No Logical Positivist I

Fol­lowup to: Mak­ing Beliefs Pay Rent, Belief in the Im­plied In­visi­ble

De­grees of Free­dom ac­cuses me of rein­vent­ing log­i­cal pos­i­tivism, badly:

One post which reads as though it were writ­ten in Vienna in the 1920s is this one [Mak­ing Beliefs Pay Rent] where Eliezer writes

“We can build up whole net­works of be­liefs that are con­nected only to each other—call these “float­ing” be­liefs. It is a uniquely hu­man flaw among an­i­mal species, a per­ver­sion of Homo sapi­ens’s abil­ity to build more gen­eral and flex­ible be­lief net­works… The ra­tio­nal­ist virtue of em­piri­cism con­sists of con­stantly ask­ing which ex­pe­riences our be­liefs pre­dict—or bet­ter yet, pro­hibit.”

Log­i­cal pos­i­tivists were best known for their ver­ifi­ca­tion­ism: the idea that a be­lief is defined in terms of the ex­per­i­men­tal pre­dic­tions that it makes. Not just tested, not just con­firmed, not just jus­tified by ex­per­i­ment, but ac­tu­ally defined as a set of al­low­able ex­per­i­men­tal re­sults. An idea un­con­firmable by ex­per­i­ment is not just prob­a­bly wrong, but nec­es­sar­ily mean­ingless.

I would dis­agree, and ex­hibit log­i­cal pos­i­tivism as an­other case in point of “mis­tak­ing the sur­face of ra­tio­nal­ity for its sub­stance”.

Con­sider the hy­poth­e­sis:

On Au­gust 1st 2008 at mid­night Green­wich time, a one-foot sphere of choco­late cake spon­ta­neously formed in the cen­ter of the Sun; and then, in the nat­u­ral course of events, this Boltz­mann Cake al­most in­stantly dis­solved.

I would say that this hy­poth­e­sis is mean­ingful and al­most cer­tainly false. Not that it is “mean­ingless”. Even though I can­not think of any pos­si­ble ex­per­i­men­tal test that would dis­crim­i­nate be­tween its be­ing true, and its be­ing false.

On the other hand, if some post­mod­ernist liter­a­ture pro­fes­sor tells me that Shake­speare shows signs of “post-colo­nial aliena­tion”, the bur­den of proof is on him to show that this state­ment means any­thing, be­fore we can talk about its be­ing true or false.

I think the two main prob­a­bil­ity-the­o­retic con­cepts here are Min­i­mum Mes­sage Length and di­rected causal graphs—both of which came along well af­ter log­i­cal pos­i­tivism.

By talk­ing about the un­seen causes of visi­ble events, it is of­ten pos­si­ble for me to com­press the de­scrip­tion of visi­ble events. By talk­ing about atoms, I can com­press the de­scrip­tion of the chem­i­cal re­ac­tions I’ve ob­served.

We build up a vast net­work of un­seen causes, stand­ing be­hind the sur­face of our fi­nal sen­sory ex­pe­riences. Even when you can mea­sure some­thing “di­rectly” us­ing a sci­en­tific in­stru­ment, like a volt­meter, there is still a step of this sort in in­fer­ring the pres­ence of this “voltage” stuff from the visi­ble twitch­ing of a dial. (For that mat­ter, there’s a step in in­fer­ring the ex­is­tence of the dial from your vi­sual ex­pe­rience of the dial; the dial is the cause of your vi­sual ex­pe­rience.)

I know what the Sun is; it is the cause of my ex­pe­rience of the Sun. I can fairly read­ily tell, by look­ing at any in­di­vi­d­ual ob­ject, whether it is the Sun or not. I am told that the Sun is of con­sid­er­able spa­tial ex­tent, and far away from Earth; I have not ver­ified this my­self, but I have some idea of how I would go about do­ing so, given pre­cise telescopes lo­cated a dis­tance apart from each other. I know what “choco­late cake” is; it is the sta­ble cat­e­gory con­tain­ing the many in­di­vi­d­ual tran­sient en­tities that have been the causes of my ex­pe­rience of choco­late cake. It is not gen­er­ally a prob­lem for me to de­ter­mine what is a choco­late cake, and what is not. Time I define in terms of clocks.

