Abstract and Concrete

In contrast to later traditional “metaphysics”, Aristotle recommended we start with the concrete, but then aim to dialectically rise to higher understanding, which is still of the concrete. In any inquiry, we should begin with the things closer to us, but as Wittgenstein said in a different context, we should ultimately aim to kick away the ladder upon which we climbed.

What Aristotle would have us eventually kick away is by no means the concrete itself, but only our preliminary understanding of it as a subject of immediate, simple reference. Beginnings are tentative, not certain. We reach more solid, richer understanding through development.

Aristotle’s discussion of “primary” substance in Categories has often been turned into a claim that individuals are ontologically more primary than form. This is to misunderstand what Categories is talking about. Aristotle explicitly says Categories will be about “things said without combination” [emphasis added], i.e., about what is expressed by kinds of apparently atomic sayings that are used in larger sayings.

The initial definition of substance in the strict or “primary” sense — which he will eventually kick away in the Metaphysics — is of a thing (said) “which is neither said of something underlying nor in something underlying”. (Aristotle often deliberately leaves it open whether he is talking about a referencing word or a referenced thing — or says one and implies the other — because in both cases, the primary concern is the inferential meaning of the reference.)

This initial definition is a negative one that suffices to distinguish substance from the other categories. By implication, it refers to something that is said simply of something, in the way that a proper name is. As examples, he gives (namings of) an individual human, or an individual horse.

“Socrates” would be said simply of Socrates, and would thus “be” — or refer to — a primary substance in this sense. The naming of Socrates is an apparently simple reference to what we might call an object. As Brandom has noted, this picks out a distinctive semantic and inferential role that applies only to references to singular things.

Aristotle then says that more universal namings or named things like “human” and “horse” are also “substances” — i.e., can also refer to singular objects — in a secondary sense, as in “that horse”. Then substance in general is further distinguished, by saying it is something A such that when something else B is said of it, both the naming and the “what-it-is” of B are said of the primary or secondary substance A. (See also Form; Things in Themselves; Definition.)

If a horse as such “is” a mammal of a certain description, then that horse must be a mammal of that description. If a mammal as such “is” warm-blooded, then that horse “is” warm-blooded.

These are neither factual nor ontological claims, but consequences of a rule of interpretation telling us what it means to say these kinds of things. Whether or not something is a substance in this sense is surely a key distinction, for it determines the validity or invalidity of a large class of inferences.

Based on the classification of A as an object reference and B as something said of A, we can make valid inferences about A from B.

When something else C is said of the non-substance B, by contrast, we still have a “naming” of B, but the “what-it-is” or substantive meaning of C does not apply to B itself, but only modifies it, because B is not an object reference. Applying the substantive meaning of C to B — i.e., making inferences about B from the meaning of C — would be invalid in this case.

Just because, say, warm-blooded as such “is” a quality, there is no valid inference that mammals “are” qualities, or that that horse “is” a quality. The concern here is with validity of a certain kind of inference and interpretation, not ontology (or epistemology, either).

In the Metaphysics, the initial referential notion of substance as something underlying is explicitly superseded through a far more elaborate development of “what it was to have been” a thing that emphasizes form, and ultimately actuality and potentiality. The appearance of what might be mistaken for a sort of referential foundationalism is removed. (See also Aristotelian Dialectic.)

I also think he wanted to suggest that practically, a kind of preliminary grasp of some actuality has to come first in understanding. Actuality is always concrete and particular, and said to be more primary. But potentiality too plays an irreducible role, in underwriting the relative persistence of something as the “same” something through change, which motivated the earlier talk about something underlying. The persistence of relatively stable identities of things depends on their counterfactual potentiality, which can only be apprehended in an inferential way. (See also Aristotelian Demonstration.)

It does make sense to say that things like actuality and substance inhere more in the individual than in the species, but that is due to the meanings of actuality and substance, not to an ontological status.

