### Grant McDermott

Assistant Professor
Dept. of Economics
University of Oregon

# The limits of reductio ad absurdum

Unlearning Econ has a new post up on Milton Friedman in which he, among other things, criticises Friedman's use of reductio ad absurdum arguments to win debates. I have a number of reservations about the use of reductio ad absurdum in the social sciences myself, and this seems as good a time as any to write them up. (I'll refrain here from commenting on UE's direct criticisms of Friedman.)

Reductio ad absurdum (RAA) is a reasoning technique where a set of hypotheses are shown to result in absurd or untenable situations if taken to their full logical conclusion(s). An invaluable tool in much of mathematics and pure logic $$-$$ where it is really a form of proof by contradiction $$-$$ I'm less convinced of RAA's usefulness in human affairs.

Interestingly, RAA appears particularly popular with groups on the extreme ends of the ideological spectrum. To the best of my knowledge, for instance, anarcho-capitalists base much of their belief system on some form of RAA reasoning or another (abetted perhaps with an appeal to natural rights $$-$$ a rather dubious concept to my mind). However, absolutist or deontological reasoning can take you to some pretty uncomfortable places very quickly. Even perfectly sound concepts are not immune to being overwhelmed by RAA-type arguments.

Consider that fundamental pillar of any market-based economy: property rights. It's hard to imagine that any prosperous and vibrant society could be sustained for long in the absence of property rights. However, a property rights regime doesn't fare particularly well under the scrutiny of RAA reasoning. For one thing, it implies that we should hold the wishes of the property owner as sacrosanct. I can then easily hypothesize a situation where the productive activities of the world are dramatically constrained by a small group of individuals who refuse to compromise on any violations of their own property. For example, here's an older post that considers the case of climate change and a group of radical environmentalists whose love for nature is not for sale. I think that my conclusion remains valid:
Libertarians that slavishly hold personal property rights above all else would inadvertently open the way for eco-fundamentalists to enjoin virtually all industrial activity. In doing so, they would threaten to form an unholy coalition that makes it impossible for society to react to an immensely complex problem [i.e. climate change] in any sensible way. They would, in effect, become Baptists and Bootleggers for the 21st century.
Another example of dubious RAA reasoning that I encountered recently was on the subject of gay marriage. One of the conservative discussants in our group cautioned that if men (or women) were allowed to marry other men (women), then what grounds did we have to stop someone from marrying a tree or their dog? Leaving aside the problems of mutual consent $$-$$ how does Fido feel about this? $$-$$ the problem here is that this remorseless logic applies equally to marriage between a man and woman! If John and Judy are allowed tie the knot, then why can't Ken take his vows with that splendid bougainvillea over there? The point here is that sometimes you can't salvage an argument by logical reasoning alone, especially where social institutions and ethics are concerned. The boundaries that we place on things may be arbitrary in the scheme of things, but that doesn't make them senseless. I am also comforted by the fact that social norms evolve over time, even if the pace on certain subjects like gay marriage is unacceptably slow.

THOUGHT FOR THE DAY: Be cautious of arguments that are "won" by reductio ad absurdum. Very few things in our social and moral landscape are black and white, so that even the soundest concepts may not survive the absurdity of being taken to their full conclusions.