According to that theory, knowledge does not require that the believer possess/possesses positive reason.
While the subject "believer" would take a third-person singular verb conjugation in the present indicative (possesses), this is a subjunctive construction, so it can take the infinitive form.
Not everyone uses the subjunctive in English. I would say "possess" here, but a lot of people might say "possesses."
So, in short, using "possesses" is certainly not required, but it also wouldn't necessarily be considered wrong.