It's not quite that simple, unfortunately. Logic and critical thinking does not, by itself, ensure convergence of beliefs. You can in fact have two entirely logical and rational people who, when faced with the same evidence, and after incorporating this same evidence with all due logical and critical diligence, will be further from agreeing than they were before.

Here's an example: person B goes on TV to claim that a certain dictator H has nukes. Viewers U, V initially have no opinion on the matter, but U considers B a lying windbag who can't be trusted, while V considers him an honourable person deserving much respect.

After watching the broadcast, U believes (as he did before) that B has deliberately lied, so the opposite of his claim must be more likely, ie H probably has no nukes. However, V respects B (as he did before) and now believes that H probably has nukes.

Logic on its own is not good enough for convergence of beliefs. You have to take into account the full set of prior beliefs of a person, and this is why it's a waste of time to talk seriously to religious people or conspiracy nutters to question their delusions, for example.

Scientists tend to believe that logic and critical thinking alone brings convergence, but that is only so because they all have highly compatible prior beliefs on everything that matters in their work, obtained from highly similar educational backgrounds.

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