  Now for the relevance to the Metaphysics 101 argument.  On either reading of the relevant quantifiers in the Metaphysics 101 argument (those in steps 1, 2, and 4), the argument is valid.  But on the domain-conditions reading, premise 1 (at least) is, if not false, then at least dubious — a piece of controversial ontology.  On the inferential-role reading, all the problems go away, and the argument appears completely shallow.  The Janus-faced character of the argument comes from oscillating between the two readings.  Moreover, given the close relations between the two readings, it is understandable that the metaphysician fails to realize her mistake in thinking that the argument establishes the existence of propositions. 