The term ‘tautology’ is ambiguous between two closely related meanings.

In the stricter sense, it refers to a statement that is both true by definition and grasped immediately — similar to how the term ‘axiom’ was understood in Euclidean mathematics.

In the broader sense, it refers to a statement that is true by definition, regardless of whether it is grasped immediately. In this latter sense, nearly the whole of mathematics is tautologous.

When something is called a tautology, the above ambiguity is played on by implying that something is tautological in the stricter sense, i.e. that it states something obvious and uninformative, when it is merely tautological in the broader sense. But the fact that something is contained in the meaning of a term implicitly does not imply that it is contained in the meaning of the term explicitly.

The notion of a tautology further suffers from being part of a longstanding, albeit false dichotomy between claims that are true by meaning, or analytic, and those that are statements of empirical facts. Particularly, claims of existence are thought to belong to the latter category, while claims that bear on the meanings of things are thought to be irrelevant to questions of whether something exists.

But every relevant proof of any conclusion relies on predicating meaningful descriptive claims of objects mentioned in those arguments. When those things exist, meaningful truths about those existing things are deduced from non-empirical claims. Furthermore, not all existence proofs are themselves empirical. Proofs of the existence of fixed points in mathematics, for instance, are non-empirical. Likewise, the existence of the planet Neptune was first implied by a proof from irregularities in the orbit of the planet Uranus, and then confirmed by observation.