Tom quoting me: "There are no quantities by which 'A' may be expressed. There are quantities by which 'B' may be expressed."
Retracing the history behind my statement:
Me: "...kilograms is a defined unit. It is a defined unit because it is defined in terms of pre-existing units."
Tom: "James, try and define "pre-existing.""
Me: "There are simpler and more fundamental quantitites in terms of which 'B' may be expressed. Those simpler and more fundamental quantities pre-exist 'B'.
There are no simpler or more fundamental quantities in terms of which 'A' may be expressed. No quantity pre-exists 'A'. 'A' pre-exists all quantities that may be expressed in terms of 'A'."
Tom: "What differentiates A from B?"
Me: "There are no quantities by which 'A' may be expressed. There are quantities by which 'B' may be expressed."
Each of my statements is correct physics.
The following is assumed to refer to my position that only length and time are proper indefinable properties:
Tom: "You have no relation between A and B, only the sound of one hand clapping."
There was no relation expressed. However, going along with what I think you are getting at:
If A is an object's acceleration and B is defined in terms of acceleration then that 'clapping hand' is acceleration and its units are those of acceleration.
If, in the case of f=ma, A is a for acceleration and B is m for mass, defined as an inverse acceleration, then B is defined in the same terms as is its empirical evidence A. In other words, mass has defined units that consist of a combination of meters and seconds, the fundamental indefinable units of its empirical evidence.
James Putnam