Is mass mental or physical ?

I need some help.

Yesterday I  made the claim that strings
are massless and so are nonphysical (mental, by my definition).
But you can show theoretically that strings have mass, based on
line tension and other variables. So is mass physical ?

Unless I am mistaken, mass is always defined in terms of other variables,
much like in a dictionary words are defined in terms of other words..
For example, m = E/c^2, where E is energy and c is the speed of light.
But energy is the ability to do work, which in turn is defined as
W = F*d, where F is a force moved through distance d. But
Force is mass*acceleration. So we are back wihere we started,
since m =E/c*2.

To me this means that we must empirically define some force
like the weight of a selected and saved lump of lead as say a Newton of force,
and a length given by some metal rule to be saved, and proceed from
there.

To me this means that all physical variables are actually nonphysical
(theoretical or mental).  Which is the basic foundation of idealism or
platonism.
Everything, even mass, is mental in the sense of being theoretical
or mathematical. Is this correct ?

Dr. Roger B Clough NIST (ret.) [1/1/2000]
See my Leibniz site at