You have to consider that computer science is soemthing we do; it is, in a sense, a way that we talk about a way that we conceptualize our own ability to solve

You have to consider that computer science is soemthing we do; it is, in a sense, a way that we talk about a way that we conceptualize our own ability to solve problems. This issue only comes up because people confuse our theories about problem solving with our abilities to solve problems. Or put another way, the halting problem is disappointment about metaproblems, that we can't model the model. Even more deeply, we encounter a world in which we have these things ready-made; we come into the world with the capability to do things, but because of that, our capability comes before our understanding of our capabilities, and the whole thing becomes a jumble. This opens up onto philosophical traditions that have mostly been obscured behind modern ideas about us being like computers, but you may want to consider something like Merleau-Ponty's The Phenomenology of Perception (or if you're really strong of heart, Husserl's Crisis of European Sciences and Transcendental Phenomenology).