Humans can apparently commit to beliefs that are ultimately contradictory or incompatible. For instance, the one person, unless they're shown a reason to think otherwise, could believe that both quantum mechanics and relativity correspond to reality. What I wanted to ask is -- the ability to hold contradictory beliefs might sometimes be an advantage; for instance, both lines of inquiry could be pursued simultaneously. Is this an advantage that only organic brains have? Is there any good reason a computer couldn't be designed to hold, and act on, contradictory beliefs?

Fantastic question. Just a brief reply (and only one mode of several possible replies). Suppose you take away the word "belief" from your question. That we can "hold" or "consider" contradictory thoughts or ideas is no big deal -- after all, whenever you decide which of multiple mutually exclusive beliefs to adopt, you continuously weigh all of them as you work your way to your decision. Having that capacity is all you really need to obtain (say) the specific benefit you mention (pursuing multiple lines of inquiry simultaneously). When does a "thought" become a "belief"? Well that's a super complicated question, particularly when you add in complicating factors such as the ability to believe "subconsciously" or implicitly. On top of that let's throw in some intellectual humility, which might take the form (say) of (always? regularly? occasionally?) being willing to revisit your beliefs, reconsider them, consider new opposing arguments and objections. Plus the fact that we may easily change our minds as new evidence arises. That said, it seems to me, that in general there's not much incentive to determine exactly how/when a "thought" becomes a "belief." Maybe that happens when you "commit" (to use your word) to the thought in some strong sense, but then again, when/how does that occur? How often must you "declare" what you believe? So with these mitigating considerations in mind, I'd agree with you that yes, we easily hold and consider contradictory thoughts, there may well be advantages to doing so, (there may well also be disadvantages, worth thinking about), and though I can't say much about artificial intelligence/cognition, if computers can be designed to express thoughts in the first place, it's hard to imagine what would inhibit them from expressing contradicting thoughts ...

A couple of good primary sources relevant to your question: Daniel Dennett's book Consciousness Explained (he develops a theory wherein the brain expresses many different, often contradictory, thoughts simultaneously), and some work by Tamar Gendler, particularly a paper comparing "Beliefs" with "A-liefs" (where the latter are thoughts that don't quite rise to the level of beliefs) .... don't have the title handy, but you should be able to find it.

hope that helps--
ap

Read another response by Andrew Pessin
Read another response about Logic, Mind