- #1

madness

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Netwon's laws can be phrased as follows (from Wikipedia):

First law: In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

Second law: In an inertial frame of reference, the vector sum of the forces

**F**on an object is equal to the mass

*m*of that object multiplied by the acceleration

**a**of the object:

**F**=

*m*

**a**.

Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

In the first law, neither force nor frame of reference have been defined. In the second law, force is given a relationship to mass and acceleration. We might presume that acceleration can be measured and needs no definition. However, mass and force are defined through this equation as far as I understand. Therefore, the first and second law can't yet make any empirical predictions, as we still have two unknown quantities for each measurement of acceleration. In other words, the first two laws (along with the definition of an inertial frame) define mass and force. The third law implicitly tells us that bodies can apply forces to each other (which wasn't apparent from the first two laws), but more explicitly it adds a constraint of reciprocity between the forces of interacting bodies. This still doesn't seem to provide any empirical content given that force and mass are underdetermined from measurements of acceleration according to these laws. However, once we finally posit a functional form for force, for example via Netwon's law of gravitation, it looks as though we have something empirically testable - that is, using measurements of acceleration, we can falsify the theory. So would it be correct to state that Newton's 3 laws are purely definitional, and that only with the additional specification of further laws defining the forces do they become testable? If so, can we claim that this choice of definitions is a good one, as opposed to some other choice?