Can first principles thinking help entrepreneurs make decisions between equity dilution and control?

Yes, absolutely, and this is precisely the kind of "dilemma" that first principles thinking is best at solving.

To put it plainly, the reason we often perceive "equity dilution" and "control" as contradictory is that we treat them as ultimate goals. But when you think with first principles, you have to dig a layer deeper and ask yourself a fundamental question:

What is my ultimate purpose in starting this business?

The answer to this question isn't "to maintain control" or "to avoid diluting shares." These are processes and means. Your fundamental purpose might be:

To build a successful product that millions use.
To solve a societal problem and create immense value.
To build a great company that transforms an industry.
To ultimately achieve personal financial freedom.

Once you've clarified this underlying "original intention," let's revisit "equity" and "control."

1. Redefining "Equity" and "Control"

What is equity? It's not a scoreboard for your personal wealth; it's the fuel you use to attract resources (capital, talent). Without fuel, the sports car called "company" won't go far.
What is control? It's not about satisfying your desire to be the "boss"; it's the steering wheel that ensures the company car stays on track towards the "destination" you initially set.

2. Decisions Become Clear

Now, when you face a fundraising decision that requires equity dilution, the question is no longer, "Should I give up X% of my equity?" Instead, it becomes:

"Will the capital, resources, and partners I gain by giving up this X% equity allow my company to reach that 'ultimate goal' faster and more steadily?"
"If I stubbornly cling to my equity, will the company die midway due to lack of funds? How then can I achieve my 'original intention'?"

Similarly, for control, the question transforms into:

"Is the control I retain (e.g., board seats, veto power) sufficient for me to maintain the core strategic direction?"
"Am I rejecting a top-tier investor who could take the company to new heights, all for 100% absolute control? Will this kind of 'control' actually limit the company's growth and move me further away from my 'original intention'?"

Here's a simple example:

Your goal is to make a "big cake" of immense value.

Clinging to it: You knead the dough yourself and can at most make a 1-pound small cake, which you own 100%.
Diluting equity: You give up half your equity and bring in a top-tier baker (investor) who provides the best oven and ingredients (capital). Together, you make a 100-pound giant cake. You only own 50%, but the value of your 50% is far, far greater than the 100% of that small 1-pound cake.

First principles thinking is like clearing the fog, allowing you to always focus on the goal of that "big cake," rather than obsessing over the amount of "dough" in your hands. It helps you understand that both equity and control are merely tools. Your decision criterion is singular: which choice maximizes your ability to achieve your ultimate entrepreneurial purpose?

So, it's not a choice between "dilution" and "control," but rather a choice between "clinging to a small dream" and "collaborating with others to achieve a big dream."