Joseph: My encyclopedia says that the mathematician Pierre de Fermat died in 1665 without leaving behind any written proof for a theorem that he claimed nonetheless to have proved. Probably this alleged theorem simply cannot be proved, sinceas the article points outno one else has been able to prove it.
Therefore, it is likely that Fermat was either lying or else mistaken when he made his claim.
Laura: Your encyclopedia is out of date. Recently someone has in fact proved Fermat's theorem. And since the theorem is provable, your claimthat Fermat was lying or mistakenclearly is wrong.
Joseph's statement that "this alleged theorem simply cannot be proved" plays which one of the following roles in his argument?
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