Newtownian and Lagrangian mechanics are equivalent only in their predictions, not in their complexity - one requires three assumptions, the other just one. Now you say the fact that they have the same predictions makes them equivalent, and I agree. But it's clearly not compatible with what the other poster said about looking for the simplest possible way to explain a phenomenon. If you believe that that's how science should work, you'd need to discard theories as soon as simpler ones that make the same predictions are found (as in the case of Newtownian mechanics). It's a valid philosophical standpoint imho, but it's in opposition to how scientists generally approach Occam's razor, as evidenced eg by common physics curricula. That's what I was pointing out. Having to exclude Newtownian mechanics from what can be considered science is just one prominent consequence of the other poster's philosophical stance, one that could warrant reconsidering whether that's how you want to define it.