Proving Too Much

by Scott Alexander2 min read14th Apr 20131 comment


Personal Blog

The fallacy of Proving Too Much is when you challenge an argument because, in addition to proving its intended conclusion, it also proves obviously false conclusions. For example, if someone says “You can’t be an atheist, because it’s impossible to disprove the existence of God”, you can answer “That argument proves too much. If we accept it, we must also accept that you can’t disbelieve in Bigfoot, since it’s impossible to disprove his existence as well.”

I love this tactic so much. I only learned it had a name quite recently, but it’s been my default style of argument for years. It neatly cuts through complicated issues that might otherwise be totally irresolvable.

Because here is a fundamental principle of the Dark Arts – you don’t need an argument that can’t be disproven, only an argument that can’t be disproven in the amount of time your opponent has available.

In a presidential debate, where your opponent has three minutes, that means all you need to do is come up with an argument whose disproof is inferentially distant enough from your audience that it will take your opponent more than three minutes to explain it, or your audience more than three minutes’ worth of mental effort to understand the explanation.

The noncentral fallacy is the easiest way to do this. “Martin Luther King was a criminal!” “Although what you say is technically correct, categories don’t work in the way your statement is impl – ” “Oh, sorry, time’s up.”

But pretty much anything that assumes a classical Aristotelian view of concepts/objects is gold here. The same is true of any deontological rules your audience might be attached to.

I tend to get stuck in the position of having argue against those Dark Artsy tactics pretty often. And the great thing about Proving Too Much is that it can demolish an entire complicated argument based on all sorts of hard-to-tease-apart axioms in a split second. For example, After Virtue gave (though it does not endorse) this example of deontological reasoning:

I cannot will that my mother should have had an abortion when she was pregnant with me, except perhaps if it had been certain that the embryo was dead or gravely damaged. But if I cannot will this in my own case, how can I consistently deny to others the right to life that I claim for myself? I would break the so-called Golden Rule unless I denied that a mother in general has a right to an abortion.

It seemed unfair for me to move on in the book without at least checking whether this argument was correct and I should re-evaluate my pro-choice position. But that would require sorting through all the weird baggage here, like what it means to will something, and whether your obligations to potential people are the same as your obligations to real people, and how to apply the Golden Rule across different levels of potentiality.

Instead I just thought to myself: “Imagine my mother had raped my father, leading to my conception. I cannot will that a policeman had prevented this rape, but I also do not want to enshrine the general principle that policemen in general have no right to prevent rape. Therefore, this argument proves too much.” It took all of five seconds.

Sometimes a quick Proving Too Much can tear apart extremely subtle philosophical arguments that have been debated for centuries. For example, Pascal’s Wager also proves Pascal’s Mugging (they may both be correct, but bringing the Mugging in at least proves ignoring their correctness to be a reasonable and impossible-to-critique life choice). And Anselm’s Ontological Argument seems much less foreboding when you realize it can double as a method for creating jelly donuts on demand.

Interestingly, I think that one of the examples of proving too much on Wikipedia can itself be demolished by a proving too much argument, but I’m not going to say which one it is because I want to see if other people independently come to the same conclusion.