There are 24 hours in a day. Not two sets of 12 hours.
It might have made sense to pretend that there are two 12-hour halves to the day when analog clock faces were all we had, but I doubt it. I've seen analog clocks with a single hand that display how far through the day we are. If what you're doing is unimportant enough that you can use an analog timepiece, what do you care if you can't distinguish seconds or even minutes? That analog clock's probably not NTP synchronized anyway, so the extra precision won't give you any more accuracy.
If you tell Evolution to use the 24 hour clock for its calendar it will do so, though that isn't the default setting. Unfortunately, Evolution will continue to use the 12 hour clock for your mail. So sent/received times use the 12 hour clock, and there's no way to change that.
Blogger lets you choose a date format for posts (as you see, I use ISO 8601 dates), but it doesn't automatically use that format for its interface. At the bottom of the text area I'm composing this in (which, for reasons I don't understand given the really cool stuff DHTML/CSS gurus can do, doesn't stretch to anywhere near the bottom of the window) there's an option to "Change Time & Date" that reads 11:00 PM Aug 12 2004. The rest of the interface is similar: 12 hour clocks and weird US date formats. At least I'm a native English speaker and the month is given as a word. Otherwise I'd be really confused.
Mac OS lets me ask for metric units, and ISO 8601 dates and 24-hour times, but it insists on a distinction between "long dates" and "short dates", and won't let me specify ISO 8601 for the latter. The nearest I can get is 2004-Aug-12. And not all applications pay attention to these settings. Address Book, for example, shows birthdays in the form 11 August 2004 (for someone born yesterday).
It doesn't look like it's going to get better any time soon, either. The movie "I, Robot" relies in part on us using the 12 hour clock in 2035. Will Smith is almost killed because of this system that's out of date even now.
We have 31 years left in which to prevent this. Fix these broken programs now, and stop writing new ones.