Syllogism

Aristotle invented logic as a discipline, and in Prior Analytics developed a detailed theory of so-called syllogisms to codify deductive reasoning, which also marks the beginning of formalization in logic. Although there actually were interesting developments in the European middle ages with the theory of so-called supposition as a kind of semi-formal semantics, Kant famously said Aristotle had said all there was to say about logic, and this went undisputed until the time of Boole and De Morgan in the mid-19th century. Boole himself said he was only extending Aristotle’s theory.

The fundamental principle of syllogistic reasoning is best understood as a kind of function composition. Aristotle himself did not have the concept of a mathematical function, which we owe mainly to Leibniz, but he clearly used a concept of composition of things we can recognize as function-like. In the late 19th century, Frege pointed out that the logical meaning of grammatical predication in ordinary language can be considered as a kind of function application.

Aristotle’s syllogisms were expressed in natural language, but in order to focus attention on their form, he often substituted letters for concrete terms. The fundamental pattern is

(quantifier A) op B
(quantifier B) op C
Therefore, A op C

where each instance of “quantifier” is either “some” or “all”; each instance of “op” is either what Aristotle called “combination” or “separation”, conventionally represented in natural language by “is” or “is not”; and each letter is a type aka “universal” aka higher-order term. (In the middle ages and later, individuals were treated as a kind of singleton types with implicit universal quantification, so it is common to see examples like “Socrates is a human”, but Aristotle’s own concrete examples never included references to individuals.) Not all combinations of substitutions correspond to valid inferences, but Prior Analytics systematically described all the valid ones.

In traditional interpretations, Aristotle’s use of conventionalized natural language representations sometimes led to analyses of the “op” emphasizing grammatical relations between subjects and predicates. However, Aristotle did not concern himself with grammar, but with the more substantive meaning of (possibly negated) “said of” relations, which actually codify normative material inferences. His logic is thus a fascinating hybrid, in which each canonical proposition represents a normative judgment of a material-inferential relation between types, and then the representations are formally composed together.

The conclusion B of the first material inference, which is also the premise of the second, was traditionally called the “middle term”, the role of which in reasoning through its licensing of composition lies behind all of Hegel’s talk about mediation. The 20th century saw the development of category theory, which explains all mathematical reasoning and formal logic in terms of the composition of “morphisms” or “arrows” corresponding to primitive function- or inference-like things. Aside from many applications in computer science and physics, category theory has also been used to analyze grammar. The historical relation of Aristotle to the Greek grammarians goes in the same direction — Aristotle influenced the grammarians, not the other way around. (See also Searching for a Middle Term; Aristotelian Demonstration; Demonstrative “Science”?)

Aristotelian Causes

I’ve explained each of the four classic Aristotelian “causes” as playing what Brandom would call an expressive role, helping to explain other meaning, and pointed out how different this is from standard modern notions of what I’ve been calling univocal causality. An Aristotelian cause (aitia) is much more like a nonexclusive reason than it is like anything expressed by mechanical metaphors.

There is another very important modern way of thinking about these matters, inspired by Hume’s critique of realism about causes in the modern sense. Hume pointed out that modern-style talk about cause and effect involves a kind of inferential extrapolation from observed regular patterns of succession. Implicitly influenced by this, much work in the sciences relies directly on statistical correlations observed in data from controlled experiments. What particular causes are said to be at work then becomes a matter of optional statistical inference, subject to possible debate.

Then, too, from the side of subject matter, in fields concerned with complex dynamical systems that can only be modeled in a very tentative way — like ecology, economics, and medicine — it has come to be widely recognized that many causes combine to produce the results we see.

Both the statistical approach and what I’m gesturing at as a “complex systems” approach to causality avoid reliance on mechanical metaphors. Neither of these perspectives rules out underdetermination or overdetermination, or the simultaneous presence of both.

Aristotelian “causality” is simultaneously underdetermining and overdetermining. That is to say, in advance it leaves room for varying outcomes, but in hindsight it provides multiple rationales for a given outcome. Its purpose is to provide not certain prediction, but intelligibility and reasonableness.

