How a reductio ad absurdum does not work

by George J. Dance

Ever heard of Grab World? Matt Bruenig, an attorney who used to troll libertarians on progressive website Demos until he was fired for Twitter trolling, once used the idea of Grab World (a thought experiment invented by libertarian philosopher Roderick Long) to allegedly show how ridiculous the non-aggression principle is. When challenged by some libertarians, who in his words "couldn't handle this," Bruenig wrote a follow-up column on his own blog  "as a learning opportunity to help people understand how the reductio ad absurdum works."

He began by explaining that "A reductio is a type of argument in which you accept a premise and use it to generate a conclusion that strikes people as absurd," and then gave the argument form:

1. If X, then Y.
2. Y is totally absurd.
3. Therefore X is not true.

Next he fleshed out the form with his Grab World example: "the premise was justice requires that we follow the non-aggression principle and the conclusion was people can come into the house you live in and grab up the stuff and you cannot use force to prevent that. So we plug it in.

1. If justice requires that we follow the non-aggression principle, then people can come into the house you live in and grab up the stuff and you cannot use force to prevent that.
2. It is totally absurd to say that 'people can come into the house you live in and grab up the stuff and you cannot use force to prevent that.'
3. Therefore it is not true that justice requires that we follow the non-aggression principle."

Almost every part of Bruenig's explanation is wrong. First, that is not "how the reductio ad absurdum works". His argument form is not even a reductio ad absurdum (RAA). An RAA, or indirect proof, works by positing an assumption (or supposition), and then proving it false by showing logically that it leads to a contradiction.

Second, Bruenig is confused about what premises and conclusions are. The premises in his argument are steps 1 and 2, and the conclusion is step 3. What he calls "the premise" and "the conclusion" are actually called the antecedent and consequent of a conditional. Third, what he calls "the premise" does not "generate" what he calls "the conclusion" - he merely asserts both together, as two halves of one unproven premise (step 1). 

Fourth, the above is not even a valid argument form (although it looks like one: modus tollens, or denying the consequent). It does not logically follow, from "If X, then Y" and "Y is totally absurd," that "X is not true" - all that would follow is "X is totally absurd," whatever Bruenig means by that. (He does not mean what logicians mean by "absurd," being contradictory or logically impossible.) 

Fifth, even if Bruenig's argument were valid, it would not be sound. A sound argument is a valid one with all true premises, which proves that its conclusion is true. There is no reason to think that either of Bruenig's premises is true. Almost every libertarian would deny the truth of his premise 1. Premise 2 looks a bit more plausible, but there is no reason to think it is true, either. (What if the "people [coming] into the house you live in" were bailiffs - or police seizing stolen goods - or even movers?)

In conclusion, let me show how an RAA argument really works:

1. Someone who knows logic would know what a valid argument is, and what the terms premise, conclusion, and reductio ad absurdum mean. (premise; see any logic text)
2. Assume Matt Bruenig is someone who knows logic. (assumption; beginning of RAA)
3. Then Matt Bruenig knows what a valid argument is, and what the terms premise, conclusion, and reductio ad absurdum mean. (1,2 hypothetical syllogism)
4. But Matt Bruenig does not know any of that. (premise; see above)
5. Therefore, Matt Bruenig is not someone who knows logic, (2-4 RAA)

I hope that readers find that argument instructive.

All that Bruenig's argument proves, on the other hand, is that he can pontificate on subjects about which he knows little or nothing: something that readers might find useful to keep in mind when reading his criticisms of libertarianism.