Computer proof ‘blows up’ centuries-old fluid equations • Hacker News Board

Re: Computer proof ‘blows up’ centuries-old fluid equations

#221

Post by auggierose » Tue, Nov 22, 2022, 4:34 PM UTC

musingsole wrote: post #220

auggierose wrote: post #217

Earlier quoted context omitted.

I can point you to my favourite logic ;-) Here false is defined as false = (∀x. x) So in this case, it derives its meaning from whatever the meaning of the ∀ operator is. Its meaning is the result of applying the ∀ operator to the identity operation. Nobody is questioning that there are different possibilities for logical systems, and different possible semantics for them. The choice of logical system is up to you, a…

You draw lines and insist there's no space between them.

Not sure what you are trying to say. Care to elaborate?

Re: Computer proof ‘blows up’ centuries-old fluid equations

#222

Post by guipsp » Wed, Nov 23, 2022, 8:03 PM UTC

bheadmaster wrote: post #146

guipsp wrote: post #139

Earlier quoted context omitted.

We have a model of physics which is pretty accurate. The engineers who designed the skyscraper did not even use this model, they used a much simpler one, with known errors. Why? It is simply good enough™. But you can't claim it is even "true" when we know more accurate methods.

My claim is not that the model itself is true - I'm claiming that the underlying mechanisms that rule the world are true and are not subject to change by social consensus. The model is "good enough" for the purpose of creating a building, but that doesn't make the act of "creating a building" any less real, nor the underlying rules that govern matter any less true. Our descriptions are not real - the rules themselves…

Nothing about mathematics describes how the world works.

Re: Computer proof ‘blows up’ centuries-old fluid equations

#223

Post by rsj_hn » Wed, Nov 23, 2022, 8:12 PM UTC

postalrat wrote: post #124

bheadmaster wrote: post #65

Earlier quoted context omitted.

The fact that mathematics gives us power to predict events in the real world makes it independent of social consensus. If everyone in the world believes that 2+2=5, that doesn't make it less true that 2+2=4 - in the sense that I know for sure, if I take throw two rocks on a pile of two rocks, I'll get a pile of four rocks, not five rocks. I hate this sociologist view that everything depends on the social consensus. G…

2+2=4 stops being true when you use a different method of counting.

That's like saying "I am five foot tall" stops being true when you use a different definition of "tall" (switch it to weight, for example). This isn't insightful and it's also false.

People have agreed on how the plus sign should be defined when it comes to adding two integers, and they've agreed on how to write integers, in which case 2+2 is always four. The only way to change that is to change the meaning of at least one of the four symbols "2", "4", "=", or "+" to some private meaning which no one else shares -- e.g. to distort the language in order to sow confusion, which the use of agreed upon meanings for symbols is designed to eliminate.

Moreover this idea that a sentence changes its truth value the moment someone changes the meaning of one of the words in the sentence is not some deep statement or interesting observation, it's just pointing out that language is useful only if people agree on the meaning of the words.