Belief in Belief

Carl Sa­gan once told a parable of some­one who comes to us and claims: “There is a dragon in my garage.” Fas­ci­nat­ing! We re­ply that we wish to see this dragon—let us set out at once for the garage! “But wait,” the claimant says to us, “it is an in­visi­ble dragon.”

Now as Sa­gan points out, this doesn’t make the hy­poth­e­sis un­falsifi­able. Per­haps we go to the claimant’s garage, and al­though we see no dragon, we hear heavy breath­ing from no visi­ble source; foot­prints mys­te­ri­ously ap­pear on the ground; and in­stru­ments show that some­thing in the garage is con­sum­ing oxy­gen and breath­ing out car­bon diox­ide.

But now sup­pose that we say to the claimant, “Okay, we’ll visit the garage and see if we can hear heavy breath­ing,” and the claimant quickly says no, it’s an inaudible dragon. We pro­pose to mea­sure car­bon diox­ide in the air, and the claimant says the dragon does not breathe. We pro­pose to toss a bag of flour into the air to see if it out­lines an in­visi­ble dragon, and the claimant im­me­di­ately says, “The dragon is per­me­able to flour.”

Carl Sa­gan used this parable to illus­trate the clas­sic moral that poor hy­pothe­ses need to do fast foot­work to avoid falsifi­ca­tion. But I tell this parable to make a differ­ent point: The claimant must have an ac­cu­rate model of the situ­a­tion some­where in their mind, be­cause they can an­ti­ci­pate, in ad­vance, ex­actly which ex­per­i­men­tal re­sults they’ll need to ex­cuse.

Some philoso­phers have been much con­fused by such sce­nar­ios, ask­ing, “Does the claimant re­ally be­lieve there’s a dragon pre­sent, or not?” As if the hu­man brain only had enough disk space to rep­re­sent one be­lief at a time! Real minds are more tan­gled than that. There are differ­ent types of be­lief; not all be­liefs are di­rect an­ti­ci­pa­tions. The claimant clearly does not an­ti­ci­pate see­ing any­thing un­usual upon open­ing the garage door. Other­wise they wouldn’t make ad­vance ex­cuses. It may also be that the claimant’s pool of propo­si­tional be­liefs con­tains the free-float­ing state­ment There is a dragon in my garage. It may seem, to a ra­tio­nal­ist, that these two be­liefs should col­lide and con­flict even though they are of differ­ent types. Yet it is a phys­i­cal fact that you can write “The sky is green!” next to a pic­ture of a blue sky with­out the pa­per burst­ing into flames.

The ra­tio­nal­ist virtue of em­piri­cism is sup­posed to pre­vent us from mak­ing this class of mis­take. We’re sup­posed to con­stantly ask our be­liefs which ex­pe­riences they pre­dict, make them pay rent in an­ti­ci­pa­tion. But the dragon-claimant’s prob­lem runs deeper, and can­not be cured with such sim­ple ad­vice. It’s not ex­actly difficult to con­nect be­lief in a dragon to an­ti­ci­pated ex­pe­rience of the garage. If you be­lieve there’s a dragon in your garage, then you can ex­pect to open up the door and see a dragon. If you don’t see a dragon, then that means there’s no dragon in your garage. This is pretty straight­for­ward. You can even try it with your own garage.

No, this in­visi­bil­ity busi­ness is a symp­tom of some­thing much worse.

Depend­ing on how your child­hood went, you may re­mem­ber a time pe­riod when you first be­gan to doubt Santa Claus’s ex­is­tence, but you still be­lieved that you were sup­posed to be­lieve in Santa Claus, so you tried to deny the doubts. As Daniel Den­nett ob­serves, where it is difficult to be­lieve a thing, it is of­ten much eas­ier to be­lieve that you ought to be­lieve it. What does it mean to be­lieve that the Ul­ti­mate Cos­mic Sky is both perfectly blue and perfectly green? The state­ment is con­fus­ing; it’s not even clear what it would mean to be­lieve it—what ex­actly would be be­lieved, if you be­lieved. You can much more eas­ily be­lieve that it is proper, that it is good and vir­tu­ous and benefi­cial, to be­lieve that the Ul­ti­mate Cos­mic Sky is both perfectly blue and perfectly green. Den­nett calls this “be­lief in be­lief.”1

And here things be­come com­pli­cated, as hu­man minds are wont to do—I think even Den­nett over­sim­plifies how this psy­chol­ogy works in prac­tice. For one thing, if you be­lieve in be­lief, you can­not ad­mit to your­self that you merely be­lieve in be­lief. What’s vir­tu­ous is to be­lieve, not to be­lieve in be­liev­ing; and so if you only be­lieve in be­lief, in­stead of be­liev­ing, you are not vir­tu­ous. No­body will ad­mit to them­selves, “I don’t be­lieve the Ul­ti­mate Cos­mic Sky is blue and green, but I be­lieve I ought to be­lieve it”—not un­less they are un­usu­ally ca­pa­ble of ac­knowl­edg­ing their own lack of virtue. Peo­ple don’t be­lieve in be­lief in be­lief, they just be­lieve in be­lief.

