It is a familiar enough point that while logic texts for beginners often fall into talking about sets (sets of premisses entailing conclusions, sets of objects being extensions of predicates, sets of objects being domains of quantification, etc.), this set talk is doing no substantive work at least in elementary contexts. It can be construed in a decaffeinated way, as talk about no more than virtual classes in Quine’s sense.
I found myself making a few remarks to this effect at scattered places in IFL2, but doing so distracted a bit from the flow of exposition. So I’ve decided to gather together various remarks into one four-page chapter. Here it is:
What do people think? I’d very much welcome comments. I don’t want to avoid distractions of one kind by e.g. being thought distractingly misguided!