A continuation of Inflation as an Arbitrary Concept.
Peter G. Klein left a comment that indicates that Scott Sumner and I are not the only economists leery of the concept of inflation:
Mike, you and Scott have some distinguished predecessors. Gottfried Haberler made
the same argument in his 1927 book _The Mean of Index Numbers: An Inquiry in the
Concept of the Price Level and the Methods of Its Measurement_. E.g.: "The relative
position and change of different groups of prices are not revealed, but are hidden
and submerged in a general index. Not the movement of the general price level, but
the chronological succession of special price and price combinations ... are regarded
as significant for the waves of business life.... Such a general index rather conceals
and submerges than reveals and explains those price movements that characterize and
signify the movement of the cycle."
I have to admit, my knowledge of the history of thought in economics is quite limited, so I quite enjoyed learning this (it was new to me). I decided to do some additional research (a.k.a. a Google search), and found Gottfried Haberler: A Centenary Appreciation, a summary of the man's work. I found it quite enlightening.
I figure there have to be more economists to take this view - any other names to add to the list? I still suspect, though, that we are in the minority. Too many textbooks treat the concept of inflation as an objective concept that we try our best to estimate. It is not, because our basket of goods changes over time and any attempts to account for this are based on subjective 'judgment calls'.

Comments
Hayek showed that a “stable price level” (i.e. ‘no inflation’) was a mirage — a “stable price level” could contain within it an dis-equilibrium set of prices that must produce disequilibrium effects over time, unemployment, business failures, etc.
That said, try going to any high inflation country and tell them there is no such things as inflation.
As an empirical phenomena in a world, inflation is real.
It’s important to remind ourselves not to reify the mistakes of economists.
But it’s also important to get out of the ivory tower now and then.
The view that statistical price levels were limiting, if not, misinforming indications of economic relationships, was rather common before the triumph of Keynesian Economics beginning in the second half of the 1930s.
One other example of this, besides Gottfried Haberler, was Benjamin M. Anderson. From the early 1920s to the mid-1930s, Anderson was the senior economic analyst for Chase Bank, and was the single author of the 4 to 6 times a year “Chase Economic Bulletin.”
The May 8, 1929 issue was entitled, “Commodity Price Stabilization: a False Goal of Central Bank Policy.” Anderson said, at one point:
“The general price level is, after all, merely a statistician’s tool of thought. Businessmen and bankers often look at index numbers as indicating price trends, but
no businessman makes use of index numbers in his bookkeeping. His bookkeeping runs in terms of the particular prices and costs that his business is concerned with . . . Satisfactory business conditions are dependent upon proper relations among groups of prices, not upon any average of prices.”
As a result of a far more microeconomic monetary process analysis, partly based on his knowledge of “Austrian” business cycle theory which at that time was only available in German-language publications, Anderson was explaining from the middle of the 1920s that the Federal Reserve’s monetary policy was distorting the patterns and structures of relative prices, including interest rates, beneath the apparent “calmness” of a stable price level.
He emphasized in many of these “Chase Economic Bulletins” in the second half of the 1920s that this was setting up the American economy for a “correction crisis.”
Thus, Anderson was anticipating the inescapably of an eventual downturn and recession due to the mismanagement of the money and credit system. And he did so by not limiting his analysis to a variety of economic aggregates and averages, including various price level indexes.
Richard Ebeling