We can describe a whole class of repeatable experiments/observations that could be performed. We could then point out the patterns in those observations and describe those patterns in the form of simple mathematical equations. We can then define mass as a specific term that appears in those equations.

Very simple example:

It is observed in various experiments conducted close to the surface of the Earth that various measurements related to the set of observations that we collectively refer to as an "object" fit this pattern:

mgh =

^{1}/

_{2}mv

^{2}

Note: we don't

*have to*think of any of the terms in this equation as representing anything other than the measured results of an observation or a constant. We don't

*have to*care what the constants represent. We don't

*have to*speculate as to what the dependant variables represent.

The measured quantities represented by the letters 'h' and 'v' in the above can be made to vary by changing the height and velocity of the object. However we vary them, if the quantity represented by 'g' is some constant (doesn't matter what it represents at this stage), then it is found that the above equation works if the quantity represented by 'm' also remains constant, for a given object. And it is found that different objects have different values for 'm' which satisfy the above equation. We can conclude this without having first made any decisions as to what we think 'm' represents. It's simply part of a pattern that we've noticed in our observations, expressed in precise, unambiguous mathematical terms. All we need to know about it is that, in equations like the one above and many others, it appears to remain constant for a given object however that object moves around, so long as we don't slice bits off it or stick bits onto it.

But if we like, we can call the quantity represented by 'm' "mass" and we can hypothesise that this "mass" concept is a property of the object which appears to be different for different objects but seems to remain constant for any given object. That seems a useful thing to propose.

We can take it from there, doing more experiments to gradually fill out this property that we've invented and called "mass". We can gradually forget that we invented it to describe and predict patterns in our observations and start thinking of it as something that "really exists" (whatever that means) if we want to. But we don't have to do that. Our ability to describe and predict our observations is entirely unaffected by that metaphysical decision. We can simply think of 'm' as a quantity in an equation which describes various aspects of our observations.

In a different context, this approach was once famously summarised by the phrase: "shut up and calculate!".

I'm happy to "unpack"/expand on the above further if necessary.