Classical logic operates off the "All or Nothing" paradigm. And we intuitively think in classical logic terms, because that is how classic logic was developed (apply intuitive logic to itself, to identify faults in our intuitions, then correct them to produce the minimally modified intuitive logic that is coherent). This is why there is so much appeal to classical logic, to yes/no either/or thinking, and to ideologies and dogmas. We humans intuitively think that way.
We have, however, developed a completely different way of thinking which we do in parallel to our intuitive logic either/or. This is empiricism. Empiricism treats the "truth" as uncertain, and subject to investigation. And "truth" models as improvable. See for example sporting stars who, rather than declaring their play to be perfect, continually strive to improve upon excellence, for an example of tentative empiricism in action. Tentative empiricism leads to "likely" or useful answers, which are only locally valid. "Under these conditions, kicking the ball this way works well". The bundle of local answers that empiricism gives us is NOT and CANNOT be logically coherent. It is jsut a bundle of useful rules and guidelines that is incomplete, and may lead to many mutual contradictions.
Science is a formalization of our informal empiricism. As such, it is intrinsically incomplete, incoherent, and a pluralist amalgam of very different and incompatible models. This is a reality about science that rationalists, seeking their One True TRUTH, have tried to gloss over. Our more insightful philosophers of science -- James, Pierce, and Popper leading among them -- realized that science is incompatible with the rationalist vision of One True Truth. The spread of this realization has been a slow process, with many who lean toward science starting from the Logical Positivist view of science as a step-child of logic and an assistant in finding the One Truth.
But today, the consensus among philosophers of science is in favor of pluralism: that science can NEVER be integrated into One True Theory of Everything. AND that not all knowledge is discoverable thru science -- so science is one of several ways to discover "truths". See section 5 of the SEP article on scientific reduction: https://plato.stanford.edu/entries/scientific-reduction/
Most of us humans STILL instinctively think in all/nothing either/or terms. And if pluralism is the case for our world, and even mighty science cannot by definition develop a logically coherent worldview -- then for all/nothing thinking there must be NO truths!!!
But Pragmatism offers a different answer. We have LOCAL truths -- ways to act, ways to think, that are IMMENSELY valuable. We need to learn these local truths, and abide by them. And when they end up in conflict, due to the intrinsic incoherence of pluralism -- there are BETTER and WORSE ways to try to resolve those conflicts. Dogmatism, and violence, are among the worst ways. Openness to self-doubt, dialog, compromise, and possible fusion into a new and mutually compatible local "truth", a Hegelian synthesis, are better ways.
To live in this world, we need to develop judgement, and operate thru humility. There is no formula that we can live by and just turn the crank and get the answer. Thinking thru how to live, is work, and work we need to do, and no answer we have will be the "final answer". But some answers are far better than others. This is the reply to nihilists and "post truth".