Non-contradiction is a fundamental basis of logic (less so for paraconsistent logics, of course, but I’m talking about normal logic here), and logic seems to be a fundamental organizing principle of semiotic thought, so it’s not without its merit. Often, intolerance of contradiction leads us to throw out ridiculous propositions and even enables us to maintain our sanity. However, an absolute commitment to non-contradiction in all areas, which is an implied virtue (if not always actually maintained), would probably be overdoing it.
As humans, a species of animal, which is a kingdom of Darwinianly evolved biological organisms, we weren’t necessarily optimized for the correct apprehension of truth. We were made to breathe, eat, drink, reproduce, socialize, perhaps make habitats and apparel, etc., and to do and understand all the natural things and elements that go with those things. Truth-in-general, on the other hand, encompasses a much broader arena than beliefs attendant to those specific abilities, even if truth is fundamentally based in utility. (It may seem counterintuitive, but truth-as-utility is a very strong philosophical theory, which I argue for in one of the paragraphs in https://myriachromat.wordpress.com/2022/01/19/the-truth-is-not-out-there/.)
So, there are indubitably many things the average person gets wrong, and, as evidence for this, consider how many things people in general disagree on and sometimes argue over. If two people disagree, one of them has to be wrong. If 12 people all believe different things regarding a particular fact, 11 of them have to be wrong (notwithstanding https://i.imgur.com/8dSrPKA.jpg).
So, how does this relate to the need to be more comfortable with contradiction? When two or more beliefs contradict each other, if we don’t tolerate any contradiction, we must throw out one or both beliefs. We’ll probably choose the belief that’s more fundamental/systemic, is more strongly believed, and/or agrees with the most other beliefs (especially those that are more fundamental/systemic and/or are more strongly believed). If we happen to choose the wrong belief to keep and conform the other belief, then we’ll be wrong about two things instead of one. If we just allow contradiction to exist, on the other hand, we can safely be wrong about any of our strongly held beliefs without compromising other beliefs.
Of course, as implied earlier, sometimes it’s prudent to adhere to the principle of non-contradiction. So, when should we allow for contradiction and when shouldn’t we? I would say we should probably allow for contradiction when it allows us to hold beliefs or perspectives that are beautiful, divine, hopeful, constructive, brightening, forgiving and/or uplifting of ourselves or others, or that connect us with others or with life in the larger sense.
To be perfectly fair, I think there are many exceptions even in most of those categories; in other words, we don’t want to be so open-minded our brains fall out. So, just take the idea of ignoring certain contradictions to heart and use it judiciously. Probably you’ll make some wrong decisions about when to use or not use contradiction, because of wrong beliefs, especially those that are held so deeply that to abandon them would threaten your sanity. But you’ll probably still end up being a little bit Less Wrong, especially about some of those things that are vitally important.
Regarding the likelihood of a more fundamental/systemic belief or frame of reference being wrong, consider that, besides the inherent individual-level weakness in our ability to determine truth, there are the falsities promulgated under any given society via indoctrination and osmosis, and these tend to include fundamental aspects of our worldview. Westernism and the The Enlightenment in particular pose a very deadly frame of reference, which I write more about in some of my other essays. Religion is also a source of misguided fundamental beliefs.
There are some arenas of knowledge in which we may want to be even more tolerant of contradiction, and some in which we should be less tolerant. Mathematics, obviously, is an arena in which there should be zero tolerance of contradiction, because its proofs and consequent “truths” are absolute, so there’s no danger of adhering to non-contradiction causing one to be wrong twice. Also, non-contradiction is a fundamental pillar of math. You can’t have math, or can’t have it in remotely the same form, without non-contradiction. After all, math is nothing more than a specific application of logic, as shown by Frege, etc.
We probably want to be more adherent to non-contradiction in the sciences, too, particularly the hard sciences, because the scientific method makes for a somewhat more objective body of acquired truths. Even it is flawed, though (see The Crisis of Science and the reproducibility problem), so maybe we should allow for some amount of contradiction even in the sciences. On the other hand, non-contradiction is how science progresses, uprooting old and inaccurate theories, so perhaps we shouldn’t.
Note that the presuppositions of physicalism, anti-psi, anti-mysticism, etc. are not scientific per se, they’re just considered to be in accord with science because a lot of scientifically minded people prefer them, they’re more scientistic per se than scientific, and I especially encourage tolerating contradiction with respect to these convictions.
Speaking of mysticism, this is a prime example of an arena in which we should be even more tolerate of contradiction. I don’t mean only with respect to its contradictions with scientism and physicalism, but with respect to contradictions within the domain of mysticism itself. Mystical truths are so holistic, nuanced, complex, subtle, interconnected, multifaceted, multidimensional and open-ended that it’s not readily amenable to strictly logical analysis. I wrote more about this at https://myriachromat.wordpress.com/2018/04/13/notes-on-science-scientism-mysticism-religion-logic-physicalism-skepticism-etc/#Mysticism.
And, since they’re so profound and transcendental, translating them into language is usually a brutal, butchering and misleading reduction, so it’s like the finger pointing to the moon: you’re meant to look at the moon, not the finger. Or it’s like a sign post, so that once you arrive at a certain awareness, you can reflect on the concepts you’ve learned to help clarify it and lead you onward. So, picking apart verbal representations of mystical truths by exposing contradictions, or selecting between them on this basis, can be very misguided.
Note, by the way, that, as hinted at earlier re “(if not always actually maintained),” many people already do hold a lot of contradictions between everyday beliefs and positions and their more philosophical takes, they just don’t do it intentionally or consciously, so they’re kind of hypocritical in that respect. Mostly these are people with the metaphysical convictions of physicalism and/or anti-spiritualism.
If a physicalist were to take their physicalism to heart in every context, they’d probably become a nihilist. If not that, they’d at least not be able to appreciate (and would probably also scoff at) a wide variety of things like song lyrics, poetry, nuances of interpersonal interaction, intuitions and thought constructs that they entertain on a daily basis, because all of these things tend to contain truths or other constructs that ultimately don’t make sense in any way that doesn’t assume something spiritual or mystical. Most people just aren’t conscious enough to realize the contradictions. This is good for the physicalist’s psychological health, though, or bad for their philosophical convictions, depending on how you look at it. I wrote some about these contradictions at https://myriachromat.wordpress.com/2018/04/13/notes-on-science-scientism-mysticism-religion-logic-physicalism-skepticism-etc/#Naturalism, too.