Re:The physicalization of metamathematics and the implicatio...
by solveit on Thursday April 07, 2022 @05:42PM
(#30950688)
> The particular thing that comes to mind repeatedly when reading this is the fact that more or less all of mathematics can be derived starting either from set theory or from logic theory.
No, most of mathematics can be expressed in set theory. It's like saying every program can be written in C. It's more or less true, but the philosophical implications are overblown. That is, it's important that set theory and C are so powerful, but there's nothing[1] special about them in particular, we could just as well choose different foundations/Turing complete languages.
[1] Disclaimer: I am not a set theorist and I presume there's a reason set theorists study ZFC and its more powerful cousins so intensively.
No, most of mathematics can be expressed in set theory. It's like saying every program can be written in C. It's more or less true, but the philosophical implications are overblown. That is, it's important that set theory and C are so powerful, but there's nothing[1] special about them in particular, we could just as well choose different foundations/Turing complete languages.
[1] Disclaimer: I am not a set theorist and I presume there's a reason set theorists study ZFC and its more powerful cousins so intensively.