Todistettava

Todistettava is a Finnish adjective derived from the verb todistaa, meaning to prove or to witness. The word is used to describe something that must be proven or that is capable of being proven. In mathematical, logical, scientific, and legal language, todistettava is common for labeling statements, claims, or steps that require proof.

Etymology and grammar: Todistettava is the present passive participle (-ttava) of todistaa. It is related to todistus, meaning proof or evidence, and todistaminen, the act of proving. As a modifier, it agrees with the noun it describes in case and number, for example todistettava väite (a proposition to be proven) or todistettavan seikan (a matter that must be proven).

Usage and nuance: In mathematics and logic, todistettava väite translates roughly to "a statement to be proven" or "a provable statement." In legal or argumentative writing it can refer to assertions that require demonstration or supporting evidence. The English translations vary by context: sometimes it conveys “provable” (having a proof) and other times “to be proven” (requiring proof).

Examples:

- Todistettava väite vaatii matemaattisen todistuksen. (A proposition to be proven requires a mathematical proof.)

- Kyseessä on todistettava lause. (This is a statement to be proven.)

Note: Todistettava is a technical term frequently encountered in formal texts, and its precise meaning depends on whether the emphasis is on provability (there exists a proof) or the necessity of proving it.