Drowning in a drop of water

Once upon a time, a man drowned in a river, so they put the river on trial.

“It is clear from the evidence,” Outraged Prosecutor declared, “That this river caused the death of this poor man!”

But Clever Defense Attorney was clever. He twirled his black mustache and made direct eye contact with the jury as he smiled, and said: “Let’s approach this rationally and scientifically, shall we?”

The heads of the jury members bobbed in unison: it’s always good to approach things rationally and scientifically!

“I have in my hand a drop of water from that river. Look at this tiny drop of water! Can you provide any evidence that this drop of water has killed this man? Moreover: can you provide any evidence that this drop of water is even capable of killing a man? What an absurd and irrational thing! Of course, a drop of water cannot kill a man. What a ridiculous notion!”

Clever Defense Attorney shuffled in his briefcase, and brought out an eyedropper. “Here I have another drop of water from that river, as well. I put it to you that this drop is also incapable of killing anyone, although….” And here Clever Defense Attorney paused for dramatic effect, and looked wide-eyed and innocently toward the Outraged Prosecutor, “…if Opposing Counsel can provide concrete, factual evidence that this specific drop of water has killed someone, then I will happily concede!”

After a momentary pause, Clever Defense Attorney pressed on in the passionate tones of a gospel preacher. “But of course, he cannot provide such evidence!” His voice ran up and down baritone scales like a mighty church organ, “because no such evidence exists. Ladies and gentlemen of the jury, in a matter of such importance as this, don’t you think it behooves us to base our judgments on concrete, scientific evidence?  And if the prosecuting attorney can provide no concrete, scientific evidence that any single droplet from this river has, itself, caused the death of this man… then surely this entire trial is nothing but a sham! Without evidence, we must acquit this poor, beleaguered river, who is only on trial because the opposing counsel has some kind of academic theory, some kind of post-modern feeling without evidence, that water,” and here he paused just long enough to chuckle softly, “…is actually able to kill people!”



With the rise in popularity of Donald Trump, and the general backlash against “political correctness“, this argument has been on the rise. Speech isn’t harmful. People should be able to say whatever they want, because it’s just speech. Speech can’t actually harm anyone.

Can you provide specific, scientific evidence that anyone has become more racist because they heard something that Trump has said? Can you provide evidence that a particular sexist sentence has actually caused someone to become more sexist?

Of course you can’t. Therefore, speech can’t be harmful.  People should never be criticized for saying whatever they want, because speech can’t make anyone racist or sexist.

Speech clearly cannot influence thoughts or feelings in any way.



I’ve warned of the dangers of a “good argument” before. This argument sounds good because people are bad at thinking about probabilities and continuous variables. People are much better at thinking in black and white: yes or no, true or false, on and off. And it’s easy to lead people along with a plausible story from point A to point B to point C.

The same problem arises when talking about gun control: you can’t prove that any specific gun law could have prevented any specific crime… therefore gun laws can’t prevent crime.

Also with climate change: you can’t prove that any specific storm was caused by any specific greenhouse gas… therefore greenhouse gasses can’t affect the weather.

The lure of this “good story” is so strong that even when it leads to an absurd conclusion– “speech can’t ever change people’s feelings”–some people are tempted to just go with it.

Especially when they can use that conclusion to justify verbally attacking people they don’t like.



This flawed type of reasoning is related to a logical puzzle first highlighted by Henry Kyburg in a 1961 philosophy paper entitled “Conjunctivitis”: Probability and the Logic of Rational Belief. The puzzle, known as the “Lottery Paradox”, goes like this:

In a lottery with 1000 tickets, the probability that the first ticket T1 will lose is 0.999. Since 0.999 is very high, we are justified in believing that ticket T1 will not win. This same statement is true of the second ticket, T2. Therefore, we are justified in thinking that T2 won’t win. If we are justified in thinking that T1 won’t win and we are justified in thinking that T2 won’t win, then we are justified in thinking “Both T1 and T2 will not win”.

However, this holds true for all tickets; therefore, we are justified in believing that no ticket will win… which is clearly false, since we know that one ticket will win.

The paradox is perplexing, because the line of reasoning sounds good. Each individual step of the way, it seems convincing. But even though it is a “good argument”, it has a flaw: you can’t just consider the probability of each ticket winning on its own, and then generalize by grouping each individual conclusion together. You have to consider how each piece of the puzzle works together, and how your belief in one of the outcomes influences the probabilities of all of the others. (For those who are interested, the solution to the “paradox” lies in the application of Bayes’ Theorem.)

In other words, you have to start thinking in terms of conditional probabilities, and continuous measurements of likelihood, rather than just thinking in terms of black and white, yes or no, on or off.

But people are bad at that, which is why things like the “Lottery Paradox” seem so compelling.



There is another reason the argument used against “political correctness” feels compelling: we know instinctively that we should value diversity and should not judge people merely for being different from ourselves. So where does the line get drawn? Do we really fall into the trap of saying that, since we can’t prove that any individual sentence does any harm to society, therefore every speech-act is ultimately the same?

He talks more loudly than I like, but that doesn’t make him a bad person.

He tells dirtier jokes than I like, but that doesn’t make him a bad person.

He insults people who dress poorly more than I would like, but that doesn’t make him a bad person.

He makes demeaning jokes about women more than I would like, but that doesn’t make him a bad person.

He says things like “All Jews should die” more often than I would like, but that doesn’t make him a bad person….


Yes, there is a legitimate gray area. The notion that anyone who ever tells a rape joke is causing rape in America (by “promoting rape culture”) is, in my opinion, wacky and a gross mis-representation of the way causal relationships work in our culture. I don’t think rape jokes are funny, but I don’t think they are exactly destroying society, either.

Even the idea that people shouldn’t be allowed to think (or say) that being gay is a sin is abhorrent to me, simply because I actually want to live in a culture that embraces a diversity of opinions. I don’t mind if people think or say things that I find gross. I simply avoid those people, and go on with my life.

But, at some point along the “free speech” continuum, there is an inflection point. If you pretend that all speech is the same, and that a presidential candidate saying that Muslims are sub-human animals who are destroying civilization is “the same as” you expressing an opinion about your favorite ice cream flavor, then you are just living in a delusion that is divorced from reality.

At some point, you have to realize that when you add enough droplets of water together, it becomes a river that is capable of drowning people.

Drowning in a drop of water