Ask HN: Looking back, what have you wasted lots of time on?

Re:Ask HN: Looking back, what have you wasted lots of time on? by mnemonicsloth on Friday August 30, 2019 @04:46PM (#20842542)

I think it depends on what you mean by false. I've always thought of falsity as a continuum. At one end are obvious non sequiturs like 1=3. A little further along are the novice blunders everybody makes while learning the theory. At the far end are propositions where you have to cook up a really abstruse counterexample to show they aren't true. But that's tantamount to saying that they almost are true. And in fact a lot of the time you can treat them as true and not get into trouble.

Physicists, to take a notorious example, spend a lot more time on the real line than mathematicians do, but in their day to day work they ignore most of what we know about the real number system.

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Re:Ask HN: Looking back, what have you wasted lots of time on? by FiberBundle on Friday August 30, 2019 @05:13PM (#20842758)

> At the far end are propositions where you have to cook up a really abstruse counterexample to show they aren't true. But that's tantamount to saying that they almost are true. And in fact a lot of the time you can treat them as true and not get into trouble.

It seems as if you totally didn't get the point of proof based mathematics. Falsity is not a continuum, either something is false or its true. If you can produce a counterexample the proposition is false.

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Re:Ask HN: Looking back, what have you wasted lots of time on? by kxyvr on Friday August 30, 2019 @05:44PM (#20843004)

This is not entirely true and depends on the logic system that you choose. Something that helped open my eyes to the different possibilities is this article, which talks about producing a formal logical system for statements in Buddhism:

https://aeon.co/essays/the-logic-of-buddhist-philosophy-goes...

This is written by a professor that I think has produced some really interesting results. Anyway, he discusses something called a plurivalent logic, which is a kind of paraconsistent logic:

https://en.wikipedia.org/wiki/Paraconsistent_logic

These logical systems allow for more than true or false. For example, they allow for neither true nor false as well as both true and false. Outside of their general theoretical interest, there are direct applications to systems with contradictory information. I like the paper "A Useful Four-Valued Logic" by Nuel Belnap:

https://link.springer.com/chapter/10.1007/978-94-010-1161-7_...

which discusses a 4-value logic system and its application to databases.

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Re:Ask HN: Looking back, what have you wasted lots of time on? by mnemonicsloth on Friday August 30, 2019 @05:25PM (#20842871)

What are you, some kind of Bourbakiste?

Let a little intuition into your life.

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