Syncategorematic term

rdf:langString Syncategorematic term

rdf:langString In logic and linguistics, an expression is syncategorematic if it lacks a denotation but can nonetheless affect the denotation of a larger expression which contains it. Syncategorematic expressions are contrasted with categorematic expressions, which have their own denotations. For example, consider the following rules for interpreting the plus sign. The first rule is syncategorematic since it gives an interpretation for expressions containing the plus sign but does not give an interpretation for the plus sign itself. On the other hand, the second rule does give an interpretation for the plus sign itself, so it is categorematic. 1. * Syncategorematic: For any numeral symbols "" and "", the expression "" denotes the sum of the numbers denoted by "" and "". 2. * Categorematic: The plus sign "" denotes the operation of addition. Syncategorematicity was a topic of research in medieval philosophy since syncategorematic expressions cannot stand for any of Aristotle's categories despite their role in forming propositions. Medieval logicians and grammarians thought that quantifiers and logical connectives were necessarily syncategorematic. Contemporary research in formal semantics has shown that categorematic definitions can be given for these expressions in which they denote generalized quantifiers, but it remains an open question whether syncategorematicity plays any role in natural language. Both categorematic and syncategorematic definitions are commonly used in contemporary logic and mathematics.