It is very difficult to have a discussion
using words to discuss the semantics of non-word or non-symbolic semantics. I was pointing at several different plausible spaces for semiotics and how these spaces could be spaces for reasoning in the hopes that one of them might be relatable.
If you use words in your mind when you use math, and you use words in your mind when you make or listen to music, etc., then it is very difficult to find a common ground where it is possible to see that these other realms of thought are capable of not only prediction, but also producing evidence that leads to judgement. That is to say, the key aspects of "reasoning." I picked them because I thought they had broad enough appeal to be relatable, and because I do not personally hear words in my head when doing any of these activities, whether it's calculus or tango, but I still find calculus and tango to be places where reasoning occurs.
Some of them, like math or music, are closer to the kind of symbolic thought we use when we discuss things with words. Others, like the experience of g-forces, are not. I present them as a sliding scale between "word based" reasoning and "non-linguistic" reasoning. Perhaps you can think of a realm that better fits for your personal experience of intuition, and inspect whether these intuitions are capable of "real" reasoning in the absence of language, or whether intuition should never be trusted even when you have a great deal of experience in that area. Perhaps in your estimation, anything that cannot produce evidence that is articulable in word form is suspect.
Personally, I find all these methods, including language, to be suspect. I don't find language to be especially better at producing the kind of evidence for prediction, correct judgement, or discourse for reasoning than other methods, unless you reduce "reasoning" to tautologically require it.
One of the best tools of language is that we have writing that allows easy inspection or iteration of the written content; but these things are possible in other realms, too, it's just that we didn't have great tools for introspecting and iterating on their "ideas" except within our own minds. These days, those tools are readily available in many more realms of human insight.