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I am unconvinced that "first-principles thinking" is the problem here. Surely one can refute the original argument without having to debunk axiomatic logic itself.

For example, one could argue something like this: Even though increased access to other people's money can cause founders to make irresponsible decisions, raising money has other advantages that tend to offset this.

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I think the idea is, when you argue from first principles, you are implicitly assuming that you know all of the relevant first principles. Since you're human and imperfect, there is always a chance that you don't. How to know?

Well, empirically, check whether the conclusions you get, seem to hold up to reality. The author's experience was that taking investment $$ was necessary (or at least often useful) in a startup, so this put him on the lookout for what missing first principle would explain this.

It doesn't mean axiomatic logic isn't useful, it means that just because the logic seems sound, doesn't mean the conclusion is reliable, because there could be missing axioms (in this case, that profitability is the objective of a company, when cash flow is a more fundamental fact and profit is often either present or not depending on how you do the accounting).

Thanks Ross for the reply. I believe that this is a misunderstanding of how propositional logic works. If the propositions or axioms that you start with are sound, and if you correctly apply all inference rules, then the propositions that you derive will also be sound. "Missing axioms" that you did not use do no matter, regardless of their soundness.

A "missing" axiom, in my experience, is not truly a missing axiom that otherwise has no impact on other axioms. A "missing" axiom is one that exposes a bad assumption in another axiom currently being relied upon.

For instance. Socrates is a man, all men are mortal, therefore Socrates is mortal.

But then you discover that a couple of eons have passed and Socrates is still alive. Clearly there must be a "missing" axiom. And after some investigation you realize that Socrates is a Venusian man, and Venusians are immortal.

"Socrates is Venusian" is a missing axiom, but really the problem is that "All men are mortal" is actually false, since it had implicit assumptions that "All men are human" (false) and "All humans are mortal" (true).

Again, I am sorry for being direct, but this does not make sense. If a Venusian man is immortal, then the "axiom" (preposition) that all men are mortal is false. In other words, the issue is not that the preposition "Socrates is Venusian" was missing but that the preposition "all men are mortal" is false.

It is possible to develop significant mathematical theory without using some axioms. For example, mathematicians sometimes choose not to use the "axiom of choice" when working with Zermelo–Fraenkel set theory. That does not mean that mathematical theorems proven without using the axiom of choice are invalid, even if you later assume that this axiom is true (or false).

The point is that the axiom that all men are mortal was thought to be true, and then was later discovered to be false. My comment was actually in agreement with your previous comment.

Of course they matter. We're discussing arguments that apply in the real world, not in math theory.

In math, if you have this axiom:

  f(x) > 5 for all x >= 20

you are not then allowed to change it with a later axiom

  except when x is divisible by 240

However, in real life this happens a lot. I have a company that is taxed a fixed amount per year... except for the years where I make over 100k euros, in which case things become quite complicated. If I omit the second part (which is not impossible, given that I never made over 100k euros a year with that company), and suddenly get a big payout from someone, the result will be very different from my initial estimation - as sound as it was WITHOUT that additional axiom / assumption / rule.

This has definitely nothing to do with any of what I said.

This is the entire crux of the article's critique of first-principles (axiomatic) thinking being a full-proof way to guide decision-making.

The inability to logically prove that first principles comport with, or not, (some unknown) aspect of reality due to missing information.

"The map is not the territory", "unknown unknowns" come to mind...

Let me just add to this. Discovering new information (or new "axioms") will not change the truth of your previous conclusions if you did everything correctly, but you may find that the information you believed before was incorrect. In general, I believe it will be better to use a probabilistic model for most real-world cases since it is very difficult to find "axioms" for almost anything.

The logic isn't sound though, that's the issue. Let me try to simplify it even more and annotate

    1. Not raising money give you more skin in the game (valid observation)
    2. Skin in the game is an advantage (valid observation)
    3. There exists at least one advantage of not raising money (valid conclusion)
    4. You should not raise money (NOT VALID conclusion)

You can't go from a single argument in favor of something to that thing being favorable overall.

I think this is the difference between a valid argument and a sound argument. A valid argument means the conclusion follows from the premise, kinda like the quoted argument in the article which seems to be valid.

A sound argument is one whose premises are also true. This is where the quoted argument in the article fails. The premises either are false or don't apply to all startups. This is basically what the author means by a argument that is missing premises. It's not really that a premise is missing, but that without additional into it may seem like the argument is sound,but with additional into you realize it is not sound and therefore leads to a different conclusion instead.

Isn't it sort of like Gödel's incompleteness theorem, there's no way to prove your first-principle was a correct axiom to start from. Experience will guide this.

>debunk axiomatic logic itself

He's not though. Your assumptions can be wrong, even if your incremental logic is correct according to the first principle. He's saying the correctness of axiomatic logic will lead you down the wrong path.

No, he is saying that he agrees with the assumptions and the way they are used to construct other propositions, but disagrees with the outcome, and therefore there must be something wrong on a higher level with the logical system itself that is being used here. I think what's actually happening here is much more banal.

>Isn't it sort of like Gödel's incompleteness theorem

Forgive me for being curt, but no, this is absolutely nothing like either of Gödel's incompleteness theorems.

He's saying there's something wrong with getting fooled by a series of valid logical assertions into thinking the original axiom applied to the context in which one is making it... there are "unknown unknowns". There's something wrong with trusting that principled thinking will always hold because it held before, in what might have been a different context.

He's not debunking the validity of the chain of truth statements, but "first principles thinking"...letting this logic guide one down a path that doesn't comport with reality (which might have context one is unaware of).

I think it matches up with incompleteness quite well.

Any set of axioms can never tell you for sure if you're in a context that has other missing and more valid axioms.

You can modify your axioms with experience, but then you're back in the position of not knowing if this is the final set of axioms that will always comply with reality.

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