Beyond true and false provides a high level overview of non-classical logic. With origins from Buddhist philosophy, they hint at something more utilitarian than mathematical constructs. Paradox is fundamental to our model of the world. Many states can exist beyond the simple true and false. Claims can be Both true AND false, Neither true NOR false, or ineffable. Or potentially any combination of the above. It is also fair to assume that we have not identified all possible combinations.
Freeing yourself from a true/false constraint is a powerful advancement in mindset. The hard part about thinking is asking the right questions. We have the idea that properly posing a question can quickly reveal a solution. Consider that depending on how you pose a question, it may not have an answer. Perhaps your time is better spent on a reframe.
The language we use frames our conventional reality (our Lebenswelt, as it is called in the German phenomenological tradition)
As a thought experiment, consider a typically politicized question or topic. Is it answerable? Can one theorize a data set and empirical model which would yield an answer that all sides could agree to? If not, the core issue is likely something else.