Tag: al-Farabi

“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.

Demonstrative “Science”?

The “historiographical” notes on the history of philosophy I offer here from time to time are a sort of compromise. For much of my life, I’ve been very concerned with the fine grain of such history, and with casting a broad net encompassing many historical figures. Here, I made a strategic decision to focus instead on a mere handful of philosophers I consider most important.

Discussion of actualization in Hegel led to actualization in Aristotle, which led me to indulge my fascination with the Aristotelian commentary tradition. To the extent that it is possible to generalize about the historic readings discussed in the Greek, Arabic, Hebrew, and Latin commentaries, my own view of Aristotle is quite different on a number of key points, having more in common with some modern readings. Nonetheless, I am enormously impressed by the levels of sophistication shown by very many writers in this tradition.

I just mentioned al-Farabi again. As previously noted, al-Farabi (10th century CE) played a great historic role in the formulation of Arabic (and consequently, Hebrew and Latin) views of Aristotle. The Syrian Christians who did the majority of the translating of Aristotle to Arabic from Syriac had access to most of Aristotle’s works, but publicly only taught from the logical treatises. It was al-Farabi who initiated public teaching of the full range of Aristotelian philosophy in the Islamic world. He flourished during the so-called Islamic golden age, a time of tremendous interest in ancient learning not only by aristocrats but by many literate skilled crafts people. The political climate of the Islamic world at the time was much more embracing of secular learning than it came to be between the 13th and 19th centuries CE.

One unfortunate aspect of al-Farabi’s reading was a very strong privileging of a notion of demonstrative “science” over Aristotle’s own predominant use of dialectic in philosophical development. This was based on a reading of Aristotle’s Posterior Analytics as propounding a model of “science” as a deductive enterprise expected to result in certain knowledge, which is still dominant today, but which I (following a number of modern interpreters) think involves a misreading of the basic aims of Aristotelian demonstration.

The idea that Aristotle was fundamentally concerned to develop “sciences” yielding certain knowledge gave a more dogmatic cast to his whole work, which has been a contributing factor in common negative stereotypes of Aristotle. Many modern commentators who still accept this reading of Posterior Analytics have been puzzled by the huge gap between this and Aristotle’s actual practice throughout his works, which in fact is mainly dialectical. I think a careful reading of the Topics (on dialectic) and Posterior Analytics (on demonstration) with consultation of the Greek text on the originals of some key phrases yields a view that is far more consistent with Aristotle’s actual practice.

Demonstration is a pedagogical way of showing very clear reasons for certain kinds of conclusions. It works by assuming some premises are true, whereas dialectic makes no such assumption. Thus the only necessity that results from demonstration is the “hypothetical” one that if the premises are true, then the conclusion is also true. But the more important point in regard to the classic syllogistic form is that the common “middle term” that allows the major and minor premises to be both formally and materially composed together illuminates why we ought to consider it appropriate to assume the conclusion is true if we believe the premises are true.

Dialectic, as I have said, is cumulative, exploratory discursive reasoning about meanings in the absence of initial certainty. This is how Aristotle mainly approaches things. Dialectic implicitly relies on the same logical form of syllogistic argument explicitly used in demonstration, but Aristotle distinguishes dialectic and demonstration by whether premises are treated as hypotheses to be evaluated, or as hypothetically assumed “truths” to be interpreted.

It is also important to note that in the Latin scholastic tradition, the dogmatic trend resulting from wide acceptance of claims about demonstrative science was significantly mitigated by a strong counter-trend of evenhandedly analyzing arguments pro and con, which effectively revived a form of dialectic. (See also Foundations?; Fortunes of Aristotle; Scholastic Dialectic.)