What makes people irrational thinkers?

[Neo-Scholastic]

@polymath257  hasn't proven either his nominalism or radical empiricism but expects everyone else to take it for granted.

No, I don't. I simply see it [nominalism and radical empiricism] as the simplest explanation consistent with the facts as we know them.

Simple explanations are indeed to be preferred when they explain all the relevant phenomena. No philosophical system is complete though there may be degrees of perfection. In your case, qualia and intentionality seem woefully unaccounted for.

Mere consistency is very far from being enough.

So, in mathematics, there is the notion of formal proof....any proposed truth must be reducible to...axioms.

In the sciences, when there is a dispute, an experiment is proposed to resolve the dispute. Then actual observation determines who is wrong.

True consistency with observations is not enough. Degree of completeness is a important too. I see two independent systems: formalism and empiricism. What's their connection? You have not yet expressed any reason. What is common to formal systems that correspond with observations and those that do not? At some point you have to connect the phenomenal with the noumenal. IMHO such that is not a satisfactory position.

Also, you and a few others seem very concerned about who is wrong.