quantifikation

Quantifikation, in English quantification, is the process of determining, expressing, or measuring the quantity of something. It is used across disciplines to relate a property or a set of items to a numeric value or to a logical assertion about elements of a domain. In science, quantification enables comparability, statistical analysis, and formal reasoning.

In logic and formal semantics, quantification refers to operators that bind variables in predicates. The universal quantifier ∀ denotes that a property holds for all elements of a domain, as in "All humans are mortal." The existential quantifier ∃ asserts that there exists at least one element for which the property holds, as in "There exists a person taller than six feet." The scope of quantifiers affects meaning and truth conditions.

In measurement and statistics, quantification means assigning numerical values to observations or properties. This includes selecting scales—nominal, ordinal, interval, and ratio—defining units, and assessing measurement error and reliability. Quantification supports data analysis, hypothesis testing, and model fitting, and it underpins concepts such as probability, estimation, and inference.

In linguistics and natural language semantics, quantifiers are words or phrases that express quantities, such as every, some, many, and few. They interact with scope, negation, and plurality, producing phenomena such as quantifier raising and scope ambiguity. Quantification thus links syntax, semantics, and pragmatics in language understanding.

Historically, quantification traces to measurement concepts in empiricism and to developments in logic during the 19th and 20th centuries. It remains central to mathematics, computer science, and the empirical sciences, providing a formal and practical basis for describing and analyzing amounts, probabilities, and logical assertions.