Are mass and force defined simultaneously? Everything I am talking about here takes place in the Newtonian mechanics, but it is also interesting to discuss everything in the context of special theory of relativity, quantum-mechanics or even QFT.
We say that the mass is something that measures the resistance to acceleration. In practice, in order to get the body to accelerate, we need to apply force. But want to define the force, we say that the 1N of force measures the needed force in order to accelerate the 1kg body with the acceleration $1 \frac{m}{s^2}$. Thus we completed the loop - in order to define the acceleration, we need the force and in order to define the force we need the acceleration.
Does that mean that we need to define the mass and force simultaneously? If you think about it, the concept of mass, historically speaking, was very intuitive and known in the ancient times and they could also measure it (using balance scale for example). Force on the other hand, even though very intuitive did not have any way to be measured in the ancient times. Only after the Newton's second law $F =  ma$ we finally get the formula that permits us to measure the force (and maybe even define it quantitatively? ). Going back to my question, I want to find out if we can define the mass and the force before introducing the Newton's second law?
 A: I believe that force is also known from ancient times, linked to the elastic displacement of stuff (bow and arrow for example are very old).
So, it is possible to measure the force (with a spring) and the acceleration of an object. And change the mass by changing the volume while keeping the same material.
What happens is that after the second law was verified many times, net force became defined as the product of mass and acceleration.
And if a spring shows some experimental deviation (when $F = ma \neq kx$), after careful measurements, we say that it is not perfectly linear in the range.
A: Qualitatively speaking, Mass is just an amount of matter contained in an object you don't need force to define that and force is an interaction or an external agent which if is unbalanced gives rise to the motion. We have other types of forces too which doesn't depend upon masses at all ( Lorentz Force) but in classical mechanics (Newtonian Mechanics) force happen to be linked mass. In advanced mechanics we don't even give emphasize on concept of force at all.
