Patterns of changes of velocity can be measured with respect to distance or with respect to time. The a in f=ma represents changes of velocity with respect to time called acceleration. The evidence appears in f=ma only as combination of units of meters and seconds. We have only meters and seconds to work with for the purpose of defining force and mass. If we arbitrarily add, for whatever reason, other units or anything invented we interfere with the meaning of the patterns of accelerations of objects. If we leave the equation in its empirical form, meaning before we interfere with it, then we find that there are choices available to us about how to proceed to define mass and force using only the empirical evidence. The logical possibilties are to try either property as periods of time, or lengths of distance, or as a velocity, or as an acceleration. Each of these possibilities arise purely from the empirical evidence. One will prove to be the correct choice and reveal itself by its usefulness. It, possibly with modifications due to that which we learn from more patterns of acceleration, will prove to be sufficient, along with length and duration, to derive the rest of mechanics. Nothing will need to be added. This can be known because all other units are derivable from those of mass, assumming that mass is chosen to be the first property to be interpreted, length and duration.
James Putnam