First, thanks for engaging this topic with me. There are plenty of people who visit my blog who agree with me, so it's healthy to be challenged on my views.
It's interesting you make the statement that we are all metaphysicians, as Lakoff makes the same statement in Philosophy of the Flesh. And it's true, in the sense that we ask ourselves questions like "What is the self", "what is causality", etc. etc., and these have been at least traditionally seen as metaphysical questions. But my point is, along the lines of Lakoff, that the use of the term is antiquated. My concern is whether metaphysical propositions are worth taking seriously, or if 'metaphysics' is a valid intellectual discipline unto itself – one that can answer questions science cannot. I do not think it is.
Let me start by addressing your concerns about model-dependent realism:
First, let it be made clear that model-dependent realism is itself a metaphysical position. That is, by claiming that we don’t have unfettered access to absolute truth Mike is claiming something about the nature of reality.
MDR is a statement about our epistemological relationship to reality, not a statement about what reality is. It does operate on certain assumptions, of course, namely:
• I exist
• My sensory experience is sometimes correct
And, that's about it. Those are basic beliefs (or as I like to call them, 'foundational assumptions') because it is irrational to doubt them. You cannot doubt your own existence, nor can you assume that your sensory experience is never correct. But once you've established these foundational assumptions, MDR becomes a necessary and logical epistemological framework for understanding reality. Creating models of reality is what the brain does; intersubjectively, it's what science does. MDR itself says nothing about the content of reality; indeed it does not concern itself at all with what is 'real'. Models that are more reliable and more parsimonious win out over less reliable, less parsimonious ones – that's it. MDR does not seek what is 'real', but what is reliable. This addresses your statement, "If we’re subject to invalid models of reality, then the only way we could know this is if we can tell valid models of reality from invalid ones." We make that distinction through predictive hypotheses that establish reliable models of reality and allow us to identify and discard unreliable models.
First, it is not nonsensical. In fact, physicists do this all the time. Physicists, in order to best make sense of certain states of the universe, invoke such spatiotemporal language even where such language is out of context. They constantly talk about what it would be like inside a black hole, or what characterizes a singularity, or the weirdness of the quantum world, even though the language employed doesn’t exactly get it right. But, does anyone claim that what these physicists are saying is therefore nonsensical and meaningless?
I think this is a false analogy. The language of physics is mathematics. Sometimes, it can be a bit difficult to communicate mathematical abstractions into language (and while I'm on this Lakoff kick, his book Where Mathematics Comes From is outstanding) and physicists may try to communicate with analogies, but their fundamental language is always constrained by the framework in which they're working. For example, we can use the language of general relativity to describe what it might be like to fall into the event horizon of a black hole, but to describe the quantum behavior of black holes requires a totally different semantic framework. This is precisely why, in his debate with Bill Craig, Sean Carroll repeatedly emphasized that "causality" is not even a relevant component of cosmological models because (due to their use of QM) they must be described using an entirely different semantic framework than classical physics.
what’s important is not just that concepts like identity can be applied anywhere—whether to things in space-time or not—but that they must be applied everywhere on pain of contradiction. That is to say, if one were to attempt to deny (anywhere) a necessary existent like identity, they would defeat themselves logically. A perfect example of this is the first law of logic. Try to deny such a law and you’ll find yourself entangled in self-refutation. And this means that such a proposition cannot fail to be predicated anywhere--for the same thing would happen. Thus stated, we see that metaphysics can, and must, reach beyond the bounds of our experience.
I don't feel like you've addressed my argument at all here; I feel like you just re-stated the original position against which I was arguing in the first place.
Take the word "everywhere" in the statement "[the laws of logic] must be applied everywhere". "Everywhere" is a word that denotes spatiotemporality and derives its very meaning as an abstraction of spatiotemporality; using it devoid of that context renders it meaningless.
It's true that the laws of logic must 'always' (notice the temporal metaphor) apply in their relevant contexts, but that merely means that the laws of logic must be internally semantically coherent. That is, they must consistently describe the the ontologies we ascribe to them, otherwise they fail to be useful. This is precisely what Lakoff meant in the quote I pulled from him:
...philosophers engaged in making metaphysical claims are choosing from the cognitive unconscious a set of existing metaphors that have a consistent ontology. That is, using unconscious everyday metaphors, philosophers seek to make a noncontradictory choice of conceptual entities defined by those metaphors; they then take those entities to be real and systematically draw out the implications of that choice in an attempt to account for our experience using that metaphysics.
The very idea you're asserting, that the laws of logic must hold true "beyond the bounds of our experience" is itself nonsensical. The laws of logic are a semantic framework for developing a consistent ontology of observable phenomena. It is impossible to know, as human beings, what (if anything) exists "beyond our experience" – and again, notice that you are employing a spatiotemporal metaphor! Our brains are not capable of abstracting anything "beyond our experience". Our cognitive and linguistic models are by definition formed, given meaning, and constrained by our experience. How can we possibly have cognitive access to anything "beyond our experience" – given that our ability to comprehend it would, in fact, make it part of our experience?
What you're doing here is making assumptions about the semantic framework from which you are operating. That is, you are making the assumption that words like "beyond" or "everywhere" can be (and are) meaningful without the empirical framework from which their meaning is abstracted. My objection here is that you've provided no reason whatsoever why that assumption is justified. As I said in the original post, the very idea that there is a "non-physical" or "supernatural" reality is itself an assumption that must be established and defended independently before you can claim that the semantic structure underlying the laws of logic can meaningfully describe such things. In other words, you can't just claim that that statements like "beyond our experience" or "beyond the universe", which are predicated on a spatiotemporal metaphor, actually describe a non-spatiotemporal 'supernatural reality' until you can first provide a coherent and semantically meaningful description of that reality.
This is where we get into the big conundrums of supernatural assumptions: what exactly is "supernatural", and why should it be seen as distinct from "natural"? How can change or causality exist independently of time, since both describe spatiotemporal relationships? How can a mind be disembodied, since our conceptual reasoning is derived from our embodiment (notice your consistent use of spatiotemporal metaphors)? The problem is not simply that these concepts are 'mysterious' or in some way ineffable; the problem is that they are semantically incoherent because they attempt to cantilever empirical metaphors into non-empirical contexts. The answer to questions like, "what was before time" or "what lies beyond our experience" is always, "that is an ill-formed question".
Addendum (5/17): I re-read this post tonight and another objection occurred to me. You make a statement like "what’s important is not just that concepts like identity can be applied anywhere—whether to things in space-time or not" (emphasis mine) without acknowledging that the very statement itself assumes the existence of things 'not in space-time' which, last I checked, is precisely what your argument is supposed to prove. This seems like assuming the consequent/begging the question.