>>13353359no, they are another arm of the trilemma
>>13352795>- WeiningerI suppose this was more an incel shitpost than anything else.
In formal logic, it's also a question of the grammar of the language. Is A a constant?
In OP's pic, when interpreted in first order logic for example, the statement really is
>for all A holds that A = AWhat can you do with equality? E.g. substitution.
How does one prove equality?
A=A is interesting when considering how to implement equality.
E.g. Peano arithmetic judges (1+2)^2 = 9 but of course the left hand side is intentionally different. E.g. we have to put work in to find out what normal form expression (SSSSSSSSS0, here) is is.
See e.g.
https://en.wikipedia.org/wiki/ExtensionalityA big topic is how your logic system / type theory implements function equality.
Are two functions f,g the same if, given the same inputs, they give the same outputs?
>for all x. f(x)=g(y)Or are two functions the same if all their properties are the same? More decidably, are they the same once the result of passing them to any higher order function is the same
>for all F. F(f) = F(g) (indecernables)
All interesting questions.
