The replacement indistinguishability is not transitive.
I assume that’s a typo for “is transitive”.
Regardless of how many are replaced in any order there cannot be a behavior change, even if it goes as A to B, A to C, A to D.
Why not? If you assume absolute identity of behaviour, you’re assuming the conclusion. But absolute identity is unobservable. The best you can get is indistinguishability under whatever observations you’re making, in which case it is not transitive. There is no way to make this argument work without assuming the conclusion.
All proofs at least implicitly contain the conclusion in the assumptions or axioms. That’s because proofs don’t generate information, they just unravel what one has already assumed by definition or axioms.
So yes, I’m implicitly assuming the conclusion in the assumptions. The point of the proof was to convince people who agreed with all the assumptions in the first place but who did not believe in the conclusion. There are people who do believe the assumptions but do not agree with the conclusion, which, as you say is in the assumptions.
I assume that’s a typo for “is transitive”.
Why not? If you assume absolute identity of behaviour, you’re assuming the conclusion. But absolute identity is unobservable. The best you can get is indistinguishability under whatever observations you’re making, in which case it is not transitive. There is no way to make this argument work without assuming the conclusion.
All proofs at least implicitly contain the conclusion in the assumptions or axioms. That’s because proofs don’t generate information, they just unravel what one has already assumed by definition or axioms.
So yes, I’m implicitly assuming the conclusion in the assumptions. The point of the proof was to convince people who agreed with all the assumptions in the first place but who did not believe in the conclusion. There are people who do believe the assumptions but do not agree with the conclusion, which, as you say is in the assumptions.