On more than one occasion in the past week alone, I’ve been accused of fallacious reasoning for the use of a reductio ad absurdam. This is a bit of a tricky issue, because a reductio is only useful when someone hasn’t taken into account all of their own premises. What you do is to stress the failings of someone’s premises by taking their argument to an extreme and seeing if they think that it is a reasonable outcome. This is a form of reasoning from final consequences, which is fallacious only if a necessary consequence of the premises is not evaluated for truth before its use to discredit a premise. An example of a fallacious argument from final consequences would be:

If X then Y. Y is an undesirable consequence, therefore not X.

An example of a non-fallacious argument from final consequences would be:

If X then Y, not Y, therefore not X.

The way that I’ve always found reductios useful is in demonstrating that someone has more premises than they actually take account of. For example, in a recent conversation I was told that a certain law would be enforced “regardless of cost”. My response was to ask whether the law should be enforced if the cost were 100% of GDP or 200% of GDP. If the person actually only cared about enforcing this law, the reductio would still serve to illustrate that, but if they also cared about being able to buy cars and food and shelter and healthcare, they would have to take into account the fact that either their premise of “enforcement irrespective of cost” must fail or their premise of “we should be able to buy food and shelter” must fail. The form of the argument is then:

If X then Y. If Z then not Y. Therefore, not X and Z.

Note that the effect is not to say that X is not true, just that both X and Z cannot be true at the same time. It also doesn’t say anything about the truth of Z. It can be true that neither X or Z is true.

Note that this is also not just a way to dash someone’s arguments. It’s also a very useful tool for your own thinking. Take any of your cherished positions and try and bring them to the extreme. “I think free speech should be upheld universally” becomes, “I would kill everyone I loved so to uphold a Nazi’s non-precedential (that is to say that this is a complete one-off) right to call Jews filthy” – maybe you think you would do that, or maybe you would come to the conclusion that free speech doesn’t have the intrinsic value that your premise assumes. And once you know that your premises aren’t consistent in that absurd context, you can walk it back and try and find out where the premises are consistent to try and formulate a new rule that includes only the essential elements of the original premise.

Similar Posts:

• Thinking about logic and information, Part II
• Some terrible arguments about gay marriage
• Initial Thoughts on Rationality in Social Science

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Logic, Logical Discourse by Paul Ganssle