I wasn't sure quite what you meant by "steps", i.e., whether they were mental instructions or actual behavior. If the former, then yes, that's a model. My point there was any individual would obtain a similar result if they used the same model, i.e., it is objective. If you had literally meant the "steps" taken by that individual, it might reference specific behaviors that are subjectively connected to that person (say, they counted on their fingers, while someone else might have memorized the sums, that sort of irrelevent behavioral element that one might include in "steps" if that had been the meaning).

Circularity is often not troubling at all. It is only a problem in a formal logical process, not in a process that has some objective that is testable.
I figured that was where you were going, but again, that type of circularity is no kind of problem. It is only a problem with clunky analyses that are not allowed to simply consider what the model is and test its results. Fortunately, the latter is just what we do in science, so the circularity of saying that words require models of their own is just no problem at all. It's just how thinking works!

Indeed, some see self-reference as a crucial element of conscious intelligence, and again, if that implies circularity it is no problem. Conscious intelligence is a process that is capable of generating logic, but it need not be a logical process itself. Indeed, I doubt it is, as it invented logic so it had to pre-exist logic, or at least it had to be something else developing concurrently with logic.

Not only could a model do that, but I have no doubt such models already exist. One merely has to model the process of analyzing possible prime-number models, i.e., one has to model the action of intelligence. It is difficult, and we are in the early stages of that type of model, but they do exist and difficulty is not evidence of impossibility.

That is simply false. Your circle model is addressed in your mind under the label "circle", so when someone mentions that label, you call up the model. No problem at all. Alternatively, if they don't use the word "circle" but instead describe a model of a circle, you call up your model by comparing its attributes to the description given. In neither case do I need to know what a circle is independent of my model, I merely have to be able to scan my own memory addresses and attributes. That humans have that capability is perfectly clear, or we could not use language at all.

This argument rather flies in the face of the simple fact that I have indeed explained my notion of model, if is a definition, and that definition accomplishes exactly what I want it to. For one thing, it empowers me to create models and to recognize when I'm using others' models. So frankly, I find it pretty silly to claim that the concept is unexplained. The concept of a model works wonderfully, and I'm fully satisfied with it. If you are not, then perhaps that merely undercuts your own ability to use them effectively (or more likely, you simply pretend you are not using them when in fact you are, you just insist on behavioral models even when other types are more direct).
Again there's nothing "troubling" about that, it's the simplest answer of all-- you "stop" whenever you want to, whenever you feel the goals of the scientific model have been met. That is independent of the specific model, no problem there. Note that in pure mathematics, you don't make models, you simply define the attributes of some conceptual object. What makes it a "mathematical model" is when you use it as a unifying device for something else, something from the world of actual experience.

In other words, we have to test out models before we know if they are good or not. I'm sorry, I don't find that surprising. The real issue here is the "individual and the environment" piece, if taken too seriously, will bring in all kinds of subjective elements that will only serve to bog down the understanding of the model. The more objective the focus, the sharper will be the understanding of the scientific model.
In other words, the only people who can use the models are those who have learned how to use the models. Again, this is not a news flash. Behavioral modeling is rich in generating the obvious, and thin in generating any useful insights, that's the whole reason science doesn't use it (except behavioral science, of course).

That claim flies in the face of what I see as a fairly clear fact, that the vast majority of the concepts we claim to "understand", we make that claim based on a self-referential impressions in our own minds. Rarely do we wait for confirmation from anywhere else before we generate our own concept of understanding. We can often be wrong, but that doesn't change the place where that impression comes from: our own minds. Still, it would make no important difference were that not true, a model would still be the same thing.

Certainly, we can practice our model.

It is the performance of the model that counts, of course. That also does not change the most direct and useful way to understand what a model is.

You haven't learned a lot of models, have you? That is exactly what the experience is like. I don't know what you mean by "right away", obviously you have to think about it sometimes. But the testing of one's understanding is quite a different experience than the generation of the sensation of understanding. Personally, I rarely wait to be told I understand something before I get the sense that I understand it, whether I'm right or not.

So you think you can draw a meaningful differentiation between "mastery of one's life in the world" with "private contentment"? Sitting back with brandy and a cigar sounds like sufficient "mastery" to me, that would be quite nice. I'm afraid your insistence on behavior over conceptual content is biting you there.
I'm afraid I don't know what you mean by "beyond" the models in our heads. We are talking about the models in our heads, why do we need to get "beyond" them?
It is tautological that humans are simply not capable of anything except behavior, as one can even define thought as a behavior. The issue is, do I need to clutter up the understanding of what a model is by embedding it in a larger behavioral context. I claim what is really happening there is that people who have had success understanding certain things (largely in behavioral science) by modeling the connections with behavior often make the incorrect extrapolation that this will always be an essential or even useful thing to do. But in many cases, such as physics models, it is demonstrably true that this is counterproductive.

This whole affair boils down to the simple question: Are you actually suggesting that physics will produce better models, perhaps unifying quantum mechanics and gravity, if they would just pay more attention to how their models are examples of "achievement in the environment", rather than simply imagining that the model is being checked against experiments?

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Logic is the grammar of truth.

Meaning and absolute certainty are incompatible, and profound meaning and absolute certainty are profoundly incompatible.

The only thing intelligence is capable of is recognizing itself.