Can states secede?

It always has seemed to me that the (sainted) Founders made a mistake by not including a formal exit provision in the constitution. Perhaps it seemed like a good idea at the time as a way to discourage exit or perhaps they assumed the possibility under some common law of contract in place at the time. In any case, their failure led to the great human disaster that was the Civil War.

Over at the Volokh conspiracy, there is a debate going on about whether the Civil War settled the legal question, including a link to a letter from Justice Scalia indicating that he thinks it did. Should wars settle legal questions? We don't assume that other choices made in the 1860s settled constitutional questions?

Moreover, the fact that the South was wrong on the question of slavery does not imply that they were wrong on the question of a right to secession. These are (completely) different issues.

The constitution, though we have mostly put this fact in the memory hole, was a contract between states, not a contract to set up a state. It was originally much more like the EU (or some hybrid of the EU and NATO) than we think about it today.

I worry sometimes, as some political scientists have, about the similar absence of an explicit exit mechanism in the laws that underlie the EU.