I'm not so convinced that logic is completely unrelated to the senses. How did you learn to count, add, and subtract mentally? You used your fingers. I don't know about you, but even though I don't count my fingers anymore I still tend to "visualize" math operations. Would I be capable of that if I were born blind? Maybe I'd figure out how to do the same thing in a different dimension of awareness, but I have no doubt that being able to conceptualize visually helps my own logic. As for more complicated math, I can't do that mentally either, I need a calculator and/or scratch paper. Maybe analogues to those can be implemented into the model? Maybe someone should just train a model on khan academy videos, and it'll pick this stuff up emergently? I'm not saying that the ability to visualize is the only roadblock though, I'm sure that improvements could be made to the models themselves, but I bet that it'll be key to human-like reasoning