syncategoremata, (1) in grammar, words that cannot serve by themselves as subjects or predicates of categorical propositions. The opposite is categoremata, words that can do this. For example, ‘and’, ‘if’, ‘every’, ‘because’, ‘insofar’, and ‘under’ are syncategorematic terms, whereas ‘dog’, ‘smooth’, and ‘sings’ are categorematic ones. This usage comes from the fifth-century Latin grammarian Priscian. It seems to have been the original way of drawing the distinction, and to have persisted through later periods along with other usages described below. (2) In medieval logic from the twelfth century on, the distinction was drawn semantically. Categoremata are words that have a (definite) independent signification. Syncategoremata do not have any independent signification (or, according to some authors, not a definite one anyway), but acquire a signification only when used in a proposition together with categoremata. The examples used above work here as well. (3) Medieval logic distinguished not only categorematic and syncategorematic words, but also categorematic and syncategorematic uses of a single word. The most important is the word ‘is’, which can be used both categorematically to make an existence claim (‘Socrates is’ in the sense ‘Socrates exists’) or syncategorematically as a copula (‘Socrates is a philosopher’). But other words were treated this way too. Thus ‘whole’ was said to be used syncategorematically as a kind of quantifier in ‘The whole surface is white’ (from which it follows that each part of the surface is white), but categorematically in ‘The whole surface is two square feet in area’ (from which it does not follow that each part of the surface is two square feet in area). (4) In medieval logic, again, syncategoremata were sometimes taken to include words that can serve by themselves as subjects or predicates of categorical propositions, but may interfere with standard logical inference patterns when they do.
The most notorious example is the word ‘nothing’. If nothing is better than eternal bliss and tepid tea is better than nothing, still it does not follow (by the transitivity of ‘better than’) that tepid tea is better than eternal bliss. Again, consider the verb ‘begins’. Everything red is colored, but not everything that begins to be red begins to be colored (it might have been some other color earlier). Such words were classified as syncategorematic because an analysis (called an expositio) of propositions containing them reveals implicit syncategoremata in sense (1) or perhaps (2). Thus an analysis of ‘The apple begins to be red’ would include the claim that it was not red earlier, and ‘not’ is syncategorematic in both senses (1) and (2). (5) In modern logic, sense (2) is extended to apply to all logical symbols, not just to words in natural languages. In this usage, categoremata are also called ‘proper symbols’ or ‘complete symbols,’ while syncategoremata are called ‘improper symbols’ or ‘incomplete symbols.’ In the terminology of modern formal semantics, the meaning of categoremata is fixed by the models for the language, whereas the meaning of syncategoremata is fixed by specifying truth conditions for the various formulas of the language in terms of the models. See also FORMAL SEMANTICS , QUANTIFICA — TION , SYLLOGIS. P.V.S.