In principle, nothing would stop us from combining this with statistical or complex-systems views, but these are still very different approaches. The statistical approach is quantitative and relies on counting minimally interpreted facts, where the Aristotelian approach is qualitative and puts the whole emphasis on rational interpretation. The complex-systems view relativizes causes in the modern event-based sense, without making them like any of the Aristotelian ones, none of which corresponds to an event. It is also not interpretive in the sense developed here.

One might consider mathematical-physical law as a kind of formal cause. Statistics and things like dynamic models could be taken as modern, quantitatively oriented descriptions of what I have called material tendencies. (See also Secondary Causes; Form; Aristotelian Matter; Efficient Cause; Ends; Natural Ends; Aristotelian Identity; Aristotelian Demonstration.)

Natural Ends

Early modern science sought to banish consideration of ends from the empirical world, in favor of purely mathematical and factual description. Kant recovered a heuristic use of teleology, especially in biology (see Kant’s Recovery of Ends), and numerous more recent biological researchers have followed suit.

It is relatively easy to see that any kind of desire (say on the part of an animal) is a desire for something that is usually more general than a concrete object that satisfies the desire. More broadly, living things can also plausibly be said to have indwelling tendencies of nutrition and reproduction.

The case of inorganic nature is a bit more challenging for us to understand this way, but where modern science sees abstract mathematical-physical laws in operation, the effect of which may be modified by various circumstances, Aristotle saw concrete material tendencies for things to develop in certain ways, subject to similar modifications. At a certain level of abstraction, observable material tendencies can be viewed as “moving” things in a way broadly analogous to desire. The heavy object “wants” to fall. This just refers back to the observed fact that heavy objects have a tendency to fall, when not impeded by something else. At a level of common-sense interpretation of experience, this does not lead to any false conclusions.

There is no reason why the mathematical-law description and the material-tendency description cannot coexist. The predictive power of mathematically formulated laws makes them invaluable for engineering applications. But for ordinary life, what we are usually interested in are qualitative distinctions that have practical significance.

Thus, in addition to rational ends, there seem to be three kinds or degrees of natural ends or endlike things: ends of desire; primitive vital ends; and endlike tendencies associated with Aristotelian matter of various kinds and descriptions. (See also Ends; Aristotelian Matter.)

Aristotelian Equality

Aristotle explains justice as a kind of proportionality, or equality of relations between people and similar objects of concern. The pseudo-Aristotelian treatise Magna Moralia virtually identifies justice with equality between people, but then disappointingly goes on to say that since, e.g., there is no equality between father and son or master and servant, the concept of a justice between them does not apply. Aristotle himself was careful to point out that empirically existing distinctions between people in the positions of masters and servants do not necessarily reflect inherent ones between people, and this ought to be generalized. Surviving texts do not explicitly put the same caveat on, e.g., existing inequalities between the sexes, but it seems to me the same logic should apply.

It also seems to me that equality of relations between people and similar objects of concern actually implies effective equality between people. A generalized equality between people would have been a highly controversial assertion in Aristotle’s time, and it seems to me he should be commended for implying it, rather than criticized for failing to make it explicit. It is in this spirit that I consider the Kantian emphasis on ethical univerality a welcome addition, complementing rather than conflicting with Aristotle’s highly cultivated sensitivity to the nuances of particular situations.

Theory and Practice

Unlike Plato, Aristotle did not make theoretical knowledge an ethical criterion, although he played a great role in the development of many fields of inquiry. Nonetheless, he placed intellectual “virtue” alongside friendship or love as an essential component of the highest ethical development.

I previously suggested there is an indirect way in which any inquiry can help make us better deliberators. Knowledge can of course help, but only if it is relevant to the question at hand. But the ethical value of inquiry lies more in a kind of theoretical practice than in the particular knowledge that may result. Intellectual virtue, I want to say, has to do especially with practices of free and well-rounded interpretation.

