Is inflation meaningful? Is it useful?

In several recent posts, Tyler Cowen has stressed the need for better models of inflation. In one case, he expressed exasperation at my claim that (price) inflation is an almost meaningless concept:

4b. More seriously, Scott seems to dismiss the price level concept altogether. For instance he once wrote: “In the past, I’ve frequently argued that inflation is an almost meaningless and useless concept. I’m not even aware of any coherent definitions of the concept.” I don’t think this is a defensible point of view...