So let's start over. And as we do, let's notice that, at least when you first began playing with LEGO, you really didn’t know what you could build. You probably didn’t even consider that question. You just tinkered: snapping bricks together, pulling them apart, configuring and reconfiguring them endlessly. In other words, you experimented with these brightly colored playthings, slowly developing a feel for how they could and couldn't be arranged, how you'd need to balance a structure to keep it from toppling, how much lateral pressure the stud connection could bear, and so on. Very little of this was explicit knowledge—you couldn’t articulate much of it. But it was knowledge nonetheless.
Ignoring all this is one of the deeper problems with the imagination- based story. What’s so wonderful about the imagination is that it isn’t constrained by our background knowledge—by all those things we’ve learned about how the world works. (And it’s a good thing too: if it were so constrained, fiction would be a whole lot more boring. Consider a version of The LEGO Movie in which LEGO people behave just as they actually do in the real world—which is to say, not at all.) But we need those constraints when we’re trying to figure things out about the world. After all, we don’t make up the facts about what we can build; they aren’t ours to stipulate. What you can build is determined by the facts about the bricks. So whatever our story about how we know what we can build, it had better be one that factors in our background knowledge, since that’s what makes the imagination useful.
In fact, my guess is that you’ve already seen this constraint at work, though you probably didn’t recognize it at the time. Recall my question about whether there could be a three-headed LEGO guy. I’ll bet you didn’t even consider the possibility of an extra-wide, tri-posted torso, since you know that there aren’t any. Of course, you could have imagined such a torso—so it isn’t the case that you can build whatever you can imagine—you just didn’t imagine it, and this is precisely because your background knowledge spared you from an implausible answer.
This line of reasoning leads us to a better proposal. What you can build is determined by the facts about LEGOs; so, you come to know what you can build by getting a better handle on those facts. It’s your working knowledge of those little pieces that allows you to make judgments about what can and can’t be done with them.
Crucially, there are various ways to make those judgments. Sometimes, the imagination plays an active role, guided by our background knowledge. But not always. Sometimes it just seems to you that something is buildable. In other cases, it’s a more abstract, conceptual affair: you conceive of a structure, and thereby come to know that you could build it. In short, there are lots of ways to extrapolate from what you already know—imagining, considering how things seem to you, conceiving—but they all work (when they do) because they’re drawing out the consequences of what you already know about LEGO.