See blog post links in Priors. A priori incoherent means that you don't need data about the world to come to a conclusion (i.e. in this case the statement is logically false).
This doesn't really answer the question, though. I know that a priori means "prior to experience", but what does this consist of? Originally, for something to be "a priori illogical", it was supposed to mean that it couldn't be thought without contradicting oneself, because of pre-experiential rules of thought. An example would be two straight lines on a flat surface forming a bounded figure-- it's not just wrong, but inconceivable. As far as I can tell, an irreducible entity doesn't possess this inconceivability, so I'm trying to figur...
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