One Argument Against An Army

I talked about a style of rea­son­ing in which not a sin­gle con­trary ar­gu­ment is al­lowed, with the re­sult that ev­ery non-sup­port­ing ob­ser­va­tion has to be ar­gued away. Here I sug­gest that when peo­ple en­counter a con­trary ar­gu­ment, they pre­vent them­selves from down­shift­ing their con­fi­dence by re­hears­ing already-known sup­port.

Sup­pose the coun­try of Free­do­nia is de­bat­ing whether its neigh­bor, Syl­va­nia, is re­spon­si­ble for a re­cent rash of me­teor strikes on its cities. There are sev­eral pieces of ev­i­dence sug­gest­ing this: the me­te­ors struck cities close to the Syl­va­nian bor­der; there was un­usual ac­tivity in the Syl­va­nian stock mar­kets be­fore the strikes; and the Syl­va­nian am­bas­sador Trentino was heard mut­ter­ing about “heav­enly vengeance.”

Some­one comes to you and says: “I don’t think Syl­va­nia is re­spon­si­ble for the me­teor strikes. They have trade with us of billions of di­nars an­nu­ally.” “Well,” you re­ply, “the me­te­ors struck cities close to Syl­va­nia, there was sus­pi­cious ac­tivity in their stock mar­ket, and their am­bas­sador spoke of heav­enly vengeance af­ter­ward.” Since these three ar­gu­ments out­weigh the first, you keep your be­lief that Syl­va­nia is re­spon­si­ble—you be­lieve rather than dis­be­lieve, qual­i­ta­tively. Clearly, the bal­ance of ev­i­dence weighs against Syl­va­nia.

Then an­other comes to you and says: “I don’t think Syl­va­nia is re­spon­si­ble for the me­teor strikes. Direct­ing an as­ter­oid strike is re­ally hard. Syl­va­nia doesn’t even have a space pro­gram.” You re­ply, “But the me­te­ors struck cities close to Syl­va­nia, and their in­vestors knew it, and the am­bas­sador came right out and ad­mit­ted it!” Again, these three ar­gu­ments out­weigh the first (by three ar­gu­ments against one ar­gu­ment), so you keep your be­lief that Syl­va­nia is re­spon­si­ble.

In­deed, your con­vic­tions are strength­ened. On two sep­a­rate oc­ca­sions now, you have eval­u­ated the bal­ance of ev­i­dence, and both times the bal­ance was tilted against Syl­va­nia by a ra­tio of 3 to 1.

You en­counter fur­ther ar­gu­ments by the pro-Syl­va­nia traitors—again, and again, and a hun­dred times again—but each time the new ar­gu­ment is hand­ily defeated by 3 to 1. And on ev­ery oc­ca­sion, you feel your­self be­com­ing more con­fi­dent that Syl­va­nia was in­deed re­spon­si­ble, shift­ing your prior ac­cord­ing to the felt bal­ance of ev­i­dence.

The prob­lem, of course, is that by re­hears­ing ar­gu­ments you already knew, you are dou­ble-count­ing the ev­i­dence. This would be a grave sin even if you dou­ble-counted all the ev­i­dence. (Imag­ine a sci­en­tist who does an ex­per­i­ment with 50 sub­jects and fails to ob­tain statis­ti­cally sig­nifi­cant re­sults, so the sci­en­tist counts all the data twice.)

But to se­lec­tively dou­ble-count only some ev­i­dence is sheer farce. I re­mem­ber see­ing a car­toon as a child, where a villain was di­vid­ing up loot us­ing the fol­low­ing al­gorithm: “One for you, one for me. One for you, one-two for me. One for you, one-two-three for me.”

As I em­pha­sized in the last es­say, even if a cher­ished be­lief is true, a ra­tio­nal­ist may some­times need to down­shift the prob­a­bil­ity while in­te­grat­ing all the ev­i­dence. Yes, the bal­ance of sup­port may still fa­vor your cher­ished be­lief. But you still have to shift the prob­a­bil­ity down—yes, down—from what­ever it was be­fore you heard the con­trary ev­i­dence. It does no good to re­hearse sup­port­ing ar­gu­ments, be­cause you have already taken those into ac­count.

And yet it does ap­pear to me that when peo­ple are con­fronted by a new coun­ter­ar­gu­ment, they search for a jus­tifi­ca­tion not to down­shift their con­fi­dence, and of course they find sup­port­ing ar­gu­ments they already know. I have to keep con­stant vigilance not to do this my­self! It feels as nat­u­ral as par­ry­ing a sword-strike with a handy shield.

With the right kind of wrong rea­son­ing, a hand­ful of sup­port—or even a sin­gle ar­gu­ment—can stand off an army of con­tra­dic­tions.