I think you're mistaking my claim for something else. When I say logical reasoning here, I mean the dead simple reasoning that tells you that 1 + 1 - 1 = 1 or that, by definition, x <= y and y <= x imply x = y. You can reach these conclusions because you understand arithmetic or aspects of order theory and can use the basic definitions of those theories to deduce others. You don't need to throw random guesses at the wall to reach these conclusions or operationally execute an algorithm every time, because you use your understanding and logical reasoning to reach an immediate conclusion, but LLMs precisely don't do this. Maybe you memorize these facts instead of using logic, or maybe you consult Google each time but then I wouldn't claim that you understand arithmetic or order theory either.

LLMs don't "throw random guesses at the wall" in this respect sky more than humans do.