When can you combine formulas?
Jul. 8th, 2005 02:28 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
guslIn physics, formulas are meant to be interpreted in terms of models: while "F = m a" can be interpreted into any body, "a = v^2 / R" only holds of objects in Uniform Circular Motion (UCM).
You can easily "make the laws of physics lie" by combining formulas to make absurd derivations.
My theory is that truth of formulas is defined on models
(e.g.
and that absurdities will only happen when the models assumed by the formulas are incompatible. But how do we decide whether two models can be combined? My current research goal is to define such a compatibility criterion.
I may need to create a meta-language (syntax for talking about models) in order to do this, but this sounds like it could be too much work.
You can easily "make the laws of physics lie" by combining formulas to make absurd derivations.
My theory is that truth of formulas is defined on models
(e.g.
UCM(body1, body2) |= a_body1 = v_body1^2 / distance(body1,body2) says that this formula is true in the set of models where body1 is in UCM around body2),and that absurdities will only happen when the models assumed by the formulas are incompatible. But how do we decide whether two models can be combined? My current research goal is to define such a compatibility criterion.
I may need to create a meta-language (syntax for talking about models) in order to do this, but this sounds like it could be too much work.