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.

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.

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.

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!

0: https://en.m.wikipedia.org/wiki/Mainstream_Science_on_Intell... an editorial written to tell the public that this is not some shocking, fringe claim. You can follow links from the page for the full text.

In particular papal infallibility was not involved in the Protestants’ complaints, and the response to their complaints (Trent) was a council and again has nothing to do with papal infallibility.

The pope was also an absolute monarch at the time, but protestants didn’t care about that aspect.

0: https://www.vatican.va/content/john-paul-ii/en/apost_letters...

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"

People just instinctively know that you need to know which side of the disjunction you're on, and they haven't been trained in classical logic to forget it.