Hi. OK, hitherto you've consistently claimed that there is an 'objective' quality to 'value'
I don't understand what you mean by this
I don't wanted to go in too much details, but in this regard "inflation" is not "inflation of money" but "inflation of a particular type of money"
E.G. if we talk about bitcoin we can measure the inflation (increase) of the number of bitcoin tokens
If we talk about gold, we can measure the quantity of gold available overground in monetary form (because non-monetary - jewels - has different value and uses)
Same for silver.
Same for USD (printed and electronics). In these case we have many types of measure Money Base, M1, M2, M3, etc. based on what we want measure and the definition of any of the previous).
But we can not measure the quantity of money "per se" because money is a property not a thing. Everything can be used as money, if it has the right features
You evidently confuse here the aggregate of money properties with money tokens as such that are objectively representing these properties. Indeed, property is not countable (unless we decide to count properties of money, but this is evidently not what you meant to say). On the other hand, money tokens (say, dollars) as well as derivatives of these tokens (for example, deposits and bank balances), which monetary aggregates of higher orders consist of, are quite countable, anyway. Further, I don't see particular difference between inflation of money and inflation of a particular type of money since it should be evident from the context that by money I meant exactly the same what you meant by a "particular type of money". If I wanted to use the term conceptually, I would obviously say "the concept of money" or "the property of money"...
In fact, I'm not very much inclined to engage in semantic gymnastics you seem to be looking for