hugh4 (u/hugh4) - Readit News

CarolineW · 9 years ago

Of course they are more likely to believe their intuitions. They also believe that it makes no difference whether or not you swap doors in the Monty Hall problem, and don't believe that with only 23 people the odds of a shared birthday are more than 50%.

To some extent, there is the problem. People trust their intuitions, and their intuitions are often wrong. That's why for some things we need proper proofs.

hugh4 · 9 years ago

But proofs always come back to axioms, and on what basis do we accept axioms? That they sound intuitively right. So we've just kicked the problem upstairs a bit, we can't avoid using our intuition.

Personally I'm more likely to believe 2 + 2 = 4, something I can easily check to my own satisfaction using four objects, than I am to believe the Axiom of Choice.

ingenter · 9 years ago

I believe you're mistaken. There is value in axioms and axiomatic proofs: two different people will most definitively have a different notion of "obvious", and even have a different understanding of a mathematical problem. So a proof may be accepted by one person and rejected by another.

Given a set of axioms and proofs it's possible to mechanically check a proof. It's not quite possible to reliably check proofs otherwise.

hugh4 · 9 years ago

But are people more likely to accept the axioms of Principia Mathematica (and the soundness of every logical step from page 1 to 300) than they are to accept the notion that 2 + 2 = 4 based on intuitive notions of what twoness, fourness and plusness are?