“Relation” in Aristotle’s Categories

Something that gets translated as “relation” (ta pros ti, literally “the toward something”) is one of the ten categories Aristotle discusses in the Categories, which was traditionally treated as a kind of introduction to Aristotelian logic, and indeed to Aristotle’s thought as a whole.

In the order of the sciences laid out by al-Farabi, for instance, I believe the Categories is treated as a source of primitive definitions along the lines of the definitions with which the systematic development of Euclid’s Elements of Geometry begins. This is to substitute a very different — straightforwardly deductive — method and pedagogy for Aristotle’s own more fluid approach. See Demonstrative “Science”?.

Plato and Aristotle devoted extraordinary attention to questions of definition, and in doing so greatly devalued the importance of any assumed definitions.

Aristotle always recommended that we begin with that is more familiar and close at hand, and then expect our beginning to be substantially modified as we move toward what is clearer and more intelligible. This is the original model for Hegel’s logical “movement”.

The “what is toward something” of the Categories is quite simply not equivalent to more modern notions of “relation” — neither to its use in Kant and Hegel, nor to its mathematical use. Whether in Kant or Hegel or in mathematics, relation in the modern sense is fundamentally bi-directional. If a has a relation R to b, then b by definition has a relation R-inverse to a. In the same sense in which Hegel points out that the positive and negative signs on numbers assigned to measure, e.g., physical forces, can be systematically reversed without changing the physical meaning, any directionality in relations in the modern sense is a superficial matter of setup, and not anything deeply meaningful.

On the other hand, Aristotle’s “what is toward something” has an irreducibly directed (i.e., unidirectional) character. If x is oriented “toward” y, it does not follow that y must have a corresponding inverse orientation toward x. The semantics of x‘s “being toward” y imply a material dependency of x on y, and thus implicitly a kind of subordination of x to y.

This is certainly an important kind of construct to have in our toolbox for explaining things, but it simply is not what is meant when Kant says we know phenomena in a purely relational way, or when Hegel adds that essence is purely relational. It would also be a serious error to assume that according to Aristotle, the subordinate or subordinating aspect of the pros ti category would apply to the different concept of “relation” used by Kant and Hegel (or to mathematical relations).

Once again, this whole confusion arises due to the influence of the Latin translation, in this case of pros ti by relatio. For Latin readers, relatio had not yet acquired the importantly different meanings that “relation” has in Kant and Hegel, or in the mathematical theory of relations pioneered by C. S. Pierce and Ernst Schröder. Thus its use did not create serious misunderstanding. But for a general modern audience, “relation” is a terrible choice to translate pros ti, for the reasons mentioned.

I think that Aristotle does also implicitly operate with a concept like that of “relation” in Kant and Hegel, but he does not give it a name, and it is certainly not the pros ti of the Categories. Rather, it comes into play in the way Aristotle uses notions like unity, diversity, identity, and difference.

Which Pragmatism?

“Pragmatism” is said in many ways. There is the crude, morally disreputable sort that means pursuit of narrow self-interest. There is the broad sort associated with a kind of flexible adaptation, which could be viewed either positively or negatively. There are several philosophical pragmatisms, none of which should be understood in terms of either of these.

Philosophical pragmatisms usually avow a deflationary, coherentist theory of truth, and stand in contrast to Cartesian, representationalist, and foundationalist views. They also tend to be associated with an instrumentalist rather than realist view of scientific explanation. I’m not in the habit of calling myself a pragmatist, but am sympathetic to all of this.

Charles Pierce (1839-1914) is generally regarded as the founder of philosophical pragmatism, and it was he who invented the word. The quite different version promulgated by William James (1842-1910), however, was initially far better known. At a very broad level it could be said that where Pierce was more Kantian, James was closer in spirit to the British utilitarians and the British empiricist tradition. Pierce apparently had severe misgivings about the work of James, and resented James’ takeover of his term. In later works, he ceded the name “pragmatism” to James and adopted the new term “pragmaticism”, in an attempt to separate their views.

Pierce’s pragmatism, I’d like to think, references the Kantian primacy of practical reason. He broadens the sense of “practical” far beyond Kant’s initial ethical focus, but without losing touch with its Kantian basis. He treats Kant’s rejection of “intellectual intuition” as decisive and deeply related to this, preferring to develop meanings through a kind of practical inference. His original “pragmatic maxim” is as follows: “Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object” (“How to Make Our Ideas Clear”). I’m no Pierce scholar, but I think that Pierce’s uses of “practical” are meant to apply in both Kantian and utilitarian/empiricist senses, whereas it seems James lost the Kantian aspect.

Though his interests were wide-ranging, Pierce was initially known for his work in mathematical logic and semiotics, and a few seminal essays. He made pioneering contributions to the mathematics of relations, and is widely regarded as the founder of modern semiotics, or the general study of signs.

