelian propositions are themselves interpretable as judgments.

“What” by Inferential Semantics

Brandom’s inferential semantics can be seen as providing a general framework for answering “what is…” questions. Semantics is about meaning — especially of concrete things said — and inferential semantics is about understanding meaning as a kind of practical doing involved with reasons. Looked at this way, a meaning reflects an inferential role, or role in real-world reasoning. Such roles always have two sides — conditions for appropriate use, and consequences of using this rather than that. Brandom identifies conceptual content with such inferential roles, and focuses on a contrast between these and simple definition, but I want to emphasize instead that all simple definition should be understood as a kind of summary of what implicitly distinguishes a particular inferential role from others.

The kind of meaning of interest here is in principle shareable rather than subjective, private, or psychological. Meaning is social and essentially involved with communication, but it is not a matter of empirical fact. Rather than explaining communication in terms of empirical facts, we should ultimately explain what we call empirical facts in terms of well-founded shareable meaning. The more we are able to explicitly spell out conditions of use and consequences of things that are said, the more substantive content we can share with others.

The “what is…” questions classically asked by Plato and Aristotle have an open-ended character because they are concerned with what something means for a reasoning being in general, which is an open-ended context. To have meaning for a reasoning being is to make a difference in the way the being reasons in life. In this way, Plato and Aristotle also were deeply concerned with the inferential roles of things, and practiced a kind of inferential semantics. This is ultimately inseparable from questions of goodness of reasoning. Here, too, inferential semantics depends on normative pragmatics.

Plato vs Aristotle?

Plato and Aristotle agreed on some matters, and disagreed on others. Throughout the modern period, authors have frequently resorted to rather stereotyped contrasts between them. In the ancient world, the neoplatonists made a serious effort to read Aristotle in terms of their own traditionally “metaphysical” reading of Plato, and thus to largely reconcile the two (see Fortunes of Aristotle; Plotinus). This resulted in a lot of distortion of Aristotle — some of which has persisted to this day — alongside a lot of original development that is only very recently again being appreciated and studied.

I’m putting forward a largely reconciling view, but going in the opposite direction from that of the neoplatonists. That is to say, while the works of Plato will always remain literary classics, I think Aristotle captured the best of Plato philosophically, while adding tremendously valuable further development. Where Aristotle criticized Plato or others in the Academy, the criticisms generally seem sound to me. I also think what are considered late works of Plato like Theaetetus, The Sophist, and even Parmenides may show development in a more Aristotelian direction, especially with regard to the theory of form.

Platonic Truth

Plato was much more concerned with what might be called truths of essence than with truths of fact. Truths of essence involve interpretation of meaning, and always have an implicit normative dimension. They are inseparably involved with questions of what is good or right. As Aristotle might say, they tell us what and why something is rather than merely “that” something is.

There is no general way to test whether we have completely grasped an essence, and not just what Hegel would call a one-sided view of it. As Brandom might say, all grasping of essences is defeasible. Plato makes his leading characters say many things that apply this in particular cases. Essences are the object of interpretation, not certain knowledge. (See also Dialogue; The Epistemic Modesty of Plato and Aristotle; Plato and Aristotle Were Inferentialists; Brandom on Truth; Foundations?)

Likely Stories

Plato had his characters engage in a good deal of speculation, but generally was very conscientious about explicitly identifying it as such. Larger speculations are often explicitly couched as myth or poetic invention. All such things are explicitly considered no more than “likely stories”. On a smaller scale, verbal cues generally abound to tell us when things are intended in a more tentative way.

Plato and Aristotle were generally — each in their own way — extraordinarily good at this sort of thing. However, the much more “dogmatic” style of the Stoic school set a new default tone for the later tradition, all the way to the time of Kant. It became standard to present what was actually speculation as if it were a simple report on the truth, or a certainty grounded in a strong kind of knowledge. (See also The Epistemic Modesty of Plato and Aristotle; Kantian Discipline.)

