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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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.
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.
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.
No? So nobody in mathematics doubts the Zermelo–Fraenkel set theory axiomatic system?
Who said an engineer should doubt
1+1=2?Doubt about axioms is basically mathematical philosophy.
So you agree doubt about everything is not reasonable in every field?
So it's essential.
Depends on what you mean by "doubt". If you mean <100% certainty, then no. If you mean 50% certainty, then yes.
No it isn't. You will never encounter it in most math fields. Philosophy mostly is what you do when you aren't busy with concrete problems.
What should an engineer do who needs to calculate 1+1 to design a bridge? I hold that anything but "answer 2 and move on" is wasting time that could be used to build a bridge.
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