Indefinite expression
In every system of theoretical axioms there are indefinite expressions .
In set theory , for example, it is said that a set is a combination of certain and well-differentiated objects of our intuition or our thinking into a whole . However, it is not explained in more detail what a summary of objects should be. This is an indefinite term.
Such indeterminacies can lead to a contradiction to the experienced reality or within the axiom system. Kurt Gödel has shown that a system cannot be used to prove its own consistency .
In the sense of David Hilbert , indefinite expressions are a necessary part of a theoretical language . According to him, a theory is just a consistent set of sentences in the beginning and is in no way related to the world. To underline the importance of keeping indefinite mathematical expressions totally abstract, he said, applied to geometry :