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What should be added at this point is: mass is also an abstraction.
Mass is a physical concept, matter a philosophical one.
Both are abstractions, but of quite a different kind.
Also, the questions:
a. what is mass?
b. what is matter?
are very different. I don't think we, as physicists, are entitled to
answer to b. We take matter as a fact of life, and go on to study how
it behaves in different condition, e. g. at very high velocities.
Maybe I am wrong on this, but I am pretty sure that you cannot speak
correctly on this matter if you identify matter and mass.