Contradiction

Contradiction is a kind of logical judgment of error in things said. It applies when things said are either syntactically or semantically incompatible with one another. To be incompatible is to be incapable of “properly” coexisting in a single context or unity of apperception. Aristotle strongly emphasized this normative aspect of the principle of noncontradiction.

In the syntactic case, the concern is with purely formal rules for the well-formedness of expressions. A syntactic contradiction would be something like “A, and also not-A”, where either A and not-A have both been explicitly said, or both are implied by things that have been said. In this case, we need know nothing at all about the meaning of “A”. We are only concerned with generic rules for the application of logical operators like “and” and “not”.

In the semantic case, contradiction involves the specific meanings of concrete expressions, applied together to some one meant reality. Unlike the syntactic case, background knowledge is essential to judging whether or not meanings can compatibly coexist. We may also think we know the whole story when we don’t. New facts or understandings may change our generalizations and schemas of classification. (See also Interpretation; Error.)

Nothing follows from the principle of noncontradiction alone. Given some inputs, we can judge whether or not they are contradictory — by rigorous analysis in the syntactic case, and up to some level of practical confidence in the semantic case.

Hegel sometimes used the word “contradiction” in an idiosyncratic, highly metonymical or metaphorical way, straining language to the breaking point as part of a larger effort to draw out the complexities and subtleties involved in applying logic to concrete meanings and the real world, when no vocabulary existed for many of the subtleties involved. (See also Three Logical Moments.)

Some people, mainly Marxists, have talked about real-world conflict and social injustice as “contradictions” objectively existing in the world. Conflict and injustice are very real, but it is a misunderstanding of Hegelian dialectic and an inappropriate mixing of levels to associate them directly with contradiction. (See also Contradiction vs Polarity.)

Especially since the mid-20th century, many authors have pointed out common errors and issues associated with too-easy assumptions about identity. (See also Aristotelian Identity.) The Žižekian school has developed a sophisticated variant of the old talk about objective contradictions, by explaining it largely in terms of the issues with identity. If this were just a new metonymical or metaphorical usage in the style of Hegel, we could simply note that “contradiction” is being said in a nonstandard way, and move on. But unfortunately, the Žižekians have gone further, and also claimed that the logical principle of noncontradiction ultimately fails to hold, even though this logical (or illogical) claim is not necessary to address the social concerns that according to them need to be addressed, or to explain the things that according to them need to be explained. (See Split Subject, Contradiction.) We have to be very careful in moving back and forth between very different levels of analysis like this.

Just as on an interpersonal level we can reduce conflict by omitting those too-easy assumptions about identity, omitting those assumptions with respect to things said — and thus making more distinctions — also greatly reduces the potential for logical contradiction.

It is a category mistake to talk about contradiction driving events. Actual change does not result in contradiction either. Different things are true at different times, and the explanation for that is not “contradiction” but change.

Why is this important? The simple answer is that denial of the principle of noncontradiction allows someone to argue absolutely anything, including nonsensical and false things, and to sophistically respond to any refutation by simply introducing more inconsistency. This rejection of responsibility effectively ends the possibility of dialogue.

There ought to be no conflict between social criticism and the possibility of dialogue. Social criticism should be based on shareable, rational analysis. It may be unreasonable to suppose that all social issues can be resolved through dialogue (see Stubborn Refusal), but I do think all those concerned with doing something about those issues ought to be able to resolve their differences through dialogue.

I think Brandom has made an epic contribution in this area by finding a new way to simultaneously affirm — as Aristotle implicitly anticipated long ago — both the world’s recalcitrance to mastery and identity and its fundamentally rational, intelligible character. (See also Self-Evidence?)

Self-Evidence?

Once upon a time, mathematical axioms were considered to be statements of self-evident truth. At least since development of the so-called axiomatic method, however, they have mostly been treated more like stipulative definitions chosen for convenience.

Between the respective times of Aristotle and Kant, allegedly self-evident truths found their way into philosophy. Descartes and others pulled principles like rabbits out of a hat, much as many of the scholastics had done earlier. There was a good deal of sound reasoning based on the dubious establishment of principles, but needless to say, the selection of principles drove the results.

