I think you are conflating thoughts about laws of logic, T(L), with the actual structure of what logically holds, L.. But the painting of a pipe is not a pipe. And it doesn't need to be.

Since we can notice our thoughts, we can attempt empiricism on our rationalisms, and then we can model the structure of our thoughts on what pragmatically works when we make these attempts. We can form thoughts about what works and call those thoughts T(L). Because what worked actually worked, and what didn't work actually didn't work, we can know that T(L) corresponds to L to whatever degree our thoughts are really about what worked, which we can test empirically.