If I’ve accomplished nothing else in this series (previous post here), I hope to have somewhat dispersed the intimidating air that surrounds both Putnam’s model-theoretic argument and the current discussion of Newman’s objection. This air has two sources, I think.

First, both arguments make heavy use of formal model theory. Formal logic, model theory, and especially metatheory are imposing bodies of technical knowledge. They are mathematical. Most philosophers are only minimally acquainted with them. Most graduate programs in philosophy today no longer require students to take metatheory, and even in the old days, the requirement was generally limited to a single course. I would imagine that over ninety-five percent of professional philosophers today could not tell you off the top of their heads what the Löwenheim–Skolem theorems even say. The point is that when people like Hilary Putnam and Michael Friedman start talking about Shoenfield absoluteness and ω-models, nearly all their listeners know they can’t talk to them as equals on that subject.