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Imaginative Resistance and Cognitive DistanceThe

Imaginative Resistance and Cognitive Distance

The following is a comment that I posted to Brian Weatherson's Thoughts Arguments and Rants blog on the topic of imaginative resistance that he posted Monday 6/16. I figured that I'd post it here as well, just so I can refer back to it later if I like, but you really need to refer to Thoughts, Arguments and Rants, Brian's original paper Virtuous Resistance  and Wo's weblog entry In Defense of the Impossibility Hypothesis for the context:

I think you can probably add Bertrand Russell to the list of smart people like Wo who would have problems with the Tower of Goldbach case. I stumbled across this in The Problems of Philosophy this morning (Oxford Univ. Press edition, p.79):
"When Swift invites us to consider the race of Struldbugs who never die, we are able to acquiesce in imagination. But a world where two and two make five seems quite on a different level. We feel that such a world, if there were one, would upset the whole fabric of our knowledge and reduce us to utter doubt."

My guess (it doesn't really amount to a theory) is that something like Wo's concept of distance in belief space applies, except that distance shouldn't be measured in degree of credence but something like degree to which it enters into our daily working set of beliefs (which is some function of how long/how much effort it takes to recall and reassure ourselves of its truth). E.g., my credence in Godel's Incompleteness Theorem is quite high, having learned two different proofs of it in my undergraduate days, but my imaginative resistance to a fiction where it's not true is rather low--lower, anyway, than my imaginative resistance to 7 plus 5 does not make 12--I think because it takes some time and effort to recall the proofs to mind and deriving the consequences of its falsity are similarly "distant" and difficult. If this idea is right, I'd predict two things: that imaginative resistance would (ceteris paribus) be lower towards stories that only imply the impossible without outright stating it (because it takes work to tease out the implication, making the impossibility more distant); that people who deal with and rely on certain concepts more frequently and heavily will have greater imaginative resistance to impossibilities regarding them, so that e.g. my complexity theorist friends might have imaginative resistance towards a story that makes Godel's Incompleteness Theorem false that approaches mine towards the Tower of Goldbach.

I think that the conceptual effort/distance idea goes some way towards explaining why time-travel paradox stories don't meet much imaginative resistance, but it does have a problem with the lack of resistance you and Tamar have towards the Tower of Goldbach. I find it hard to believe that you and Tamar don't rely on arithmetic enough to find 5+7=12 virtually effortless and immediate, so there has to be some other explanation. Maybe that's where metaphysical theories about mathematics come in: maybe for some people metaphysical theories that would permit its negation are "close" enough to the daily working set of beliefs to overcome the resistance. Posted by joshua at June 18, 2003 08:54 AM