Like Leibniz, Pierce left a huge mass of unpublished manuscripts, editing of which will continue for many decades to come. According to my late father, who wrote his dissertation on Pierce in the late 1950s, Pierce’s executors deliberately impeded research into Pierce’s significant engagement with Kant and Hegel and his correspondence with Husserl, in order make Pierce fit better into the American philosophical mainstream of the day, which was a much narrower, more intolerant, and more anti-historical kind of analytic philosophy than prevails among English-speaking professional philosophers today.

John Dewey (1859-1952) was another better known American figure with whose name the term “pragmatism” also became more closely linked than that of Pierce. Like James, he was a psychologist as well as a philosopher. He is known for his writings on education and democracy.

Philosopher, sociologist, and social psychologist George Herbert Mead (1863-1931) developed a pragmatist theory of social life known as symbolic interactionism. John Herman Randall, Jr. (1899-1980) developed a pragmatist reading of Aristotle, and also argued that Italian Renaissance Aristotelianism played a larger and far more positive role in the development of modern science than is commonly recognized.

In the mid-20th century, analytic philosophers W.V.O. Quine and Wilfrid Sellars used pragmatist arguments to criticize logical positivism, initiating a gradual sea change in Anglo-American philosophy over the next several decades. Hilary Putnam, Donald Davidson, Richard Rorty, and Robert Brandom are also known as analytic pragmatists.

(“Pragmatics” in the study of natural and artificial languages — a discipline concerned with questions of use — comes from the same Greek root, but is otherwise independent of the “pragmatisms” delimited here.)

Between Transcendentalism and Pragmatism

Josiah Royce (1855-1916) was known as the leading American exponent of absolute idealism. He was recognized for contributions to philosophy of religion, psychology, and logic, as well as metaphysics. I thought of him because apparently, at least in his earlier works, he really did identify the Absolute with an all-embracing, divine consciousness that was supposed to include and underwrite all of reality, quite opposite to the way I read Hegel’s Phenomenology as an extended critique of the point of view of consciousness.

Also quite unlike the “deflationary” approach taken here, he straightforwardly identified his Absolute with God and with Being. Royce’s was a definitely personal God, also existing in time rather than eternally. Early in his career, he developed a novel argument for the existence of God based on the existence of error. According to Royce, the very existence of error presupposes the existence not only of truth against which the error can be recognized, but of a Knower who knows the truth.

Royce had strongly communitarian ethical views, sharply criticizing both the “heroic individualism” of the American Transcendentalists, with whom he shared an interest in German Idealist philosophy, and the individualist views of his close friend, the pragmatist William James. Among other things, Royce thought James in his famous Varieties of Religious Experience focused too much on intensely private experiences of extraordinary individuals, to the detriment of attention to the community aspect of religion. In his theology, Royce strongly associated God with an ideal of a Universal Community.

In his late work, he was increasingly influenced by the great founder of pragmatism, Charles Pierce. He became fascinated with Pierce’s notions of signs, semiotics, and interpretation. While this was not quite the full-fledged anti-foundationalist notion of interpretation developed here, I think it at least points in a similar direction. At this point, Royce developed a new notion of God as “the Interpreter Spirit” providing a metaphysical ground in time for all acts of interpretation, without the interpreters necessarily being aware of this. He extended his notion of the Universal Community, now explicitly calling it a “Community of Interpretation”. I think the latter is a fascinating partial anticipation of Brandom’s much more detailed work on mutual recognition, which also draws on the pragmatist Kantianism of Wilfrid Sellars.

(From Brandom’s point of view, Royce’s communitarianism would still be a one-sided overreaction to individualist trends. It seems to me that Brandom and Ricoeur converge on a very attractive alternative to this old seesaw, putting concrete relations with others and intersubjectivity before either individuality or community.)

Martin Luther King, Jr., acknowledged Royce as the source of King’s own more elaborated notion of the ideal of the Beloved Community, a vision of tolerance and mutual acceptance. I have not evaluated claims of a recent book that in spite of this, Royce also in effect promoted a cultural version of the racist “white man’s burden”.

Royce attempted to derive all of ethics from a single principle of loyalty, understood as loyalty to a cause. He claimed that loyalty to vicious or predatory causes fails to meet a criterion of “loyalty to loyalty” intrinsic to his principle of loyalty. Thus the argument seems to be that loyalty has the kind of universality that Kant claimed for the categorical imperative. However, I don’t think the argument succeeds nearly as well as Kant’s. Kantian respect for people gives a crucial human face to Kant’s formalism in ethics. Even if loyalty to loyalty is concerned to avoid undermining the loyalty of others to the cause, as Royce argued, that seems to me to be a much narrower kind of concern for others. Also, loyalty is by nature particular, whereas Kant’s various formulations of the categorical imperative are actual tests for universality.