The One?

Whether or not there is a One, it and the Others are and are not — and appear and do not appear to be — all manner of things in all manner of ways, both in relation to themselves and to each other.

Such was the cryptic conclusion of Plato’s dialogue Parmenides. The Parmenides provides the most extensive and technical example of Plato’s concept of dialectical argument, which revolved around thorough exploration of both sides of binary alternatives. Some early Platonists and a number of modern readers thought it was mainly a logical exercise.

Plotinus followed the lead of the neo-Pythagoreans in treating the One far less equivocally, as the main theological principle. He explicitly identified it with the Good from Plato’s Republic, and made it the source of all things. In the wake of Plotinus, later neoplatonists read the Parmenides as a theological treatise.

Maurice Merleau-Ponty’s 1945 Phenomenology of Perception argued that Plotinus was misguided, and really there is no One. Foucault’s 1969 Archaeology of Knowledge was devoted to questioning presumed unities of all sorts. Other pluralists from Aristotle to William James have made broadly similar arguments.

Talk about whether there “is” a One gets tricky. Plotinus associated Being only with his second principle of intellect (nous), not with the One. The 20th century theologian Paul Tillich gave a nod to this when he humorously suggested that to attribute to God the same existence we attribute to objects in the world should be considered blasphemy. In the middle ages Thomas Aquinas went somewhat in the opposite direction, identifying God with pure Being, and therefore he felt no need for a One above being. But the pure Being Aquinas spoke of was a new and innovative concept that is not the same as any worldly existence, so perhaps the two could be reconciled after all.

“The One” has historically been said in many ways. Usually it does not refer to any sort of entity, but rather to a sort of cosmic fusion in which all things participate; or, more properly, to a pure Platonic form of such fusion, perhaps even the form of something slightly anticipating Kantian unity of apperception. Sometimes on the other hand it seems to be beyond form altogether. Plotinus himself largely invented negative theology, and at one point even said the One was just a conventional name for the utterly ineffable. (See also One, Many; Identity, Isomorphism; Univocity; Theology.)

The Good

Plato suggested the idea (later much expanded upon by Plotinus) that a single ineffable Good is the highest principle of all things. The Good was characterized as hyperousia, or “beyond ousia“, where ousia is the same word Aristotle glossed as “what it was to have been” a thing, later misleadingly translated into Latin as substantia or substance. In discussions of neoplatonism, hyperousia used to be often loosely understood as “beyond being”, which is confusing and engendered all sorts of arguments. The problem is that modern people tend to think of being primarily in terms of what is really a kind of brute existence, whereas Plato and Aristotle were more concerned with intelligibility. Even existence in its Greek root has more to do with being able to be picked out than just being there indiscriminately. At any rate, Plato and Aristotle both considered ousia something definable (“intelligible being”, if you will), and they both agreed that the Good as such is undefinable, while drawing different conclusions.

The Platonic Good is the archetype of what Aristotle called an end. Plato held fast to the notion that there should be a single idea of the Good, even if we cannot comprehend or define it. He gave it a quasi-definition as that at which all things aim. Aristotle agreed that all things aim at some good, but pointed out that “good” is used equivocally when we say this. He preferred to say that each thing has its own good that is in principle intelligible. To say something is intelligible for Aristotle still does not mean all details are determined in advance. As Brandom has also emphasized, purpose and contingency are deeply interwoven.

Putting aside this difference between Plato and Aristotle for the moment, I want to suggest that for both of them, a consideration of ends and of what ought to be (and thus of ethics and meta-ethics) implicitly comes first in the order of explanation, before any ontology or any putative facts about what is. Kant made this more explicit as what he called the primacy of practical reason. Plato’s first principle is the Good. Aristotle’s nominal “First cause” of pure actuality or at-work-ness is a generalized end implicit in the ends and proper activities of particular things or kinds.