Kant tried very hard to do better, and largely succeeded. In the Transcendental Dialectic section of the Critique of Pure Reason, arguments are examined that do seem to appeal to self-evident truths, but invariably, something is found by Kant himself to be wrong with the arguments.

I’ve previously referred to his antinomies as artificially staged. There, contradictory conclusions are derived from conflicting assumptions about self-evident truth, and Reason itself is apparently blamed for the result. Some commentators have thought that the arguments on the non-creationist side actually seem stronger than those on the creationist side, which raises the possibility that the apparently symmetrical presentation was an exercise in diplomacy on these sensitive matters. On the other hand, a counter-argument could be made that Kant had sympathy for both sides. Regardless, both sides of the antinomies appeal to allegedly self-evident truths, and it is the combination of these premises that leads to contradictory conclusions.

In the introduction to the antinomies, Kant himself says that “every transcendental illusion of pure reason rests on dialectical inferences” (Cambridge edition, p. 459). This seems to invoke either the common early modern pejorative sense of “dialectic” used in denunciations of scholasticism, or an actual Aristotelian distinction between dialectic and demonstration, where they are said to use the same inferential structures, but whereas demonstration aims at showing the reasons behind conclusions that are considered to be true, dialectic particularly examines the inferential consequences of using various premises, without assuming their actual truth. In any case, it seems Reason is found guilty of leading to contradiction when it mistakenly treats dialectical premises as if they were pre-existing truths. There is nothing particularly surprising about that. (See also Kantian Discipline; Dialectical Illusion?)

Split Subject, Contradiction

The Žižekians, referencing Lacan, like to talk about a “split subject” that is noncoincident with itself. In broad terms, I think this is useful. What we call subjectivity is divided, and lacking in strong unity. (See also Pure Negativity?; Acts in Brandom and Žižek.) But it seems to me that if we try to speak carefully about this, we should not then go on using singular articles like “the” or “a”.

I tend to think subjectivity is not just fractured or un-whole, but also actually consists of a complex overlay of different things that we tend to blur together. In particular, it seems clear to me that a common-sense, biographical “self” whose relative unity over time is trackable by relation to the “same” physical body — or by Lockean continuity of memory — is not the same as what we might in a given moment view from a distance as an individualized ethos, or up close as a unity of apperception. This is, I believe, the same distinction that Brandom discusses in terms of sentience and sapience.

Ethos and unity of apperception, and their constituent values and conceptions — the very things that most properly say “I”, and play the functional role of an ethical “subject”, or of a subject of knowledge — are profoundly involved with language, social relations, and what Lacan in his earlier work called the Symbolic and the “Other”. These instances of sapience are pure forms whose identity can only be expressed in terms of sameness of form — nonempirical, but inseparable from a larger ethical world — and simultaneously intimate to us, but by no means strictly “ours”. (See also Self, Subject.)

Where I am still a bit torn is that I also feel that emotions — which I’ve been locating on the former, “self” side — are fundamental to subjectivity as a whole, but I have theoretically separated them from the main locus of transcendental ethical and epistemic subjectivity, even though they play an essential role in making it possible. One logical solution would be to say this just means subjectivity as a whole is more than just ethical and epistemic. Another would be to say that there is a separate kind of emotional subjectivity. I’m not entirely satisfied yet, because I think feeling combines these, but the noncoincidence of our factual selves with our ethical and epistemic being seems very important in understanding how we overcome empirical limitations.

The Žižekians will perhaps remind us that they were not talking about a split between self and subject, but about a split within the subject. I think we habitually overstate the degree of unity and identity we attribute to selves, subjects, and things in general, so I’m fine with that, too. They also want to expand this into a general “ontological” point, which I see as a semantic point.

Perhaps the Žižekians are more comfortable talking about “a” or “the” subject in part due to their doctrine of the ubiquity of contradiction. Todd McGowan in Emancipation After Hegel (2019) nicely distinguishes the Žižekian notion from the old confusion between contradiction and conflict or polarity — and from immediate self-contradiction — but still wants to maintain that the standard logical law of noncontradiction ultimately “refutes itself”, and that Hegel thought this as well. This argument combines a laudable awareness of some of the practical issues with identity, with a logically invalid use of the distinction between explicit and implicit self-contradiction.

