# Frege principle

The Frege principle (also compositionality principle , composition regularity , functionality principle , Frege's principle of meaning ) is a semantic principle according to which the meaning of a complex, i.e. H. expression composed of partial expressions (e.g. a sentence) is determined by the meanings of its parts and the way they are combined. It is a basic assumption of the standard approaches in semantics. It is named after the German mathematician, logician and philosopher Gottlob Frege (1848–1925).

The compositionality principle deliberately leaves open what exactly is to be understood by the term “meaning”; the only assumption is that the atomic, i.e. H. expressions that cannot be further broken down have a lexical meaning.

Occasionally the narrower extensionality principle , which in addition to general compositionality also includes specific extensionality, is referred to as the Frege principle or compositionality principle. For advocates of the extensionality thesis , according to which there is an equivalent extensional statement for every statement, both principles ultimately coincide.

## application

• At the semantic level , a sentence can be viewed as a complex expression, the meaning of which can be determined from the components, i.e. the words or their meanings, and the way they are linked.
• On the semantic level , a word can also represent a complex expression, as in the following example with word formation through composition (word composition, see morphology ). For example, the word “grass green”, which is made up of the partial expressions “grass” and “green”, can be understood as a determinative compound (i.e. the first part semantically defines the second in more detail); in this case, the meaning of the complex expression results: green as grass.
• For formal languages , compositional, often even extensional semantics are usually established. For example, the "meaning" results; H. the value of a mathematical formula such as "3 + 2" from the meanings (i.e. values) of the partial expressions and the type of their composition: The two partial expressions "3" and "2" are connected by the sign "+", i. H. the overall meaning is the result of adding 3 and 2.

## Limits and Criticism

Especially on the semantic level of words, the question can often be asked and rarely clarified beyond doubt with natural languages ​​whether an expression is actually complex or not a completely idiomatized form whose internal structure can no longer be semantically analyzed.

From a pragmatic perspective, the compositionality principle appears inadequate. It lacks the integration of word and sentence meanings "in situations of understanding and contexts of knowledge". The model of compositionality "does not (or only partially) does justice to the true functioning of language-bound communication". The principle encourages a failed "word-isolating structuralist semantics" and neglects the "textual embedding".