Does a confidence interval actually provide a measure of the uncertainty of a parameter estimate? I was reading a blog post by the statistician William Briggs, and the following claim interested me to say the least.
What do you make of it?

What is a confidence interval? It is an equation, of course, that will
  provide you an interval for your data. It is meant to provide a
  measure of the uncertainty of a parameter estimate. Now, strictly
  according to frequentist theory—which we can even assume is true—the
  only thing you can say about the CI you have in hand is that the true
  value of the parameter lies within it or that it does not. This is a
  tautology, therefore it is always true. Thus, the CI provides no
  measure of uncertainty at all: in fact, it is a useless exercise to
  compute one.

Link: http://wmbriggs.com/post/3169/
 A: It can be hard to mathematically characterize uncertainty, but I know it when I see it; it usually has wide 95% confidence intervals.
A: He's referring, rather clumsily, to the well known fact that frequentist analysis doesn't model the state of our knowledge about an unknown parameter with a probability distribution, so having calculated a (say 95%) confidence interval (say 1.2 to 3.4) for a population parameter (say the mean of a Gaussian distribution) from some data you can't then go ahead & claim that there's a 95% probability of the mean falling between 1.2 and 3.4. The probability's one or zero—you don't know which. But what you can say, in general, is that your procedure for calculating 95% confidence intervals is one that ensures they contain the true parameter value 95% of the time. This seems reason enough for saying that CIs reflect uncertainty. As Sir David Cox put it†

We define procedures for assessing evidence that are calibrated by how
  they would perform were they used repeatedly. In that sense they do
  not differ from other measuring instruments.

See here & here for further explanation. 
Other things you can say vary according to the particular method you used to calculate the confidence interval; if you ensure the values inside have greater likelihood, given the data, than the points outside, then you can say that (& it's often approximately true for commonly used methods). See here for more.
† Cox (2006), Principles of Statistical Inference, §1.5.2
