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Academian comments on Second-Order Logic: The Controversy - Less Wrong
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Ah, I was asking you because I thought using that language meant you'd made sense of it ;) The language of us "living in a (model of) set theory" is something I've heard before (not just from you and Eliezer), which made me think I was missing something. Us living in a dynamical system makes sense, and a dynamical system can contain a model of set theory, so at least we can "live with" models of set theory... we interact with (parts of) models of set theory when we play with collections of physical objects.
Of course, time has been a fourth dimension for ages ;) My point is that set theory doesn't seem to have a reasonable dynamical interpretation that we could live in, and I think I've concluded it's confusing to talk like that. I can only make sense of "living with" or "believing in" models.
Set theory doesn't have a dynamical interpretation because it's not causal, but finite causal systems have first-order descriptions and infinite causal systems have second-order descriptions. Not everything logical is causal; everything causal is logical.