definitionsstatements

Definitionsstatements are sentences that specify the meaning, reference, or conditions under which a term or symbol applies. They are used to fix semantics and avoid ambiguity, rather than to report empirical states or describe how the world is. In philosophy of language and formal logic, definitional statements aim to establish clear usage by declaring what a term names or what properties define it.

There are several forms of definitional statements. Explicit definitions introduce a term by stipulating its meaning, such as “A is defined as B,” or by giving a condition that characterizes all and only the things that satisfy it. Stipulative definitions set terms for a particular discussion without claiming universal applicability. Operational definitions tie a term to observable procedures or measurements. Recursive or descriptive definitions define a term in terms of its own instances or properties, often with a base case to ensure coherence.

In mathematics and computer science, a definitions statement frequently introduces a new symbol via a defining equation or rule, for example defining a function f by f(x) = x + 1, or defining a set A as the collection of all x that satisfy a property P. Such statements are designed to be precise and, when used as a definitional extension, should preserve the existing theorems of the theory.

Limitations of definitional statements include potential circularity, ambiguity in natural language definitions, and the risk of conflating meaning with empirical content. They anchor terminology and aid rigorous argument but do not themselves constitute empirical claims about the world.

Related concepts include explicit definitions, stipulative definitions, and operational definitions, as well as theoretical constructs that rely on definitional clarity for effective discourse.