Well-definition

In any theoretical axiom system, there are indefinite expressions.

Thus, for example, in set theory talked about that a lot a summary of specific and well-distinguished objects of our intuition or our thought to a whole [ is ]. However, it is not explained in detail what is to be a collection of objects. Here is an indefinite expression.

Such uncertainties may lead to a contradiction to the reality experienced or within the axiom system. Kurt Gödel has shown that a system can not be used as proof of his own consistency.

For the purposes of David Hilbert indefinite expressions are a necessary part of a theory of language. According to him, a theory is only at the beginning of a consistent set of system and has no connection with the world. To underline the importance that indefinite mathematical expressions must be kept totally abstract, he said, applied to the geometry:

• Philosophy of Science
• Logic