4 ms·

> 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

> 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.

mnemonicsloth 7y ago
What are you, some kind of Bourbakiste? Let a little intuition into your life.
kxyvr 7y ago
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-beyond-simple-truth 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 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_2 https://link.springer.com/chapter/10.1007/978-94-010-1161-7_... which discusses a 4-value logic system and its application to databases.

4 ms·

> 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

by FiberBundle 7y ago

mnemonicsloth 7y ago
What are you, some kind of Bourbakiste? Let a little intuition into your life.
kxyvr 7y ago
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-beyond-simple-truth 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 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_2 https://link.springer.com/chapter/10.1007/978-94-010-1161-7_... which discusses a 4-value logic system and its application to databases.