aeneasmackenzie

All describable or recognizable complexity is part of the subcountable set of computable subsets of N. Higher infinities thus mostly contain fake elements about which nothing can be said, so they don’t feel any bigger.

They don’t exist as concepts. A rational number whose square is 2 is (convenient prose for) a formal symbol describing some object. It happens that it does not describe any object. I am claiming that many objects described after the explosion of mathematics while putting calculus on a firmer foundation to resolve infinitesimals do not exist.

List functions like that need to be handled carefully to ensure termination. Summations of infinite series deal are a better example, consider adding up a geometric series. You need to add “all” the terms to get the correct result.

Of course you don’t actually add all the terms, you use algebra to determine a value.

I hold that the discovery of computation was as significant as the set theory paradoxes and should have produced a similar shift in practice. No one does naive set theory anymore. The same should have happened with classical mathematics but no one wanted to give up excluded middle, leading to the current situation. Computable reals are the ones that actually exist. Non-computable reals (or any other non-computable mathematical object) exist in the same way Russel’s paradoxical set exists, as a string of formal symbols.

Formal reasoning is so powerful you can pretend these things actually exist, but they don’t!

I see you are already familiar with subcountability so you know the rest.

This is really just the constructive/classical argument but I want to be specific.

You just named a function and specified a property you want it to have. However no function with this property meaningfully exists. We can manipulate the symbol just fine, but we can never look inside it because it’s not real. Classical mathematics was developed before computation was relevant and the question of decidability arose fairly late, it makes more sense to consider it an early attempt at what is now called intuitionistic mathematics. The halting problem disproved excluded middle.

This document plays at least two shell games, declaring that “homosexuality” as its own concept is recent (within 200 years) but then smoothly omitting this when discussing scripture, instead of analyzing scripture and then inserting the modern concept. No wonder it doesn’t find any condemnation of a concept it excluded from consideration!

It then does a similar trick where the authors of the New Testament are acknowledged to have poor Greek in many cases but then using specific word choice to claim they meant an extremely forced reading, relying on the previous trick a bit too.

There’s even a discussion of how nitpicking word choice is bad practice earlier in the same document!

Industrial knitting machines can make entire garments without human involvement, but a person will probably still fold it and sew a label onto it.

Compcert guarantees that the executable that comes out does what the code that went in said, it doesn’t guarantee much about the code that went in.

This is just a polite fiction and no one is ever punished for giving illegal orders or for following them. Bloody Sunday resulted in absolutely no consequences for 1 Para. Tiger Force had illegal orders as their priority, were investigated and found guilty, and then absolutely nothing happened. The My Lai massacre resulted in a slap on the wrist for one guy.

“The taste of their food and the beauty of their women made British men the best sailors in the world.”

Elaborate marble runs are very popular, although many people use steel balls instead.

He was “just following orders”, which has been an airtight defense for the members of Tiger Force. If they’re going to be rounded up along with all the other Americans known to be guilty of war crimes, fine prosecute nazi soldiers. But if not their immunity should be equally as strong.

AZ average students per class is 18. $21/hr for 2000 hours is $42k. Double it to overaccount for total cost of employee. Where's the $96k remaining going?

I'm not going to analyze further, I don't live in AZ. But you should check out the actual answers. Teachers could make more without spending more on education. Or rather spending more on education and less on "education"

So you claim it was a total coincidence he went after Soviet agents? The witch analogy here is that there are real witches but they are so powerful/well hidden witch hunters cannot find them and are diverted to patsies. This wouldn't mean witch hunting is bad, just that we needed better witch hunters.