No need to imagine, it's enough to look into non-Euclidean geometry (obtained by excluding Euclid's fifth axiom), non-standard models of geometry, or reverse mathematics (studying which axioms are necessary for a specific theorem to be provable).
These are not possible, as x can be 7 only if y is 7, and likewise for 8. Semantics isn't based on sets, but on non-deterministic assignments to variables: y is either 7 or 8 and x is either y or 2.
It's a social construct in the the same sense anything not directly verifiable using senses is. Is there an Eiffel tower in Paris? Most people haven't seen it, so they can only accept the social consensus that it is there.
If one can afford it, they can travel to Paris and check themselves. The same with mathematical truth: if one has means (time, intelligence, access to training), they can check the proof themselves. Otherwise they need to trust the consensus.
So again, is the truth in mathematics just a social construct? In some sense, I guess, but probably not the one some people might assume hearing such a statement.
To illustrate the point further, once you get to Paris how can you be sure it's an Eiffel tower? I guess you have to ask the man in the street. See the truth of it is a social construct. And whether you accept this as truth is a social construct, and so on. QED.
A social construct has nothing to do with simple facts about the universe. And whether the Eiffel tower exists as an object at a particular spot as indicated on maps is such a fact. And if there were maps that would place it elsewhere, those maps would be a lie. Even if the every single map ever made and every other person would deny that there is such a tower at that position one could still go there and check for oneself.
Maybe you are talking about the name? The fact that we call it the Eiffel tower? Well, that tower has a history and again one could lie about the history, who built it, how it was historically called as a matter of fact etc. But an observer would have seen who actually built this tower. It's a fact.
TikTok is not good for getting deep understanding of things, but it is great for discovery. you can get familiar with the surface level so you have a better idea where you want to dive deeper
I like the idea - does it support .gitignore though? I wasn't able to find anything in the documentation and GitHub issues seem to be confusing in that regards. If it doesn't, it might be hard to use with tools that create temporary or output files in the directory, such as compilers, LaTeX, some editors, etc.
I fully agree, thousandfold price increases would suggest that processes that control prices in free market system had become unstable. In such cases I'd agree with state intervention. Fortunately it doesn't happen that often.
> Also, this doesn't really apply to housing.
Correct, it's more complex there and some of the reasons are mentioned in the article.
No need to imagine, it's enough to look into non-Euclidean geometry (obtained by excluding Euclid's fifth axiom), non-standard models of geometry, or reverse mathematics (studying which axioms are necessary for a specific theorem to be provable).