Can first principles aid in understanding conflict in interpersonal relationships?

Of course, and I think this is an "overwhelmingly effective" tool.

When we argue, most of the time we're debating "emotions" and "opinions," rather than "facts" and "needs." First Principles are like a small brush that helps you scrub away all the emotions, accusations, and guesses plastered over the surface of a problem, revealing the core "knot" underneath.

Let me give you a common example: a couple arguing.

Surface Problem: "Why did you forget to text me back again!" This sounds like an accusation, right? The subtext is "you don't care about me."

Without First Principles, the conversation would likely go off track: A: "Why didn't you text me back?" B: "I was busy just now, can you stop being so clingy?" A: "Me, clingy? I just wanted to know what you were doing! Are you hiding something from me?" B: "Here you go again, it's so annoying!" ...See? It's over. The topic shifted from "texting back" to personal attacks like "you're annoying / you don't love me anymore."

Now, let's "break down" this problem using First Principles:

The person asking (A) can first ask themselves:

1. Why am I angry that he didn't text back? -> Because I feel ignored.
2. Why am I afraid of being ignored? -> Because it makes me feel insecure and that our relationship is unstable.
3. What is my most fundamental need? -> I need to feel "cared for" and have a "sense of security."

See? From the act of "texting back," we've dug down to the underlying need: "I need to confirm that our connection is solid, and that I am important to you." This is First Principles.

Now, communicate in a different way: "I texted you earlier, and you didn't reply. After a while, I started overthinking and worrying if something had happened to you, or feeling a bit ignored. Are you free now? I just wanted to check in and get a little reassurance."

See how the nature of the conversation completely changes? You're no longer accusing the other person of their actions, but expressing your own feelings and fundamental needs. The message the other person receives isn't "You did something wrong!" but "I need you, I need security."

At this point, the other person is also more likely to lower their guard and address your "core need," rather than refuting your "surface accusation." They might say: "Honey, I'm sorry, I was in a meeting and my phone was on silent. I'll let you know before meetings in the future, or text you back right after, okay?"

To summarize:

The role of First Principles in relationships is to push both you and the other person to move from arguing about "what you should/shouldn't do" (behavioral level) to discussing "what I need/what you need" (needs level).

Once you can clearly see each other's deepest, most authentic needs, conflict is no longer a "you versus me" zero-sum game. Instead, it transforms into a cooperative puzzle: "How can we work together to satisfy both our needs simultaneously?" This can resolve most daily conflicts.