Are Gravitons the Key to Understanding Gravity?

[JesseM]

Humanino is thinking in terms of conceptual as meaning "an accepted mathematical definition". Peter is using conceptual in the sense of a rather vague and not very-well-defined idea; i.e., lots of hand-waving (sorry for the idiom, Humanino).

Although I agree with humanino that only in mathematics do we really have totally clear concepts of anything, if you google the phrase "conceptual argument" along with "physics", you can see that in a physics context this phrase is usually used to mean an argument that relies mostly on words and mental images and not much on mathematics (this doesn't necessarily mean it's totally handwavey; for example, if someone proposes there could be a strange form matter which falls upwards in a gravitational field, a good conceptual argument for why this should be impossible in GR is that it would conflict with the equivalence principle, since this object should still move inertially if placed in the middle of an accelerating elevator, and so appear to fall down from the perspective of the person in the elevator).