Aristotelian Virtue

Aristotelian ethics is not just about cultivating virtue as a kind of good character. Although he does emphasize it a lot, ultimately character is just a means and a potentiality for actualization of the real goal of that part of living well that is under our power. The actualization itself comes from good practice (praxis), grounded in sound, well-rounded deliberation and choice. Aristotle also says the very best life is that of the philosopher. Not only is philosophy valuable in itself, but it also helps us deliberate.

The best deliberation and choice is supported by intellectual virtues, a concern for justice, and a spirit of friendship or love, but it would not even get off the ground without progress in the classic “moral” virtues, which are all said to pertain to our emotions or passions, and to how we are affected by pleasure and pain. Aristotle characterizes each of these emotional virtues as a kind of mean, or balanced emotional state.

Thus, courage is presented as a mean between rashness and cowardice. Temperance is a mean between self-indulgence and insensibility. Interestingly, justice and prudence are also included among emotional virtues, and subjected to a similar analysis. Other emotional virtues are presented as following the same pattern. Unlike the Stoics, neither Plato nor Aristotle advocated suppressing the emotions.

Auspicious Grafts

Ideas of different philosophers — or interpretations of them — cannot just be arbitrarily combined, but they may turn out to be compatible if there is some common basis, or if they have a different scope of application. My semantic Aristotle has a substantial common basis with Brandom’s Kant and Hegel, which is not too surprising, since my reading of Aristotle has among other things benefited from thinking about Brandom’s work, and at a deeper historical level, independent of Brandom, there is a common basis in guiding notions of reason and rational ethics.

I’ve recently commented on connections between Aristotelian and Hegelian dialectic, and previously on Aristotle’s partial anticipation (in his discussion of friendship) of Hegel’s key notion of mutual recognition. It also seems to me that in a very broad way, something like the idea of Kantian synthesis was implicit in Aristotle, so a fuller account can be treated as a welcome addition. Related to this, Kant’s notion of unity of apperception — particularly with Brandom’s way of reading it as an ethical goal — sounds very good from an Aristotelian point of view concerned with ends. (See also Aristotle and Kant; Hegelian Genealogy; Retrospective Interpretation.)

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.

Aristotelian Demonstration

Demonstration is literally a showing. For Aristotle, its main purpose is associated with learning and teaching, rather than proof. Its real objective is not Stoic or Cartesian certainty “that” something is true, but the clearest possible understanding of the substantive basis for definite conclusions, based on a grasping of reasons.

Aristotle’s main text dealing with demonstration, the Posterior Analytics, is not about epistemology or foundations of knowledge, although it touches on these topics. Rather, it is about the pragmatics of improving our informal semantic understanding by formal means.

For Aristotle, demonstration uses the same logical forms as dialectic, but unlike dialectic — which does not make assumptions ahead of time whether the hypotheses or opinions it examines are true, but focuses on explicating their inferential meaning — demonstration is about showing reasons and reasoning behind definite conclusions. Dialectic is a kind of conditional forward-looking interpretation based on consequences, while demonstration is a kind of backward-looking interpretation based on premises. Because demonstration’s practical purpose has to do with exhibiting the basis for definite conclusions, it necessarily seeks sound premises, or treats its premises as sound, whereas dialectic is indifferent to the soundness of the premises it analyzes in terms of their consequences.

We are said to know something in Aristotle’s stronger sense when we can clearly explain why it is the case, so demonstration is connected with knowledge. This connection has historically led to much misunderstanding. In the Arabic and Latin commentary traditions, demonstration was interpreted as proof. The Posterior Analytics was redeployed as an epistemological model for “science” based on formal deduction, understood as the paradigm for knowledge, while the role of dialectic and practical judgment in Aristotle was greatly downplayed. (See also Demonstrative “Science”?; Searching for a Middle Term; Plato and Aristotle Were Inferentialists; The Epistemic Modesty of Plato and Aristotle; Belief; Foundations?; Brandom on Truth.)