(Not sure if this is more appropriate to the Maths.SE)
The Principle of Explosion is a law of classical logic which says that if we accept inconsistency, then everything becomes possible. I am wondering how this works in the physical world, since we know QM is inconsistent with GR. The Wikipedia article goes into some details of how the proof works, so here's an attempt:
- Objects move on a single well-defined path known as a geodesic (true in GR)
- Objects follow all paths (Feynman's path integral in QM)
- Therefore the statement "objects move on a single well-defined path known as a geodesic OR objects fall upwards" is true
- However given that the above statement is true, since we know that "objects follow all paths" (i.e. objects don't follow a single well-defined path) is true, the first half of the statement is false
- Since the statement is true overall, it must follow that the latter statement, "objects fall upwards", is true
- Therefore we have proven that objects fall upwards
This result is so nonsensical I'm sure something is wrong. What? The only thing that makes sense to me is that the Principle of Explosion doesn't work in physics, in which case the next question is: why not?
I thought about using QM only for this proof, invoking Schrodinger's cat and using the two statements "the cat is alive" and "the cat is dead", but that doesn't work because neither statement is necessarily true.