The last post suggests another nuance, having to do with how “total” and “totality” are said in many ways. This is particularly sensitive, because these terms have both genuinely innocent senses and other apparently innocent senses that turn out to implicitly induce evil in the form of a metaphorically “totalitarian” attitude.

Aiming for completeness as a goal is often a good thing.

There is a spectrum of relatively benign errors of over-optimism with respect to where we are in achieving such goals, which at one end begins to shade into a less innocent over-reach, and eventually into claims that are obviously arrogant, or even “totalitarian”.

Actual achievements of completeness are always limited in scope. They are also often somewhat fragile.

I’ll mention the following case mainly for its metaphorical value. Mathematical concepts of completeness are always in some sense domain-specific, and precisely defined. In particular, it is possible to design systems of domain-specific classification that are complete with respect to current “knowledge” or some definite body of such “knowledge”, where knowledge is taken not in a strong philosophical sense, but in some practical sense adequate for certain “real world” operations. The key to using this kind of mathematically complete classification in the real world is including a fallback case for anything that does not fit within the current scheme. Then optionally, the scheme itself can be updated. In less formal contexts, similar strategies can be applied.

There are also limited-scope, somewhat fragile practical achievements of completeness that are neither mathematical nor particularly ethical.

When it comes to ethics, completeness or totality is only something for which we should strive in certain contexts. About this we should be modest and careful.

Different yet again is the arguably trivial “totality” of preconceived wholes like individuals and societies. This is in a way opposite to the mathematical case, which worked by precise definition; here, any definition is implicitly suspended in favor of an assumed reference.

Another kind of implicit whole is a judgment resulting from deliberation. At some point, response to the world dictates that we cut short our in principle indefinitely extensible deliberations, and make a practical judgment call.

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.


It seems to me that the main thing human reason does in real life is to interpret the significance of things. When we think of something, many implicit judgments about it are brought into scope. In a way, Kant already suggested this with his accounts of synthesis.

In real-world human reasoning, the actually operative identity of the things we reason about is not the trivial formal identity of their names or symbols, but rather a complex one constituted by the implications of all the judgments implicitly associated with the things in question. (See also Identity, Isomorphism; Aristotelian Identity.)

This is why people sometimes seem to talk past one another. The same words commonly imply different judgments for different people, so it is to be expected that this leads to different reasoning. That is why Plato recommended dialogue, and why Aristotle devoted so much attention to sorting out different ways in which things are “said”. (See also Aristotelian Semantics.)

I think human reason uses complex material inference (reasoning based on intermediate meaning content rather than syntax) to evaluate meanings and situations in an implicit way that usually ends up looking like simple summary judgment at a conscious level, but is actually far more involved. A great deal goes on, very rapidly and below the level of our awareness. Every surface-level judgment or assertion implicitly depends on many interpretations.

Ever since Aristotle took the first steps toward formalization of logic, people have tended to think of real-world human reasoning in terms modeled straightforwardly on formal or semi-formal logical operations, with meanings of terms either abstracted away or taken for granted. (Aristotle himself did not make this mistake, as noted above.) This fails to take into account the vast amount of implicit interpretive work that gets encapsulated into ordinary terms, by means of their classification into what are effectively types, capturing everything that implicitly may be relevantly said about the things in question in the context of our current unity of apperception.

A typed term for a thing works as shorthand for many judgments about the thing. Conversely, classification and consequent effective identity of the thing depend on those judgments.

As a result of active deliberation, we often refine our preconscious interpretations of things, and sometimes replace them altogether. Deliberation and dialectic are the testing ground of interpretations.

In general, interpretation is an open-ended task. It seems to me that it also involves something like what Kant called free play. (See also Hermeneutics; Theory and Practice; Philosophy; Ethical Reason; The Autonomy of Reason; Foundations?; Aristotelian Demonstration; Brandom on Truth.)


Like definition, classification sometimes gets an unjustified bad name. It is not a kind of truth about the world, but rather plays an expressive role, helping to explain the meaning of what is said. Classification makes it possible to substitute simple names for arbitrarily complex conditions or adverbial expressions, allowing the underlying complexity to be abstracted away, or reconstructed as needed.

In Book 1 of Parts of Animals, Aristotle shows great sophistication about this. He explicitly argues against Plato’s recommended procedure of “division” or repeated application of binary distinctions, noting that many significant real-world distinctions are better approached as n-ary or manifold than as binary.

He also explicitly notes how difficult and arbitrary it ends up being to develop real-world classifications in a strictly hierarchical manner, arguing for a more holistic approach, which cannot be reduced to a sequential application of lower-level operations.

Good real-world classifications are arrived at through dialectical trial, error, and iterative self-correction over time. Conversely, behind every ordinary referential use of simple names for things is a complex implicit dialectical/semantic development. (See also Difference; Aristotelian Identity; Substance; Aristotelian Semantics.)