Newton's 2nd - assumption or observation?

[Dale]

I just wanted to highlight the difference basically between an observable fact and an assumption.
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Assumptions are not something that's wrong (or right), they are the points at which alternative formalisms become possible - which makes them important.

Dale, surely that's a valid scientific principle?

I agree completely that there is a difference between observable facts and assumptions, but I don't think that the first and second laws are observable facts. They are also parts of the theory (or at least the inspiration for the theory) and the theory as a whole must be supported by observable facts.

As far as elements of a theory go, you can generally break the mathematical framework down into the assumptions, the definitions, and the derived implications (which is probably what you want to do here). I usually don't bother to break them apart that way except for historical reasons, since it is always possible to derive the same framework by rearranging which elements are considered assumed and which are considered defined or derived. But in any case, none of these theoretical elements are themselves observed facts.

 

[AJ Bentley]

it is always possible to derive the same framework

Yes.

Let's call it a day - I've been mauled.