I am assuming here that all the crows that we have previously seen have been black, and therefore that both theories have the same agreement, or at least approximate agreement, with what we know.
The second theory clearly has more information content.
Why would it not make sense to use the first theory on this basis?
The fact that all the crows we have seen so far are black makes it a good idea to assume black crows in future. There may be instances of non-black crows, when the theory has predicted black crows, but that simply means that the theory is not 100% accurate.
If the 270 pages of exceptions have not come from anywhere, then the fact that they are not justified just makes them random, unjustified specificity. Out of all the possible worlds we can imagine that are consistent with what we know, the proportion that agree with this specificity is going to be small. If most crows are black, as I am assuming our experience has suggested, then when this second theory predicts a non-black crow, as one of its exceptions, it will probably be wrong: The unjustified specificity is therefore contributing to a failure of the theory. On the other hand, when the occasional non-black crow does show up, there is no reason to think that the second theory is going to be much better at predicting this than the first theory - so the second theory would seem to have all the inaccuracies of wrongful black crow prediction of the first theory, along with extra errors of wrongful non-black crow prediction introduced by the unjustified specificity.
Now, if you want to say that we don't have experience of mainly black crows, or that the 270 pages of exceptions come from somewhere, then that puts us into a different scenario: a more complicated one.
Looking at it in a simple way, however, I think this example actually just demonstrates that information in a theory should be minimized.
I haven't been following the discussion on this topic very closely, so my response may be about stuff you already know or already know is wrong. But, since I'm feeling reckless today, I will try to say something interesting.
There are two different information metrics we can use regarding theories. The first deals with how informative a theory is about the world. The ideally informative theory tells us a lot about the world. Or, to say the same thing in different language, an informative theory rules out as many "possible worlds" as it can; it... (read more)
This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.