What "a measure" means in definitions?
I was trying to find a proper definition of temperature and then I got into some troubles. I always thought of temperature as:
Temperature = a measure of the average kinetic energy of the particles in an object
My problem is how we interpret these two definitions. For example in the first definition, what is meant by "a measure". I can't understand it. Maybe it is silly for others but I just can't get it. It is like temperature is another measure of average kinetic energy. It says "a measure" not "the measure". Is temperature "a member" of the "set of measures of average kinetic energy"?
Compare the first definition of the temperature with the definition of volume and mass:
Volume = the amount of space an object occupies
Mass = a measure of body's inertia
Why it says "the amount" and not "a measure of space an object occupies"?
What is a physical quantity?
Physical QUANTITY = A PROPERTY of a material or system that can be quantified by measurement Wikipedia.
From this definition it is clear that when we refer a physical quantity we refer to a property. So when we refer to mass and we say that is a physical quantity then it must be a property which can be measured. Therefore what is the measure of mass?
It seems definitions in physics are not as formal as mathematical definitions are. I don't look for how we should think of mass (relativity) or the proper definition of temperature (partial derivative of internal energy with respect to entropy). I am asking about the "form" of the definitions. In mathematics and generally in axiomatic systems a definitions serves as an abbreviation. Therefore in physical sciences what that abbreviation refers to?