Hegel meditated profoundly on the difficulties of applying logic to meaningful content and to real life. He strained language to the breaking point trying to express his conclusions.

On the frontiers of mathematical logic today, the so-called law of identity has been replaced by a requirement to specify identity criteria for each formally defined type, and identity in general has been weakened to isomorphism. (See also Form as a Unique Thing.)

Real-world applications of strong identity typically involve loose “extensional” reference to things assumed to be the same, and a lot of forgetting. The linchpin of old “identity thinking” was inattention to difficulties of formalization from ordinary language — basically an illegitimate moving back and forth between formal and informal domains, resulting in lots of homogenizing confusion of things that ought to be distinct. Weaker, “intensional” assertions about identity as specifiable sameness of form make it the exception rather than the rule. What come first conceptually are distinctions within the manifold, not pre-synthesized things already possessed of identity. Where things are not the same to begin with, contradiction — far from being omnipresent — is not even potentially at issue. (See also Self-Evidence?)

Meanwhile, Sellars and Brandom have revived material inference about meant realities in contrast to formal logic, which deals with purely syntactic relations between presumed extensional “things” with presumed identity. Things Kant and Hegel said about Understanding and Reason can be nicely understood in terms of the relation between syntactic inference about symbolic terms standing for formless extensional “things” and substantive, material inference about the actual form of meant realities. Especially in the reading of Hegel, not having the resource of this distinction available now seems positively crippling.

Finally, Aristotle, who originated the law of noncontradiction as a kind of ethical imperative, and stands in the background to all of Hegel’s discussions of logic, was himself rather cautious and tentative about applying identity to real things, and in his logic was also mainly concerned with (composition of) material inferences, which have more to do with the actual form of things .

Hegel never violated Aristotle’s imperative not to say opposite things about the same thing said in the same way. What he did was to constantly point out the gap between reality and traditional semi-formal logic applied to ordinary language — not to encourage us to reject logic, but rather to refine and sublimate it. (See also Aristotelian and Hegelian Dialectic.)

Contradiction vs Polarity

The simple term “day” does not contradict the simple term “night”, although they may be conventionally treated as polar opposites. If we agree to treat them that way, then the proposition “It is day” contradicts the proposition “It is night”.

Hegel developed idiosyncratic shorthand ways of talking that may have the misleading appearance of suggesting that he ignored this distinction. In popular references to Hegelian dialectic, it is very common to hear about “contradictions” between so-called opposites. This can lead to massive misunderstanding of what Hegel was really trying to say, especially if one does not realize how concerned he was to deconstruct so-called polarities.

Polarities involve pairs of terms related by classical negation. A is the opposite of B if A = not-B, where “not” satisfies not-not-X = X. In fact, Hegel routinely criticized so-called Understanding for taking such polarities at face value.

In another piece of idiosyncratic shorthand, he talked about a “unity of opposites”. This refers to a sort of conceptual interdependence, not identity in the strict sense.

A single term may be taken as shorthand for many judgments characterizing a thing. Then “contradiction” between two terms actually refers to some contradiction between implications of the associated judgments.

Platonic dialectic in its most canonical form considered in turn the implications of pairs of contradictory propositions, in order to canvas all possibilities. The important part was really the examination of implications. Hegel, too, was far more interested in analyzing extended implications of things than in some dance of polarities.

Hegel’s dialectic — like Aristotle’s — is fundamentally about improving the subtlety of our distinctions, and thus the quality of our reasoning. If we begin with a polar opposition, the intent is to supersede it. As I previously noted, the standard method for superseding a polar opposition for Hegel is to move toward the concrete — i.e., to replace the abstract, “infinite”, classical negation of polar opposition with some suitable finite difference or specific material incompatibility or “determinate negation”, as he liked to call it. (See also Aristotelian and Hegelian Dialectic; Three Logical Moments.)