Arguing “By Definition”

“This plucked chicken has two legs and no feathers—there­fore, by defi­ni­tion, it is a hu­man!”

When peo­ple ar­gue defi­ni­tions, they usu­ally start with some visi­ble, known, or at least widely be­lieved set of char­ac­ter­is­tics; then pull out a dic­tio­nary, and point out that these char­ac­ter­is­tics fit the dic­tio­nary defi­ni­tion; and so con­clude, “There­fore, by defi­ni­tion, athe­ism is a re­li­gion!”

But visi­ble, known, widely be­lieved char­ac­ter­is­tics are rarely the real point of a dis­pute. Just the fact that some­one thinks Socrates’s two legs are ev­i­dent enough to make a good premise for the ar­gu­ment, “There­fore, by defi­ni­tion, Socrates is hu­man!” in­di­cates that bipedal­ism prob­a­bly isn’t re­ally what’s at stake—or the listener would re­ply, “Whad­daya mean Socrates is bipedal? That’s what we’re ar­gu­ing about in the first place!”

Now there is an im­por­tant sense in which we can le­gi­t­i­mately move from ev­i­dent char­ac­ter­is­tics to not-so-ev­i­dent ones. You can, le­gi­t­i­mately, see that Socrates is hu­man-shaped, and pre­dict his vuln­er­a­bil­ity to hem­lock. But this prob­a­bil­is­tic in­fer­ence does not rely on dic­tio­nary defi­ni­tions or com­mon us­age; it re­lies on the uni­verse con­tain­ing em­piri­cal clusters of similar things.

This cluster struc­ture is not go­ing to change de­pend­ing on how you define your words. Even if you look up the dic­tio­nary defi­ni­tion of “hu­man” and it says “all feather­less bipeds ex­cept Socrates”, that isn’t go­ing to change the ac­tual de­gree to which Socrates is similar to the rest of us feather­less bipeds.

When you are ar­gu­ing cor­rectly from cluster struc­ture, you’ll say some­thing like, “Socrates has two arms, two feet, a nose and tongue, speaks fluent Greek, uses tools, and in ev­ery as­pect I’ve been able to ob­serve him, seems to have ev­ery ma­jor and minor prop­erty that char­ac­ter­izes Homo sapi­ens; so I’m go­ing to guess that he has hu­man DNA, hu­man bio­chem­istry, and is vuln­er­a­ble to hem­lock just like all other Homo sapi­ens in whom hem­lock has been clini­cally tested for lethal­ity.”

And sup­pose I re­ply, “But I saw Socrates out in the fields with some her­bol­o­gists; I think they were try­ing to pre­pare an an­ti­dote. There­fore I don’t ex­pect Socrates to keel over af­ter he drinks the hem­lock—he will be an ex­cep­tion to the gen­eral be­hav­ior of ob­jects in his cluster: they did not take an an­ti­dote, and he did.”

Now there’s not much point in ar­gu­ing over whether Socrates is “hu­man” or not. The con­ver­sa­tion has to move to a more de­tailed level, poke around in­side the de­tails that make up the “hu­man” cat­e­gory—talk about hu­man bio­chem­istry, and speci­fi­cally, the neu­ro­toxic effects of coniine.

If you go on in­sist­ing, “But Socrates is a hu­man and hu­mans, by defi­ni­tion, are mor­tal!” then what you’re re­ally try­ing to do is blur out ev­ery­thing you know about Socrates ex­cept the fact of his hu­man­ity—in­sist that the only cor­rect pre­dic­tion is the one you would make if you knew noth­ing about Socrates ex­cept that he was hu­man.

Which is like in­sist­ing that a coin is 50% likely to be show­ing heads or tails, be­cause it is a “fair coin”, af­ter you’ve ac­tu­ally looked at the coin and it’s show­ing heads. It’s like in­sist­ing that Frodo has ten fingers, be­cause most hob­bits have ten fingers, af­ter you’ve already looked at his hands and seen nine fingers. Nat­u­rally this is ille­gal un­der Bayesian prob­a­bil­ity the­ory: You can’t just re­fuse to con­di­tion on new ev­i­dence.

And you can’t just keep one cat­e­go­riza­tion and make es­ti­mates based on that, while de­liber­ately throw­ing out ev­ery­thing else you know.