(Those who find this con­fus­ing may find it helpful to study math­e­mat­i­cal logic, which trains one to make very sharp dis­tinc­tions be­tween the propo­si­tion P, a proof of P, and a proof that P is prov­able. There are similarly sharp dis­tinc­tions be­tween P, want­ing P, be­liev­ing P, want­ing to be­lieve P, and be­liev­ing that you be­lieve P.)

There are differ­ent kinds of be­lief in be­lief. You may be­lieve in be­lief ex­plic­itly; you may re­cite in your de­liber­ate stream of con­scious­ness the ver­bal sen­tence “It is vir­tu­ous to be­lieve that the Ul­ti­mate Cos­mic Sky is perfectly blue and perfectly green.” (While also be­liev­ing that you be­lieve this, un­less you are un­usu­ally ca­pa­ble of ac­knowl­edg­ing your own lack of virtue.) But there are also less ex­plicit forms of be­lief in be­lief. Maybe the dragon-claimant fears the pub­lic ridicule that they imag­ine will re­sult if they pub­li­cly con­fess they were wrong.2 Maybe the dragon-claimant flinches away from the prospect of ad­mit­ting to them­selves that there is no dragon, be­cause it con­flicts with their self-image as the glo­ri­ous dis­cov­erer of the dragon, who saw in their garage what all oth­ers had failed to see.

If all our thoughts were de­liber­ate ver­bal sen­tences like philoso­phers ma­nipu­late, the hu­man mind would be a great deal eas­ier for hu­mans to un­der­stand. Fleet­ing men­tal images, un­spo­ken flinches, de­sires acted upon with­out ac­knowl­edge­ment—these ac­count for as much of our­selves as words.

While I dis­agree with Den­nett on some de­tails and com­pli­ca­tions, I still think that Den­nett’s no­tion of be­lief in be­lief is the key in­sight nec­es­sary to un­der­stand the dragon-claimant. But we need a wider con­cept of be­lief, not limited to ver­bal sen­tences. “Belief” should in­clude un­spo­ken an­ti­ci­pa­tion-con­trol­lers. “Belief in be­lief” should in­clude un­spo­ken cog­ni­tive-be­hav­ior-guiders. It is not psy­cholog­i­cally re­al­is­tic to say, “The dragon-claimant does not be­lieve there is a dragon in their garage; they be­lieve it is benefi­cial to be­lieve there is a dragon in their garage.” But it is re­al­is­tic to say the dragon-claimant an­ti­ci­pates as if there is no dragon in their garage, and makes ex­cuses as if they be­lieved in the be­lief.

You can pos­sess an or­di­nary men­tal pic­ture of your garage, with no drag­ons in it, which cor­rectly pre­dicts your ex­pe­riences on open­ing the door, and never once think the ver­bal phrase There is no dragon in my garage. I even bet it’s hap­pened to you—that when you open your garage door or bed­room door or what­ever, and ex­pect to see no drag­ons, no such ver­bal phrase runs through your mind.

And to flinch away from giv­ing up your be­lief in the dragon—or flinch away from giv­ing up your self-image as a per­son who be­lieves in the dragon—it is not nec­es­sary to ex­plic­itly think I want to be­lieve there’s a dragon in my garage. It is only nec­es­sary to flinch away from the prospect of ad­mit­ting you don’t be­lieve.

If some­one be­lieves in their be­lief in the dragon, and also be­lieves in the dragon, the prob­lem is much less se­vere. They will be will­ing to stick their neck out on ex­per­i­men­tal pre­dic­tions, and per­haps even agree to give up the be­lief if the ex­per­i­men­tal pre­dic­tion is wrong.3 But when some­one makes up ex­cuses in ad­vance, it would seem to re­quire that be­lief and be­lief in be­lief have be­come un­syn­chro­nized.

1 Daniel C. Den­nett, Break­ing the Spell: Reli­gion as a Nat­u­ral Phenomenon (Pen­guin, 2006) .

2 Although, in fact, a ra­tio­nal­ist would con­grat­u­late them, and oth­ers are more likely to ridicule the claimant if they go on claiming theres a dragon in their garage.

3 Although be­lief in be­lief can still in­terfere with this, if the be­lief it­self is not ab­solutely con­fi­dent.