Right for the Wrong Reasons

One of the few things that I re­ally ap­pre­ci­ate hav­ing en­coun­tered dur­ing my study of philos­o­phy is the Get­tier prob­lem. Paper af­ter pa­per has been pub­lished on this sub­ject, start­ing with Get­tier’s origi­nal “Is Jus­tified True Belief Knowl­edge?” In brief, Get­tier ar­gues that knowl­edge can­not be defined as “jus­tified true be­lief” be­cause there are cases when peo­ple have a jus­tified true be­lief, but their be­lief is jus­tified for the wrong rea­sons.

For in­stance, Get­tier cites the ex­am­ple of two men, Smith and Jones, who are ap­ply­ing for a job. Smith be­lieves that Jones will get the job, be­cause the pres­i­dent of the com­pany told him that Jones would be hired. He also be­lieves that Jones has ten coins in his pocket, be­cause he counted the coins in Jones’s pocket ten min­utes ago (Get­tier does not ex­plain this be­hav­ior). Thus, he forms the be­lief “the per­son who will get the job has ten coins in his pocket.”

Un­be­knownst to Smith, though, he him­self will get the job, and fur­ther he him­self has ten coins in his pocket that he was not aware of—per­haps he put some­one else’s jacket on by mis­take. As a re­sult, Smith’s be­lief that “the per­son who will get the job has ten coins in his pocket” was cor­rect, but only by luck.

While I don’t find the pri­mary pur­pose of Get­tier’s ar­gu­ment par­tic­u­larly in­ter­est­ing or mean­ingful (much less the de­bate it spawned), I do think Get­tier’s pa­per does a very good job of illus­trat­ing the situ­a­tion that I re­fer to as “be­ing right for the wrong rea­sons.” This situ­a­tion has im­por­tant im­pli­ca­tions for pre­dic­tion-mak­ing and hence for the art of ra­tio­nal­ity as a whole.

Sim­ply put, a pre­dic­tion that is right for the wrong rea­sons isn’t ac­tu­ally right from an epistemic per­spec­tive.

If I pre­dict, for in­stance, that I will win a 15-touch fenc­ing bout, im­plic­itly be­liev­ing this will oc­cur when I strike my op­po­nent 15 times be­fore he strikes me 15 times, and I in fact lose four­teen touches in a row, only to win by forfeit when my op­po­nent in­ten­tion­ally strikes me many times in the fi­nal touch and is dis­qual­ified for bru­tal­ity, my pre­dic­tion can­not be said to have been ac­cu­rate.

Where this gets more com­pli­cated is with pre­dic­tions that are right for the wrong rea­sons, but the right rea­sons still ap­ply. Imag­ine the pre­vi­ous ex­am­ple of a fenc­ing bout, ex­cept this time I score 14 touches in a row and then win by forfeit when my op­po­nent flings his mask across the hall in frus­tra­tion and is dis­qual­ified for an offense against sports­man­ship. Tech­ni­cally, my pre­dic­tion is again right for the wrong rea­sons—my vic­tory was not thanks to scor­ing 15 touches, but thanks to my op­po­nent’s poor sports­man­ship and sub­se­quent dis­qual­ifi­ca­tion. How­ever, I likely would have scored 15 touches given the op­por­tu­nity.

In cases like this, it may seem ap­peal­ing to credit my pre­dic­tion as suc­cess­ful, as it would be suc­cess­ful un­der nor­mal con­di­tions. How­ever, I think we per­haps have to re­sist this im­pulse and in­stead sim­ply work on mak­ing more pre­cise pre­dic­tions. If we start cred­it­ing pre­dic­tions that are right for the wrong rea­sons, even if it seems like the “spirit” of the pre­dic­tion is right, this seems to open the door for rely­ing on in­tu­ition and fal­ling into the traps that con­tam­i­nate much of mod­ern philos­o­phy.

What we re­ally need to do in such cases seems to be to break down our claims into more spe­cific pre­dic­tions, split­ting them into mul­ti­ple sub-pre­dic­tions if nec­es­sary. My pre­dic­tion about the out­come of the fenc­ing bout could bet­ter be ex­pressed as mul­ti­ple pre­dic­tions, for in­stance “I will score more points than my op­po­nent” and “I will win the bout.” Some may no­tice that this is similar to the im­plicit jus­tifi­ca­tion be­ing made in the origi­nal pre­dic­tion. This is fit­ting—draw­ing out such im­plicit de­tails is key to mak­ing ac­cu­rate pre­dic­tions. In fact, this ex­am­ple it­self was im­proved by taboo­ing[1] “bet­ter” in the vague ini­tial sen­tence “I will fence bet­ter than my op­po­nent.”

In or­der to make bet­ter pre­dic­tions, we must cast out those pre­dic­tions that are right for the wrong rea­sons. While it may be tempt­ing to award such efforts par­tial credit, this flies against the spirit of the truth. The true skill of car­tog­ra­phy re­quires form­ing both ac­cu­rate and re­pro­ducible maps; luck­ing into ac­cu­racy may be nice, but it speaks ill of the re­pro­ducibil­ity of your meth­ods.

[1] I greatly sug­gest that you make taboo­ing a five-sec­ond skill, and bet­ter still rec­og­niz­ing when you need to ap­ply it to your own pro­cesses. It pays great div­i­dends in terms of pre­cise thought.