One way to easily demonstrate that this notion of infallible knowledge held by a fallible mind is false is to place 2 presuppositionalists in 2 separate rooms, and ask each of them to make a list of all the infallibly true doctrines/facts they have access to. Their lists will be different demonstrating at least one of them is wrong.
Will any 2 presuppositionalists agree to such a test? Highly unlikely. The project of presuppositionalist apologetics is entirely one of evasion.