but whether he has a history of lying or not is a matter of public record.

But what if the public record is not considered reliable, and is often contradictory on the topic? That is par for the course with conspiracists, which is why pointing to the facts on public record has no power to change their minds.

It's true that it is possible to start out from different assumptions and, using perfectly valid logical syntax, reach widely diverging conclusions. But for that to qualify as reasonable, the assumptions have to be not too divorced from reality.

Reality is what one can touch and see (etc.) One does not touch or see the facts reported in the public record, one only touches or sees what is _written_ (etc) in the public record, and what is written in reports referring to the public record (etc).

There is no divorce from reality as such in any case. A (hypothetically rational) conspiracist accepts what is written in the public record, thus accepting reality (so far, just like you or I), but does not infer (unlike you or I) that the facts referred in the public record are generally true events.

This is not out of lack of logic (again take a hypothetical rational conspiracist) but out of a working assumption that the record is unreliable or deliberately misinformation. Nothing in the public record contradicts the working assumption (how could it?), therefore this assumption is not revised.

--
$E(X_t|F_s) = X_s,\quad t > s$