Check Your Work — Philosophy Edition

Recently, many people have been stirred up by the notoriously sexy blogger Bentham’s Bulldog’s arguments for fanaticism and Pascal’s Wager. Many have written posts denouncing the use of Expected Value and/or Fanaticism, proposing instead that we ditch the project completely given these unintuitive results, or arguing that EV is something that is often ‘abused’ by people in contexts where it is not appropriate. Indeed, it often gets pointed out that EV is just an average over prospects, and lots of alternative theories exist, like using medians.

There is, however, a problem with these responses. And it is a problem that I see recurring in lots of debates about unintuitive theories (utilitarianism, the Repugnant Conclusion, consequentialism vs deontology, etc.). This post is about that problem.

The problem is this: these wacky theories have very-hard-to-avoid arguments in their favor. Let’s take EV-maxxing as an example. If fanatics like myself simply followed EV-maxxing because it is a nice way of “mathematizing” making choices, and because it has the guise of rationality because it is nice and “formal,” the arguments against EV-maxxing in these posts would be very convincing. Indeed, there are lots of formal alternatives to EV-maxxing. And, indeed, EV-maxxing has various unintuitive implications. It seems1 to be indifferent between a 1% chance of 100 billion dollars and a 100% chance of a billion dollars, whereas most of us are actually pretty risk averse and would strongly prefer the certainty of a billion dollars.

But it does not suffice to simply point out that some theory T has unintuitive results and that we can imagine alternatives. No, my friend. Unfortunately, we have to do one final step: we have to compare what the unintuitive results are of the alternative options. Theory T might have certain unintuitive results. But if all the alternative theories A, B, and C imply significantly more absurd things, then you should not reject T. Indeed, if A, B, and C, all imply that, say, 1+1=3, you should very probably believe T — even if you were right that T implies that I should harvest the organs of one person to save 5 others.

I call this “checking your work”. You can’t just point to some unintuitive result of a theory, and then construct an alternative. You must also check your work: does your theory involve significantly more absurd results than the original theory you were rejecting? If so, back to the drawing board you go.

This last step — checking your work — might seem obvious when put this way. But it is amazing to me how often it gets ignored in philosophy. In fact, this is astonishing because one of the ways philosophers and economists and mathematicians argue for various views is by showing that, if you reject the view, it strictly follows that any alternative theory must have absurd implications (in mathematics we have the strongest version of this argument: mathematicians can show you that if you reject their lemma, you have to give up the principle of non-contradiction).

Let me show you what I mean.

Expected Value/Fanaticism

It is easy to dunk on fanaticism. It recommends taking seriously tiny probabilities and doing crazy things like taking a 0.000001% chance of saving googolplex lives rather than saving 10 people’s lives for certain. People will often point out these ridiculous results of EV-maxxing, dunk on it, and then either end the post there or propose some alternative theory.

But here’s the problem. You have to check your work. What does your alternative theory imply? As it turns out, the arguments for fanaticism show that any alternative must recommend lots of super crazy things. If you’re a non-fanatic, you may have to believe:

• It is rationally required/permissible to lose all of my money for 0 gains (money pump arguments); AND

• It is better to take an N chance of positive utility, rather than an (N minus 0.000000000000000000000000000000000000000000000000000000000000001) chance of trillions of times as many utility ; or else transitivity is false; AND

• To figure out how I should act, I should figure out how well off the ancient Egyptians were;

• …

Yikes. Multiple super-crazy implications, for any alternative? Those alternatives aren’t looking so good now that we checked our work…

Of course, you should look into the proofs of why ~(Fanaticism) implies these propositions and various others (I’ve admittedly oversimplified a bit and there’s more nuance/other assumptions that could be rejected in some of those proofs). But that’s my point: check your work! Don’t just point out how unintuitive EV-maxxing is and then walk away. Stand up, show us your theory, and explain to us why getting money pumped is okay. Good luck! Of course, I don’t want to act like there aren’t rational, reasonable, and highly respectable ways of doing this. Very smart philosophers have attempted to do so. But once you start trying to explain all that away…you see how unbelievably difficult it is, and how comparatively easy life is as an EV-maxxer. There are a few weird things, but gosh they don’t seem nearly as unintuitive as those results.

I should add that it is also easy to check your work in this domain. People have already spelled out, in painstaking detail, what non-fanaticism will imply. You have the work already done for you! Just tell us which premises you deny, and why, or else tell us why the conclusion is acceptable.

This pattern of not checking one’s work — of simply pointing out the unintuitive features of one theory, and not checking to make sure that denying it doesn’t lead to even more unintuitive results — pervades a whole lot of Substack discourse.

Population ethics is probably the best example of this. The Repugnant Conclusion sounds crazy, and it is easy to dunk on additive theories of well-being. But, check your work. Population ethics is filled with impossibility theorems: if you reject the Repugnant Conclusion, you’re going to be faced with loads of unintuitive implications. Please, assess these for us, and explain why they are more acceptable than the RC. To be clear — I do reject the RC, and try to grapple with those unintuitive results here. But boy is it hard, and as a result, I still put quite a bit of stock in the RC being true. It’s a very reasonable view to have, once you’ve checked your work.

Similarly, people love dunking on utilitarianism and consequentialism. But they rarely ever grapple with the fact that rejecting those theories implies very weird results about what you should hope to be the case, or that you should act against how everyone would want you to act. Deontology, nebulous rights-talk, and rejecting “cold, calculating utilitarianism,” all sounds nice and obvious…until one checks one’s work and tries to grapple with these bizarre results of deontology. Again, I’m not saying that it would be irrational to be a deontologist. Of course it is! But I am merely noting that, upon checking one’s work, one starts seeing why utilitarianism is so plausible.

A similar pattern afflicted the discourse around Flo’s argument for sacrificing a human for many shrimp. Easy to shriek at the conclusion. Hard to explain away the implications of the alternative views of aggregation.

My point here isn’t actually to defend Fanaticism, EV, Utilitarianism, Consequentialism, Shrimp Welfare, or whatever else. My point is: in philosophy we cannot merely shriek at theories and propose alternatives. We must check our work, and when someone shows that alternatives to some view face some implication, you must engage with that fact if you want to argue that your alternative is better.