Hermits Rock

Go to content Go to navigation

Negative ≠ Opposite

I seem to have lost most of whatever tact I had and, at the same time, all of my already paltry logical faculties. Yesterday at work, in the middle of my yearly review, I acquiesced that it probably made sense if the vice president didn’t actually read all of everyone’s review. My boss scowled, “If he expects to be aware of everyone who works for him, then he can take the time to read all of these reviews one time a year!” She’s of course right; there’s no defensible reason to make excuses for an administrator’s laziness. Administrators are paid—paid well—not to be lazy. That wasn’t half as bad as the hour I spent today preparing an argument for a mathematician that contested her claim to the biconditionality of Martin Luther King, Jr.‘s claim, “one has a moral responsibility to disobey unjust laws.” I’ll share the ridiculousness of my argument later, but suffice it to say that no matter how hard you try—and I did try very hard—you can’t make a converse, inverse, or contrapositive from a conditional statement with opposites. Negatives, yes; but opposites just confuse the issue. When she pointed this out, I was embarrassed, but not as embarrassed as the time during my first year in graduate school when Dr. Close Reading interrupted me mid-sentence to say, “The example of free indirect discourse you’re presenting today isn’t an example of free indirect discourse.” I couldn’t speak for two days after that.



I promised to embarrass myself, so here you go. The mathematician’s comments are bold and in red:

Here’s how I reason it:

Many more people would simply reject outright any argument that laws should be disobeyed, regardless of the argument’s soundness, or a law’s justness. Right. “Moral responsibility” for them is entirely tied up in legality. In “Letter from a Birmingham Jail,” King was responding to just that argument. (The letter is addressed to several pastors in Birmingham in response to their pleas that he seek justice from the legal side of the law, through the courts and the police. As you say, context matters.) It is an unambiguously logical, but abstract claim he makes in order to affirm that disobedience is necessary to make justice happen. In short, a determination of justice implores (not implies) action. So King writes (I paraphrase):

If a law is unjust, then one has a moral responsibility to disobey it.

And the whole thing rides on the determination that law can be unjust, which, outside the bounds of social justice, is an oxymoronic thing to say. Law can’t be unjust, after all—it’s law; it defines what justice means. King is therefore in a bind because he’s trying to argue affirmatively for something that a lot of people will deny is even possible. Therefore, he must limit the scope and reaffirm the notion that whether or not something is “legal” matters. Thus, the second conditional, the inverse of the first: From here, your logic is in error. The negation having a moral responsibility to disobey a law is NOT having a moral responsibility to disobey a law. This means one does not HAVE to disobey. It doesn’t mean that one MUST obey.

If a law is just, then one has a moral and legal responsibility to obey it. This is not the inverse of the first. The inverse would be, “If a law is just, then one does not have a moral responsibility to disobey it.”

You’re right that the second conditional doesn’t add any truth value to the first; it does, however, prescribe limits to the first by asserting that “legal responsiblity” still has weight in King’s ethics. As with the first statement, justice implores action No, justice here only means one no longer has a responsibility to disobey. This is not the same as having a responsibility to obey. We’re left with a limited claim about when it is right to disobey laws (no, in fact, when it is right to disobey laws has not been addressed at all)—if and only if the law is unjust —assuming that it is biconditional, of course. If it’s biconditional, the contrapositive should also be true:

If one has a moral responsibility to obey a law, then the law is just. The contrapositive of King’s statement is not what you have here, it is, “If one does not have a moral responsibility to disobey a law, then the law is just.” Not having a responsibility to disobey does not mean that one has a responsibility to obey.

Okay… that seems truthful, but it doesn’t make perfect sense—we begin to see the abstractions that King is working with. What, in fact, defines “moral responsibility”? Is “moral responsibility to obey” the definition of justice? No, but you are basing this statement on your incorrect contrapositive. It can be, but it’s not exactly the case. Justice could have its mean outside the bounds of obedience or “moral responsibility”—the idea of fairness, for example, is a mark of justice, but it doesn’t have anything to do with obedience—though it does have something to do with morality. That said, I wouldn’t exactly argue against the truth of the contrapositive, though I do register its difficulty, and I can see how it’s a bit meaningless in terms of everyday action. After all, it’s the basic argument underlying his opponents’ claims that one must obey law because law is just. “We have a moral responsibility, given to us by God, to obey laws,” they said, “Therefore, the laws must be just because we obey them.” In the contrapositive, action defines justice. If King’s claim is truly biconditional, it’s a very complex formulation because not only because of its terms, but also because its biconditionality could be understood to make his argument rather false. No, rather if King would have stated his original statement as a biconditional, “One has a moral responsiblity to disobey a law IF AND ONLY IF it is unjust.” then it would have been entirely clear that the ONLY law one has a responsibility to disobey is an unjust law.

That leaves us with the converse, which should be truthfully equivalent to the inverse:

If one has a moral responsibility to disobey a law, then the law is unjust. Remember, this is the inverse: If a law is just, then one does not have a moral responsibility to disobey it.

Again, action defines justice. No, in fact, action in this case defines injustice. The only time one has the moral responsibility to disobey a law is when it is unjust. The contrapositive of this statement is “If a law is just, then one does not have a moral responsibility to obey it,” which is the same as the inverse of the original statement. I’d argue it’s just as fraught a claim as the contrapositive but the contrapositive is not what you stated, and I’m certain that King would have said it is wholly false. His intent is to locate the moral responsibility outside of the self and to link justice to something greater than law; this statement buries the definition of justice in a decision to disobey. It’s the wrong order for truth to be outed, in other words, and can’t really be worked.

I think what it amounts to is that in “Letter from a Birmingham Jail” King was beating out a path—also beat out before him by other proponents of social justice—of great resistance in part because, if it’s biconditional at all, If it were NOT a biconditional, then there would be just laws which we have a responsibility to disobey. it is oxymoronic—the statement and the contrapositive are both true, but argue opposite sides. King’s intent in his argument isn’t to assert a logical truth and more to assert a moral truth and to identify that is claim is limited, but very powerful. Moreover, the abstractness of his terms makes the logic more difficult.


I’m somewhat muddled here by a lack of context and timeline, and I had a heck of a time figuring out what “biconditionality” means. I’m of the belief that most muddled thinking is tied to muddled writing, although one could make a case for the reverse order being just as true.

In any case, please do not stop speaking or writing. We’d miss you. There are few enough thoughtful voices who write well (and present us with excellent musical clips from YouTube) as it is.

Don’t worry. It’d take more than a minor embarrassment to shut me up.

A statement is biconditional if the truth of a hypothesis depends upon the truth of the thesis. In geometry, it’s usually symbolized by iff (if and only if). The discussion we were having about MLK was primarily about determining whether the truth of the contrapositive (if not x, then not y) was the same as the original statement because when their truth values are equal, then a conditional statement is biconditional. But when I began working through the inverse, converse, and contrapositives, I used opposites (instead of negatives) in the hypothesis.