Hand vs. Fingers

Back to our origi­nal topic: Re­duc­tion­ism, which (in case you’ve for­got­ten) is part of a se­quence on the Mind Pro­jec­tion Fal­lacy. There can be emo­tional prob­lems in ac­cept­ing re­duc­tion­ism, if you think that things have to be fun­da­men­tal to be fun. But this po­si­tion com­mits us to never tak­ing joy in any­thing more com­pli­cated than a quark, and so I pre­fer to re­ject it.

To re­view, the re­duc­tion­ist the­sis is that we use multi-level mod­els for com­pu­ta­tional rea­sons, but phys­i­cal re­al­ity has only a sin­gle level. If this doesn’t sound fa­mil­iar, please reread “Re­duc­tion­ism”.


To­day I’d like to pose the fol­low­ing co­nun­drum: When you pick up a cup of wa­ter, is it your hand that picks it up?

Most peo­ple, of course, go with the naive pop­u­lar an­swer: “Yes.”

Re­cently, how­ever, sci­en­tists have made a stun­ning dis­cov­ery: It’s not your hand that holds the cup, it’s ac­tu­ally your fingers, thumb, and palm.

Yes, I know! I was shocked too. But it seems that af­ter sci­en­tists mea­sured the forces ex­erted on the cup by each of your fingers, your thumb, and your palm, they found there was no force left over—so the force ex­erted by your hand must be zero.

The theme here is that, if you can see how (not just know that) a higher level re­duces to a lower one, they will not seem like sep­a­rate things within your map; you will be able to see how silly it is to think that your fingers could be in one place, and your hand some­where else; you will be able to see how silly it is to ar­gue about whether it is your hand picks up the cup, or your fingers.

The op­er­a­tive word is “see”, as in con­crete vi­su­al­iza­tion. Imag­in­ing your hand causes you to imag­ine the fingers and thumb and palm; con­versely, imag­in­ing fingers and thumb and palm causes you to iden­tify a hand in the men­tal pic­ture. Thus the high level of your map and the low level of your map will be tightly bound to­gether in your mind.

In re­al­ity, of course, the lev­els are bound to­gether even tighter than that—bound to­gether by the tight­est pos­si­ble bind­ing: phys­i­cal iden­tity. You can see this: You can see that say­ing (1) “hand” or (2) “fingers and thumb and palm”, does not re­fer to differ­ent things, but differ­ent points of view.

But sup­pose you lack the knowl­edge to so tightly bind to­gether the lev­els of your map. For ex­am­ple, you could have a “hand scan­ner” that showed a “hand” as a dot on a map (like an old-fash­ioned radar dis­play), and similar scan­ners for fingers/​thumbs/​palms; then you would see a cluster of dots around the hand, but you would be able to imag­ine the hand-dot mov­ing off from the oth­ers. So, even though the phys­i­cal re­al­ity of the hand (that is, the thing the dot cor­re­sponds to) was iden­ti­cal with /​ strictly com­posed of the phys­i­cal re­al­ities of the fingers and thumb and palm, you would not be able to see this fact; even if some­one told you, or you guessed from the cor­re­spon­dence of the dots, you would only know the fact of re­duc­tion, not see it. You would still be able to imag­ine the hand dot mov­ing around in­de­pen­dently, even though, if the phys­i­cal makeup of the sen­sors were held con­stant, it would be phys­i­cally im­pos­si­ble for this to ac­tu­ally hap­pen.

Or, at a still lower level of bind­ing, peo­ple might just tell you “There’s a hand over there, and some fingers over there”—in which case you would know lit­tle more than a Good-Old-Fash­ioned AI rep­re­sent­ing the situ­a­tion us­ing sug­ges­tively named LISP to­kens. There wouldn’t be any­thing ob­vi­ously con­tra­dic­tory about as­sert­ing:

|—In­side(Room,Hand)
|—~In­side(Room,Fingers)

be­cause you would not pos­sess the knowledge

|—In­side(x, Hand)—> In­side(x,Fingers)

None of this says that a hand can ac­tu­ally de­tach its ex­is­tence from your fingers and crawl, ghostlike, across the room; it just says that a Good-Old-Fash­ioned AI with a propo­si­tional rep­re­sen­ta­tion may not know any bet­ter. The map is not the ter­ri­tory.

In par­tic­u­lar, you shouldn’t draw too many con­clu­sions from how it seems con­cep­tu­ally pos­si­ble, in the mind of some spe­cific con­ceiver, to sep­a­rate the hand from its con­stituent el­e­ments of fingers, thumb, and palm. Con­cep­tual pos­si­bil­ity is not the same as log­i­cal pos­si­bil­ity or phys­i­cal pos­si­bil­ity.

It is con­cep­tu­ally pos­si­ble to you that 235757 is prime, be­cause you don’t know any bet­ter. But it isn’t log­i­cally pos­si­ble that 235757 is prime; if you were log­i­cally om­ni­scient, 235757 would be ob­vi­ously com­pos­ite (and you would know the fac­tors). That that’s why we have the no­tion of im­pos­si­ble pos­si­ble wor­lds, so that we can put prob­a­bil­ity dis­tri­bu­tions on propo­si­tions that may or may not be in fact log­i­cally im­pos­si­ble.

And you can imag­ine philoso­phers who crit­i­cize “elimi­na­tive fin­gerists” who con­tra­dict the di­rect facts of ex­pe­rience—we can feel our hand hold­ing the cup, af­ter all—by sug­gest­ing that “hands” don’t re­ally ex­ist, in which case, ob­vi­ously, the cup would fall down. And philoso­phers who sug­gest “ap­pendigi­tal bridg­ing laws” to ex­plain how a par­tic­u­lar con­figu­ra­tion of fingers, evokes a hand into ex­is­tence—with the note, of course, that while our world con­tains those par­tic­u­lar ap­pendigi­tal bridg­ing laws, the laws could have been con­ceiv­ably differ­ent, and so are not in any sense nec­es­sary facts, etc.

All of these are cases of Mind Pro­jec­tion Fal­lacy, and what I call “naive philo­soph­i­cal re­al­ism”—the con­fu­sion of philo­soph­i­cal in­tu­itions for di­rect, veridi­cal in­for­ma­tion about re­al­ity. Your in­abil­ity to imag­ine some­thing is just a com­pu­ta­tional fact about what your brain can or can’t imag­ine. Another brain might work differ­ently.