Not ev­ery piece of new ev­i­dence makes a sig­nifi­cant differ­ence, of course. If I see that Socrates has nine fingers, this isn’t go­ing to no­tice­ably change my es­ti­mate of his vuln­er­a­bil­ity to hem­lock, be­cause I’ll ex­pect that the way Socrates lost his finger didn’t change the rest of his bio­chem­istry. And this is true, whether or not the dic­tio­nary’s defi­ni­tion says that hu­man be­ings have ten fingers. The le­gal in­fer­ence is based on the cluster struc­ture of the en­vi­ron­ment, and the causal struc­ture of biol­ogy; not what the dic­tio­nary ed­i­tor writes down, nor even “com­mon us­age”.

Now or­di­nar­ily, when you’re do­ing this right—in a le­gi­t­i­mate way—you just say, “The coniine alkaloid found in hem­lock pro­duces mus­cu­lar paral­y­sis in hu­mans, re­sult­ing in death by as­phyx­i­a­tion.” Or more sim­ply, “Hu­mans are vuln­er­a­ble to hem­lock.” That’s how it’s usu­ally said in a le­gi­t­i­mate ar­gu­ment.

When would some­one feel the need to strengthen the ar­gu­ment with the em­phatic phrase “by defi­ni­tion”? (I.e. “Hu­mans are vuln­er­a­ble to hem­lock by defi­ni­tion!”) Why, when the in­ferred char­ac­ter­is­tic has been called into doubt—Socrates has been seen con­sult­ing her­bol­o­gists—and so the speaker feels the need to tighten the vise of logic.

So when you see “by defi­ni­tion” used like this, it usu­ally means: “For­get what you’ve heard about Socrates con­sult­ing her­bol­o­gists—hu­mans, by defi­ni­tion, are mor­tal!”

Peo­ple feel the need to squeeze the ar­gu­ment onto a sin­gle course by say­ing “Any P, by defi­ni­tion, has prop­erty Q!”, on ex­actly those oc­ca­sions when they see, and pre­fer to dis­miss out of hand, ad­di­tional ar­gu­ments that call into doubt the de­fault in­fer­ence based on clus­ter­ing.

So too with the ar­gu­ment “X, by defi­ni­tion, is a Y!” E.g., “Athe­ists be­lieve that God doesn’t ex­ist; there­fore athe­ists have be­liefs about God, be­cause a nega­tive be­lief is still a be­lief; there­fore athe­ism as­serts an­swers to the­olog­i­cal ques­tions; there­fore athe­ism is, by defi­ni­tion, a re­li­gion.”

You wouldn’t feel the need to say, “Hin­duism, by defi­ni­tion, is a re­li­gion!” be­cause, well, of course Hin­duism is a re­li­gion. It’s not just a re­li­gion “by defi­ni­tion”, it’s, like, an ac­tual re­li­gion.

Athe­ism does not re­sem­ble the cen­tral mem­bers of the “re­li­gion” cluster, so if it wasn’t for the fact that athe­ism is a re­li­gion by defi­ni­tion, you might go around think­ing that athe­ism wasn’t a re­li­gion. That’s why you’ve got to crush all op­po­si­tion by point­ing out that “Athe­ism is a re­li­gion” is true by defi­ni­tion, be­cause it isn’t true any other way.

Which is to say: Peo­ple in­sist that “X, by defi­ni­tion, is a Y!” on those oc­ca­sions when they’re try­ing to sneak in a con­no­ta­tion of Y that isn’t di­rectly in the defi­ni­tion, and X doesn’t look all that much like other mem­bers of the Y cluster.

Over the last thir­teen years I’ve been keep­ing track of how of­ten this phrase is used cor­rectly ver­sus in­cor­rectly—though not with literal statis­tics, I fear. But eye­bal­ling sug­gests that us­ing the phrase by defi­ni­tion, any­where out­side of math, is among the most alarm­ing sig­nals of flawed ar­gu­ment I’ve ever found. It’s right up there with “Hitler”, “God”, “ab­solutely cer­tain” and “can’t prove that”.

This heuris­tic of failure is not perfect—the first time I ever spot­ted a cor­rect us­age out­side of math, it was by Richard Feyn­man; and since then I’ve spot­ted more. But you’re prob­a­bly bet­ter off just delet­ing the phrase “by defi­ni­tion” from your vo­cab­u­lary—and always on any oc­ca­sion where you might be tempted to say it in ital­ics or fol­lowed with an ex­cla­ma­tion mark. That’s a bad idea by defi­ni­tion!