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felipec  unbelief  1yr ago (felipec.substack.com)   3222 thread views

2+2 = not what you think

felipec.substack.com

Changing someone's mind is very difficult, that's why I like puzzles most people get wrong: to try to open their mind. Challenging the claim that 2+2 is unequivocally 4 is one of my favorites to get people to reconsider what they think is true with 100% certainty.

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there is a difference between “you should have lingering doubt in the face of certainty that you know what exactly is trying to be communicated” and “you should have doubt about things you absolutely know are true”.

“I purposefully did not mention I was thinking about modulo math and let you assume I meant the common notion of + “ doesn’t really convince me of anything except that people disagree about what it means to be dishonest.

I don't need to be thinking about modular arithmetic to doubt 2+2=4, I could do it without having a good reason to doubt.

And I explained in the article Bertrand Russell doubted something much more fundamental 1+1=2, wrote extensively about it, and it's considered serious and important work on the foundations of mathematics.

Do you think Bertrand Russell was "dishonest" for asking people to suspend their belief?

Do you think Bertrand Russell was "dishonest" for asking people to suspend their belief?

No, merely exceedingly rigorous. He set out to prove 1+1=2, then after a lot of tedious work, he indeed proved that 1+1=2 is in fact true, settling the debate confirming what everyone already knew. He didn't actually doubt it, he merely wanted to put it on a formal foundation, and he did.

He wasn't an engineer who was worried bridges would fall if everyone computed 1+1 incorrectly, he wasn't a politician who got challenged on his fiscal plan and needed to double-check his assumptions. He was a nerd who wanted clarity for its own sake, operating at the intersection between pure math and philosophy. That's the field where you would doubt 1+1=2, not because you actually doubt it, but because you expect insight from dispelling that doubt. It's the same level of abstraction as wondering whether you're actually a brain in a vat. In politics or engineering, you can't do that.

That's the field where you would doubt 1+1=2, not because you actually doubt it, but because you expect insight from dispelling that doubt.

It doesn't matter if Bertrand Russell personally doubted it or not, he acted as if it was rational to not believe with 100% certainty something which had not been proven yet, and it was.

The reason he attempted to dispell that doubt, is that absent that proof, it was reasonable to doubt.

It's the same level of abstraction as wondering whether you're actually a brain in a vat.

Which is a valid doubt in philosophy.

In politics or engineering, you can't do that.

You have to doubt in engineering, for the same reason you have to doubt in every field. Bridges have fallen because engineers did not doubt enough.

Not really. I can guarantee you that Russell used 1+1=2 when calculating his daily expenses even before he formally proved it. Had he failed at his attempt to prove it, he would have gone on believing and using it. I can guarantee you he didn't scold any colleagues for using 1+1=2 without proof.

He wanted a formal proof for itself, not because one was needed.

I can guarantee you that Russell used 1+1=2 when calculating his daily expenses even before he formally proved it.

I literally said "it doesn't matter if Bertrand Russell personally doubted it or not".

If I'm not 100% certain a particular chair is not broken, but I sit on it anyway, and you conclude that therefore I believe with 100% certainty that it wasn't broken, you are committing a converse error fallacy.

You cannot read minds, you cannot know why I did sit on that chair, and assuming that you do know is an error in logic.

Even worse is to assume you do know why I checked the chair before sitting on it, and assuming it had nothing to do with my potential doubt.

Doubt is essential in all fields. 100% certainty is extremely dangerous. And I don't see you addressing this at all.

I literally said "it doesn't matter if Bertrand Russell personally doubted it or not".

No one doubted it, because it wasn't actually reasonable to doubt it. Russell wanted to formalize a foundation, he wanted to prove that arithmetics derived from logic, not that arithmetics was true.

Doubt is essential in all fields.

Not doubt about math or fundamental logic. That is only reasonable in philosophy. An engineer who doubts 1+1=2 will never build any bridges, and no bridges will crash because an engineer assumed 1+1=2.

If you doubt the fundamentals, you're doing philosophy. If you want to get anything done, you need to stop doing philosophy. You need to choose some axioms, build a knowledge base and then get to work on questions that are actually in doubt.

100% certainty is extremely dangerous. And I don't see you addressing this at all.

Because right now a fallacious argument is being made for too little certainty, not too much. I'm addressing the bad arguments that are actually on the table.

Not doubt about math or fundamental logic.

No? So nobody in mathematics doubts the Zermelo–Fraenkel set theory axiomatic system?

An engineer who doubts 1+1=2 will never build any bridges

Who said an engineer should doubt 1+1=2?

No? So nobody in mathematics doubts the Zermelo–Fraenkel set theory axiomatic system?

Doubt about axioms is basically mathematical philosophy.

Who said an engineer should doubt 1+1=2?

So you agree doubt about everything is not reasonable in every field?

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