The Obverse

This post is part of a four-part series on logical reversal. The truth may lie on the other side or in the other direction, but there is more than one way to reverse a sentence: obverting, converting, inverting, and contraposing are four ways.

sigmundfreud

Two Jews meet in a railway carriage at a station in Galicia. “Where are you going?” asks one. “To Cracow,” replies the other. “What a liar you are!” objects the first. “If you say you’re going to Cracow, you want me to believe you’re going to Lemberg. But I know that in fact you’re going to Cracow. So why are you lying to me?”

The Obverse

Obversion is an operation from traditional logic where “No one is perfect,” for example, turns into the equivalent “Everyone is imperfect.” Or “Many young people are unemployed this summer” becomes the equivalent “Many young people aren’t employed this summer.”

It isn’t difficult to form the obverse. (Obversely, it’s easy.) Keep the subject and keep its (universal or particular) “quantity,” but reverse the (affirmative or negative) “quality” and change the predicate to its complement.

Two negations make an affirmation, so the double reversal involved in obversion makes the statement and its obverse “equivalent,” or the obverse an “immediate inference” from the statement. But obversion is no banal reiteration when the choice of a suitable complement isn’t as trivial as difficult/easy, unemployed/employed or perfect/imperfect. When you say what something isn’t, it isn’t always easy to say what it is: properly obverting a sentence can be an interesting exercise in exegesis.

Slavoj Žižek, for example, following Emmanuel Levinas, explains the equivalence of two Biblical principles: “The Jewish commandment which prohibits images of God is the obverse of the statement that relating to one’s neighbour is the only terrain of religious practice” (the Neighbour, 141). But how are these two principles related, let alone equivalent?

The exegetical question is, if a commandment disallows a religious relationship to God through worship or service of graven images, what is its positive content? What is the non-idolatrous religious relationship that it indicates only negatively?

Žižek points out that Levinas’ obversion of the anti-idolatry commandment amounts to the substitution of one obverse for another. That is, he refuses to obvert “Do not practise religion by relating to a graven image of God” into “Practice religion by relating to a divinely transcedent being beyond any such image in reality.” Levinas completely eschews such Gnostic experience, or “contact with the Irrational.” Instead, he obverts the original injunction differently, turning “Do not practise religion by relating to a graven image of God” into “Practise religion by relating to your neighbour here and now.” In his rigorously developed account of the ethical experience, Levinas describes an encounter with a command both transcendent, such that no being (and far less any image of a being) reaches its height, and immediate, such that no reality (and far less any supernatural realm) approaches its closeness. In the ethical experience, Levinas finds the proper non-idolatrous relationship to God as glimpsed in the face of the Other, God whose infinity cannot be understood as being.

To return to the logical point in this example of Biblical exegesis, the meaning of the statement depended entirely on its obverse. The statement and its obverse are equivalent, but only after the truth of the statement is revealed by obverting it in the right way.

As with Biblical exegesis, the same goes with critical media analysis. If we’re being told X, what are we not being told? The obverse is the question.

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