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jwdink comments on Open Thread: July 2009 - Less Wrong
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Certainly-- that was somewhat sloppy of me. In my defense, however, a priori and conceivability/imaginability are pretty inextricably tied. Additionally, you yourself used the word "envision."
It would perhaps be helpful if you could clarify what you meant when you said:
Your usage doesn't seem to fit into the Kantian sense of the term-- the unity of my experience of the world is not conditioned by everything being reducible. What do you mean when you say irreducibility is a priori logically incoherent?
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 figure out what Eliezer meant.
(He mentions some stuff about being unable to make testable predictions to confirm irreducibility, but as I've already said, this seems to presuppose that reducibility is the default position, not prove it.)