Contradiction and Nonmonotonicity

In standard formal logic, even one pair of contradictory assertions is traditionally deemed to make any possible conclusion vacuously derivable. Ex falso quodlibet, as the scholastics used to say — from a contradiction, anything at all follows. Meaning is thus destroyed.

As an alternative to this, Hegel in the 19th century anticipated what 20th and 21st century logicians and artificial intelligence researchers have called “nonmonotonic” reasoning. In a nonmonotonic setting, a contradiction only invalidates what is contradictorily asserted. Something must still be wrong with one of the contradictory assertions, but the damage does not spread arbitrarily.

“[W]hat is self-contradictory does not resolve itself into a nullity, into abstract nothingness, but essentially only into the negation of its particular content; … such a negation is not just negation, but is the negation of the determined fact…, and is therefore determinate negation ” (Science of Logic, di Giovanni trans., introduction, p. 33, emphasis in original).

Robert Brandom has pointed out that material inference — the kind of reasoning based on meaning that most humans really rely on most of the time — has this nonmonotonic character:

“Gil Harman sharpens the point in his argument that there is no such thing as rules of deductive reasoning. If there were, presumably a paradigmatic one would be: If you believe p and you believe if p then q, then you should believe q. But that would be a terrible rule. You might have much better reasons against q than you have for either of the premises. In that case, you should give up one of them. He concludes that we should distinguish relations of implication, from activities of inferring. The fact that p, if p then q, and not-q are incompatible, because p and if p then q stand in the implication relation to q, normatively constrains our reasoning activity, but does not by itself determine what it is correct or incorrect to do” (Brandom, Reasons: Three Essays on their Logic, Pragmatics, and Semantics, pp. 4-5).

“Monotonicity… is not a plausible constraint on material consequence relations. It requires that if an implication (or incompatibility) holds, then it holds no matter what additional auxiliary hypotheses are added to the premise-set. But outside of mathematics, almost all our actual reasoning is defeasible. This is true in everyday reasoning by auto mechanics and on computer help lines, in courts of law, and in medical diagnosis. (Indeed, the defeasibility of medical diagnoses forms the basis of the plots of every episode of House you have ever seen — besides all those you haven’t.) It is true of subjunctive reasoning generally. If I were to strike this dry, well-made match, it would light. But not if it is in a very strong magnetic field. Unless, additionally, it were in a Faraday cage, in which case it would light. But not if the room were evacuated of oxygen. And so on” (p. 6).

Defeasible

“Defeasible” (i.e., defeatable) is a legal term metaphorically used by Brandom for anything provisionally affirmed or accepted. The great majority of things we affirm or accept fall into this category.

Brandom applies a legal model of due process to ethical negotiation. We start with presumptions of innocence and good faith. This means that until a cause for reasonable doubt is shown, we act on the assumption that people have good reasons for what they say and for what they want; but anything can be challenged. (See also Things Said; Dialogue; Assumptions; Reasons; Desire, Coherence; Commitment; Mutual Recognition; Scorekeeping.)

In general, I strongly believe that ethics should drive law and not the other way around, but I would argue that the broad notion of due process actually is a good example of ethics driving law, as it should.

Beyond Subject-Object

Hegel famously wanted to move beyond the subject-object dichotomy he saw as typical of early modernity. In practical terms, Kant’s most famous concern to avoid “dogmatic” assumptions about direct possession of epistemic objects had seemed to accentuate the separation of subject and object, by focusing on the distinction between appearance and reality. But both Kant and Hegel wanted to assert the possibility of knowledge in a strong sense, while avoiding what Kant called dogmatism. They also had considerable common ground in a shared rejection of naive early modern notions of subjects and objects and their relations.

Kant had begun — seemingly unwittingly — to recover some neglected Aristotelian insights in these areas, and Hegel made this an explicit theme. Thus they both already questioned the dichotomous interpretation of subject-object relations. Kant had also already highlighted the inevitable involvement of concepts in experience. For Kant, there is no direct epistemic access to real-world objects, or things in themselves (or to our own subjectivity). All knowledge proceeds by way of concepts, but he retains the concept of objects (and subjects) as a sort of placeholders for new distinctions between appearance and reality that can always be wrapped around current concepts in a new iteration.

When dichotomous connotations have already been applied to a distinction in some communicative context, it can be tricky to simultaneously clarify the transcendence of the dichotomy and the preservation of the underlying distinction, but the general solution is not far to find — just ensure that the underlying distinction is expressed in terms of some finite relation, rather than A versus not-A. Then we have Hegelian determinate negation or Aristotelian difference between the terms, rather than classical negation. So in effect, the solution lies in recognizing that the previous understanding of the distinction in terms of dichotomy was wrong in the first place.

More positively, Hegel eliminates dichotomies by putting determinate relations, coherence, and mediation first in the order of explanation, before all particular terms. The Hegelian Absolute — or that which transcends the subject-object dichotomy — is just a handle for perspectives that put processes, relations, coherence, and mediation before any preconceived notion of the conceptual content of particular terms.

I think Hegel saw this sort of structure as common to Aristotelian substance or “what it was to have been” a thing on the one hand, and Kantian subjectivity or synthesis of apperception on the other.

Working in the Hegelian Absolute does not require epistemic super powers or specious Cartesian certainty, just a sustained honest effort that is still implicitly defeasible. Hegel intends the Absolute to be a kind of Aristotelian achievable perfection, not a kind of omniscience or theological perfection that could never be legitimately claimed by a rational animal. (See Substance Also Subject.)

In approaching these matters in A Spirit of Trust, Brandom characteristically focuses not directly on higher-order abstractions, but on their implications for what we do with ordinary concepts in ordinary experience. Like Aristotle and Hegel but following a distinct strategy of his own, Brandom avoids the impasse of a supposed transition from psychological to “metaphysical” terms, or from ordinary experience to something that would seemingly have to be like the mind of God, by clarifying what we implicitly mean by concepts in the first place.

With Aristotle, Hegel, and Frege and in contradistinction to the empiricist tradition, Brandom understands concepts and apperception in a nonpsychological, nonrepresentational, normative-pragmatic, inferential-semantic way. Through the discovery of counterfactually robust relations, concepts evolve toward increasing universality. Through the experience of error, synthesis of apperception comes to incorporate the recognition that not only its commitments but also its concepts are always in principle provisional, subject to reformulation when faced with a new case. Through both of these combined with the additional cross-checks provided by mutual recognition, synthesis moves toward increasing objectivity and what might be called contact with reality. Through Brandom’s “expansive” model of responsibility, the last remaining obstacle to a full resolution of subject-object separation — the lack of a normative interpretation of unintended consequences of actions — is removed.

Neither “subjects” nor “objects” as such are very prominent in an account of this sort. It is much more a story about processes, relations, coherence, and mediation. Aristotle, Hegel, and Brandom each develop their own ways of working that start in the middle, as it were, and do not need reified subjects and objects to begin with. This, again, is just what the Hegelian Absolute is — a name for the sort of perspective that emphasizes the in-principle provisional character of all finite concepts, as contrasted with the more directly practical sort of perspective that provisionally works with the current basis as a source of reasons for particular sayings and doings. (See also Aristotelian and Hegelian Dialectic; Contradiction vs Polarity; Three Logical Moments.)