“Notice that inflation is not the rise in prices”
True, we call that “price inflation.”
Definitions of “inflation” can vary in depth and complexity but what cannot be gotten around is that the MEASURE of “inflation” is % increase in prices. It isn’t percentage increase in monetary or credit aggregates but prices. Same is true in Deflation it is measured as % decrease in PRICES.
There is little that can be said about inflation/deflation without speaking of prices.
You won’t find “price inflation” as a term in Economics Dictionaries.