Nichtanalytische

nichtanalytische is a German adjective meaning “non‑analytic.” It is used in several scholarly contexts, most notably in mathematics, linguistics, and philosophy of science. In mathematics a non‑analytic function is one that does not possess a convergent power series representation in any neighbourhood of a point in its domain. Such functions cannot be expanded into Taylor or Laurent series; classical examples include the absolute value function, the sign function, or the function defined by \(f(x)=e^{-1/x^2}\) for \(x\neq0\) and \(f(0)=0\). These functions are smooth (infinitely differentiable) yet fail to be analytic because their Taylor series converge to a different function.

In the philosophy of language and epistemology, notelaatty is often used to describe facts or statements that are synthetic, that is, not logically entailed by the meanings of the terms involved. The distinction between analytic and synthetic propositions, introduced by Kant and revisited by philosophers such as W.V.O. Quine, underlies debates over empiricism and a priori knowledge. A nichtanalytische proposition requires empirical verification and cannot be true merely by definition. The term also appears in discussions of Wittgenstein’s rule‑following paradox, where the meaning of words depends on usage rather than innate definitions.

The adjective is thus applied in any domain where a clear boundary between “defined by the terms” and “requiring external justification” is relevant. It underscores the limitations of formal systems: not every mathematical or linguistic relation can be reduced to analytic, self‑contained expressions.