Magnanimity

Magnanimity (literally “great-souledness”) has a special place among the Aristotelian virtues. It is said to be a mean that avoids both vanity and small-mindedness. In the later tradition under Christianity, pride often tended to be regarded simply as a sin, but Aristotle made a strong distinction between vanity or arrogance and a legitimate, well-founded kind of pride that leads to good actions.

Aristotle says a person who has this legitimate kind of pride will be very willing to help others, but will generally avoid asking for help. Such a person will be open and frank, caring more about the truth than about negative judgments of others. They will generally not hide what they feel. They will have the confidence to assert themselves with others who have power and authority, but will treat others — especially those less fortunate — with kindness and respect, and perhaps ironic self-depreciation. Also, “it is not a mark of greatness of soul to recall things against people, especially the wrongs they have done you, but rather to overlook them”.

Ad Hominem

An ad hominem argument is a kind of logical fallacy that tries to argue from supposed facts about a person to a repudiation or endorsement of something specific that the person said or did (e.g., so-and-so did bad thing x, so they must be wrong about y).

Sometimes such facts are indirectly relevant to a more specific evaluation, but still there is no necessary logical connection — only at best a sort of Humean accidental association, or what a lawyer would call circumstantial evidence that does not constitute proof. In exceptional cases, careful consideration might legitimately weigh very strong circumstantial evidence enough to sway a decision, but this ought to be rare, because even strong circumstantial evidence is not proof.

Influenced by both Nietzsche and Hume, Gilles Deleuze tried to argue against the current that questions about who are more important than questions about what. I don’t think this succeeded.

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.)

Context

The better we can interpret a context, the better we can understand the significance of things within it. In deliberation, the more grasp we have of the relevant context, the more it becomes possible to reach definite determinations.

An Aristotelian sensitivity to the distinctness and complexity of each situation in no way compromises an ethical ideal of universality like Kant promoted — quite the opposite. It is what enables us to apply that ideal well in each case.

In the world, differences in context also sometimes get used as a pretext for false distinctions that negate ethical universality, or are simply self-serving. But if we truly respect ethical universality, this will be of great help in seeing those cases for what they are.

Context provides a kind of anchor for modality, which plays a very great role in the intelligibility of things. Conversely, modality gives context a greater definiteness. Context is also perhaps the most fundamental concept for historiography.

Several Aristotelian concepts are concerned with context. Potentiality captures most of the aspects related to modality, but contingent fact and circumstance as such are associated with Aristotelian “material causes”, and operating means to ends are treated as “efficient causes”. The interpretation of context complements the classic questions of what and why.

From a Brandomian point of view, practical implications of context will be especially important in normative pragmatics, but context also affects determinations of meaning in inferential semantics.

Modality and Variation

David Corfield suggests that modality has to do with ranges of variation. This seems extremely helpful. He connects Brandom’s notion of ranges of counterfactual robustness with mathematical analyses of variation. Corfield approvingly cites Brandom’s argument that in order to successfully apply empirical concepts at all, we must already be able to apply modal concepts like possibility and necessity. This always seemed right to me, but the talk about possible worlds made me worry about what sounded like impossibly strong quantification over infinities of infinities. Corfield also points out that Saul Kripke originally cautioned against uncareful extension of his possible-worlds talk.

It now seems to me that Brandom’s counterfactual robustness and Corfield’s mathematically analyzable variation together can be taken as an explanation for modal notions of necessity that previously seemed to be simply posited, or pulled out of the blue. Modality suddenly looks like a direct consequence of the structure of ranges of variation. Previously, I associated both structure and Brandom’s modally robust counterfactuals with Aristotelian potentiality, so this fits well.

Corfield also relates this to work done by the important 20th century neo-Kantian, Ernst Cassirer, on invariants behind the various systems of Euclidean and non-Euclidean geometry. He points out that Cassirer thought similar concerns of variation and invariance implicitly arise in ordinary visual perception, and connects this with Brandom’s thesis that modality is already there in our everyday application of empirical concepts.

The British Empiricist David Hume famously criticized common-sense assumptions about causality and necessity, preferring to substitute talk about our psychological tendencies to associate things that we have experienced together. Hume pointed out that from particular facts, no knowledge of causality or necessity can ever be derived. This is true; no knowledge of necessity could arise from acquaintance with particular facts. But if necessity and other modalities are structural, as Corfield suggests, they do not need to be inferred from particular facts, or to be arbitrarily posited.

The kind of necessity associated with structural determination is quite different from unconditional predestination. I want to affirm the first, and deny the second. Structural determination only applies within well-defined contexts, so it is bounded. If we step outside of the context where it applies, it no longer has force. (See also New Approaches to Modality; Free Will and Determinism.)

Leibniz is more familiar to me than Kripke, so when I hear “possible worlds”, I have tended to imagine complete alternate universes à la Leibniz. “Worlds”, however, could be read much more modestly as just referring to Corfield’s ranges of variation.

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.

“Why” by Normative Pragmatics

Brandom’s normative pragmatics can be seen as providing a general framework for answering “why” questions. Pragmatics is initially about the practical use of language, and normative pragmatics is about good use, which for Brandom especially means good inferential use. Thus, normative pragmatics ends up being broadly concerned with good informal reasoning in life, i.e., with the quality of our ethical and other judgments.

In my view, this concern with the goodness of reasons and judgments also ends up emphasizing the ethical dimensions of judgment in general. There is really no such thing as “value free” judgment. Even what is called mathematical “intuition” is really an acquired practical skill having to do with judgment of what next step is contextually appropriate.

Classically, “why” asks for reasons, or about the goodness of reasons. Taken far enough, this leads to questions about ends.

Aristotle, too, typically framed inquiries in terms of what is well “said of” something. This is a kind of analysis of language use, with a normative or ethical intent, that ends up being inseparable from questions of what is right and what is true. This general approach is actually a form of what Brandom would call normative pragmatics. Brandom would tell us that semantics — or the investigation of meaning — depends on this sort of inquiry. My ascription of a fundamentally semantic orientation to Aristotle carries a similar implication.