I haven’t read HP:MoR, so don’t know exactly what is happening in the example, but might you not have doubt about whether the supposition is false or not? Envisaging a solution is a way of interrogating the structure of the problem, including whether it is solvable at all. Sure though, if you want to use the suppostion to prove something else, rather than work backwards from it, you want to be sure of the supposition in the first place.
I’m out of my depth with mathematical and logical proofs, but wouldn’t this be just rhetorical engagement with a hypothetical. In probability theory we can use conditionals, this feels like doing that.
If you use the “suppose …” feature in a proof, you need to make sure the supposition isn’t false in context of the proof
I haven’t read HP:MoR, so don’t know exactly what is happening in the example, but might you not have doubt about whether the supposition is false or not? Envisaging a solution is a way of interrogating the structure of the problem, including whether it is solvable at all. Sure though, if you want to use the suppostion to prove something else, rather than work backwards from it, you want to be sure of the supposition in the first place.
I’m out of my depth with mathematical and logical proofs, but wouldn’t this be just rhetorical engagement with a hypothetical. In probability theory we can use conditionals, this feels like doing that.