# What are "non-trivial formal systems"? [closed]

In Godel’s incompleteness theorem, his two statements relate to “non-trivial formal system”, but how are these determined? Is 1+1=2 one of these? What about P vs NP?

• $1+1=2$ is not a system... neither is P vs NP... Begin by reading about formal systems on wikipedia. Apr 10, 2017 at 17:48
• "primitive symbols", "defined language", isn't that the very basis of mathematics? Apr 10, 2017 at 17:53
• @GoodwinLu Yes. Do you find that odd? Apr 10, 2017 at 17:59
• The point is that mathematics doesn't have to look or feel or work the way that we are used to. It depends on what symbols we have available and defined, how they interact with one another, how logical implications work, and what we take for granted at the start. The study of formal systems allows us to study abstract scenarios where things don't necessarily work the way we are used to. The system as a whole is not just an expression, but rather the collection of all possible expressions, implications, rules, etc... Apr 10, 2017 at 18:01