If ZFC (or some other theory) implements arithmetic, then the first incompleteness theorem says that if ZFC is consistent then there must be true sentences in ZFC (not necessarily sentences of arithmetic) that can’t be proved in ZFC. Correct?
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If ZFC (or some other theory) implements arithmetic, then the first incompleteness theorem says that if ZFC is consistent then there must be true sentences in ZFC (not necessarily sentences of arithmetic) that can’t be proved in ZFC. Correct?
The same way I know that it’s incomplete when formulated in ZFC (assuming ZFC is consistent), from the first incompleteness theorem.
> Suppose ZFC is part of the universe. Then arithmetic (the model of it as being part of the universe) is complete and consistent.
Why does this conclusion follow?
Are you raising the question of whether mathematical propositions can be justified a posteriori?
Or are you arguing that the incompleteness theorems don’t necessarily apply to theories formulated ‘as part of the universe’?
Then the system you are proposing, does it implement arithmetic or not?
Aren’t you just begging the question by assuming ZFC is consistent to demonstrate that arithmetic is consistent?
Presumably this hypothetical universe implements arithmetic, so it’s not complete.
I don’t think words can intrinsically have the property of “being offensive”, it can only be that particular words offend a particular person. Assume Microsoft had self-reports from every human about which words offend them. How would they turn this data into The Bad Word List? Do they just count the number of people who find each word offensive then put the top N most reported words on the list?
Would I use the algorithm if it told me which words offend the particular recipient of my email or Slack message? Usually when someone reproaches me for saying “something offensive”, they are defending some hypothetical other who they say would be offended rather than reporting that they themselves are offended. So maybe I want the algorithm to tell me which words my email recipient thinks offend other people. Or I’ll just say whatever the fuck I want and deal with the consequences.
You’re saying this expectation doesn’t match reality?
Also it might not be that I treat a human “with reverence” because I believe he is conscience, but rather because I think he is “like me”, his body is like my body, he has parents like me, he has genes like me and he moves like me.
If you say “X doesn’t deserve Y”, then roughly I hear, “I don’t like that X is getting Y”. It’s like you’re asking, “Why should I like Apple’s revenue streams?” I don’t think I can answer that, but can you tell me why I should care about whether you like Apple’s revenue streams or not?
It depends on the system. Claiming that disorder builds up in all systems is false, afaik. From a Google search: Entropy increases in a closed system. In open systems, the entropy is kept low, or decreases
Are you claiming that codebases are closed systems?
> They don't make them easier. They make them POSSIBLE.
Are you arguing about the definition of “easier” or just trying to rhetorically emphasize the impact of tests on refactoring?
Would you agree if I said tests make refactoring A LOT easier?
Seems like we both agree that we’d rather refactor a system with tests than without (all else the same).
> Good tests cover all critical sections of functional specification (what is deemed critical depends on project). If you have functional rules x, y and z somewhere there, there need to be bunch of tests for x, y and z somewhere, ideally fuzzy, fast and without blank database.
You’ve told me what parts of the code you want to test, but not what guarantees the tests make.
> No offense, but you seem new in this business, and your aggression doesn't help at all.
You’re right I’m new. Thanks for your patience.
I’ll retract my comment about formal methods since I’ve never actually used them in a refactor. And I agree that tests make refactoring easier. But none of this demonstrates for me that tests are the “best” tool for facilitating a refactor.
And so, what specific quality guarantees do good tests make?
Where the unstated goal is to prevent hijackers from turning airplanes into aimable missiles? Yeah, I like your argument, what are the counterpoints?
I don’t know much physics, but this word-soup about entropy is mistaken, isn’t it? Because something something about closed systems vs open systems and putting energy into systems (eg, people working on the codebase)?
> The best you can do is to have automatic tests, lots of them, and make them work as intended (good tests are very hard to make).
I’m not sure what “best” means here, but there are other tools for improving software quality beyond tests, including and in particular formal methods.
> Those [tests] make refactoring possible and make specific quality guaranties.
What quality guarantees do tests make? That the build passes the test suite?
I think this point is better stated without claims about value, ie “I know what is best”.
The predictions I make about the consequences of me doing something are more accurate than the predictions I make about the consequences of someone else doing something. Furthermore, my accuracy quickly degrades as the social distance increases.
> Are you this unempathic and selfish in real life?
I do as little as possible for people who do not do for me.
This tautology doesn’t inform me of anything.
Why?
Does emoting about a claim make it true somehow?
For me there is absolutely no difference in paying $1/month and $10/month for a daily driver search engine and I’m letting everyone know this to establish dominance over OP.
This is a democracy people.