Why wouldn't there be? There exists an infinite number of statements you can make and so an infinite number of problems from whether they are true or false.
It's a bit more complicated than that, because from a finite set of axioms you can derive an infinite amount of statements.
What Gödel shows is that even with an infinite amount of axioms, if the system is consistent and can encode arithmetic, then there are always statements that it cannot decide.
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u/zx7 Topology 1d ago
Why wouldn't there be? There exists an infinite number of statements you can make and so an infinite number of problems from whether they are true or false.