The claim that the OP made was that inflation is an arbitrary number. The underlying phenomenon is not a number, more accurately it would be a vector containing

The claim that the OP made was that inflation is an arbitrary number. The underlying phenomenon is not a number, more accurately it would be a vector containing all price deltas and any particular inflation measure is an arbitrary choice of how to project that vector onto a number. There is some validity to the claim. BMI is an interesting choice of comparison as many of the flaws in the measure are related to the arbitrary way that different body types produce different ranges.