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, since -- as the article points out -- no one else has been able to prove it  Ttherefore it is likely that Fermat was either lying or else mistaken when he made his claim  Laura: Your encyclopedia is out of date  Recently someone has in fact proved Fermat' s theorem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 claim -- that Fermat was lying or mistaken -- clearly is wrong
a potential objection that his argument anticipates and attempts to answer before it is raised