Existence only as a result of its presupposition?

Question

Is there an analogy in logic to the paradox that a concept comes into existence only by presupposing it as already existing?

Answer 1

You can compare with one of the basic results of mathematical logic :

Model Existence Lemma If $\Gamma$ is a consistent set of sentences, then $\Gamma$ has a model.

We can paraphrase it as follows :

"if a concept is non-contradictory, than it is instantiated."

See :

• Dirk van Dalen, Logic and Structure (5th ed - 2013), page 97.