Bring­ing to­gether the mean­ingful gen­eral con­cepts of Sun, space, time, and choco­late cake—all of which I can in­di­vi­d­u­ally re­late to var­i­ous spe­cific ex­pe­riences—I ar­rive at the mean­ingful spe­cific as­ser­tion, “A choco­late cake in the cen­ter of the Sun at 12am 8/​8/​1”. I can­not re­late this as­ser­tion to any spe­cific ex­pe­rience. But from gen­eral be­liefs about the prob­a­bil­ity of such en­tities, backed up by other spe­cific ex­pe­riences, I as­sign a high prob­a­bil­ity that this as­ser­tion is false.

See also, “Belief in the Im­plied In­visi­ble”. Not ev­ery untestable as­ser­tion is false; a de­duc­tive con­se­quence of gen­eral state­ments of high prob­a­bil­ity must it­self have prob­a­bil­ity at least as high. So I do not be­lieve a space­ship blips out of ex­is­tence when it crosses the cos­molog­i­cal hori­zon of our ex­pand­ing uni­verse, even though the space­ship’s ex­is­tence has no fur­ther ex­per­i­men­tal con­se­quences for me.

If log­i­cal pos­i­tivism /​ ver­ifi­ca­tion­ism were true, then the as­ser­tion of the space­ship’s con­tinued ex­is­tence would be nec­es­sar­ily mean­ingless, be­cause it has no ex­per­i­men­tal con­se­quences dis­tinct from its nonex­is­tence. I don’t see how this is com­pat­i­ble with a cor­re­spon­dence the­ory of truth.

On the other hand, if you have a whole gen­eral con­cept like “post-colo­nial aliena­tion”, which does not have speci­fi­ca­tions bound to any spe­cific ex­pe­rience, you may just have a lit­tle bunch of ar­rows off on the side of your causal graph, not bound to any­thing at all; and these may well be mean­ingless.

Some­times, when you can’t find any ex­per­i­men­tal way to test a be­lief, it is mean­ingless; and the ra­tio­nal­ist must say “It is mean­ingless.” Some­times this hap­pens; of­ten, in­deed. But to go from here to, “The mean­ing of any spe­cific as­ser­tion is en­tirely defined in terms of its ex­per­i­men­tal dis­tinc­tions”, is to mis­take a sur­face hap­pen­ing for a uni­ver­sal rule. The mod­ern for­mu­la­tion of prob­a­bil­ity the­ory talks a great deal about the un­seen causes of the data, and fac­tors out these causes as sep­a­rate en­tities and makes state­ments speci­fi­cally about them.

To be un­able to pro­duce an ex­pe­ri­en­tial dis­tinc­tion from a be­lief, is usu­ally a bad sign—but it does not always prove that the be­lief is mean­ingless. A great many untestable be­liefs are not mean­ingless; they are mean­ingful, just al­most cer­tainly false: They talk about gen­eral con­cepts already linked to ex­pe­rience, like Suns and choco­late cake, and gen­eral frame­works for com­bin­ing them, like space and time. New in­stances of the con­cepts are as­serted to be ar­ranged in such a way as to pro­duce no new ex­pe­riences (choco­late cake sud­denly forms in the cen­ter of the Sun, then dis­solves). But with­out that spe­cific sup­port­ing ev­i­dence, the prior prob­a­bil­ity is likely to come out pretty damn small—at least if the untestable state­ment is at all ex­cep­tional.

If “choco­late cake in the cen­ter of the Sun” is untestable, then its al­ter­na­tive, “hy­dro­gen, he­lium, and some other stuff, in the cen­ter of the Sun at 12am on 8/​8/​1″, would also seem to be “untestable”: hy­dro­gen-he­lium on 8/​8/​1 can­not be ex­pe­ri­en­tially dis­crim­i­nated against the al­ter­na­tive hy­poth­e­sis of choco­late cake. But the hy­dro­gen-he­lium as­ser­tion is a de­duc­tive con­se­quence of gen­eral be­liefs them­selves well-sup­ported by ex­pe­rience. It is mean­ingful, untestable (against cer­tain par­tic­u­lar al­ter­na­tives), and prob­a­bly true.

I don’t think our dis­course about the causes of ex­pe­rience has to treat them strictly in terms of ex­pe­rience. That would make dis­cus­sion of an elec­tron a very te­dious af­fair. The whole point of talk­ing about causes is that they can be sim­pler than di­rect de­scrip­tions of ex­pe­rience.

Hav­ing spe­cific be­liefs you can’t ver­ify is a bad sign, but, just be­cause it is a bad sign, does not mean that we have to re­for­mu­late our whole episte­mol­ogy to make it im­pos­si­ble. To para­phrase Flon’s Ax­iom, “There does not now, nor will there ever, ex­ist an episte­mol­ogy in which it is the least bit difficult to for­mu­late stupid be­liefs.”