“Now imagine I believe the Earth is flat, and you believe the earth is (roughly) spherical. Those two beliefs are mutually contradictory. Clearly, one of us is mistaken.”
Nitpick: . The given beliefs are contradictory but not exhaustive. At least one of the disputants is mistaken, but both could be wrong. The earth could have another shape.
I think theist and atheist can reasonably be defined to be contradictory and exhaustive. Agnostics do not affirm an alternate opinion about whether God exists, they’re simply undecided.
Nitpick: . The given beliefs are contradictory but not exhaustive. At least one of the disputants is mistaken, but both could be wrong. The earth could have another shape.
I think theist and atheist can reasonably be defined to be contradictory and exhaustive. Agnostics do not affirm an alternate opinion about whether God exists, they’re simply undecided.