You actually noticed something deeper than your original question — “continuity of logic”, in the sense of “continuous function”. If you imagine you have a lot

You actually noticed something deeper than your original question — “continuity of logic”, in the sense of “continuous function”. If you imagine you have a lot of inputs to a predicate, then the topology of their truthiness tells you something — and we can talk about “smooth” logic models, where being a little wrong in our assumption means we’re a little wrong in our conclusion. We can then apply tools from analysis, like bifurcation theory. The “halting problem schema” has a bifurcation at the finite/infinite boundary, which isn’t particularly uncommon for high level functions. But it’s important to know, when writing proofs. And generally speaking, places bifurcations can happen are regimes where your model is going to struggle. In the business world, knowing the “logic faults” of your model and keeping yourself in a “smooth regime” is important.