The index of synthesis and the index of fusion
The problem with the traditional fourfold classification is that languages rarely fall neatly into one of the four classes. For example, English is not quite an isolating language – it has some inflection – but it is certainly not an agglutinating or a fusional language (Old English was much closer to being a fusional language, though). Another problem is that sometimes the inflectional system of a language falls into one category, but the derivational system fits better into another. English again can serve as an illustration: English derivational morphology is actually not that far from being agglutinating, as an example like operationalizability (operat-ion-al-izable-ity) suggests.
One way of dealing with these problems is to give up the fourfold classification in favor of two different scales, which Comrie (1981/1989: 51) calls the ‘index of synthesis’ and the ‘index of fusion’. The index of synthesis looks at how many morphemes there are per word in a language. Isolating languages will have few morphemes per word – in the most extreme cases, only one morpheme per word. Agglutinative or polysynthetic languages, on the other hand, will typically have many morphemes per word. And because this is a scale, languages like Samoan, or English can fall somewhere in-between the extremes.
he index of fusion, in a rough sense, measures how many meanings are packed into each morpheme in a language. High on the index of fusion would be Latin inflection, where at least three different concepts (for example, gender, number, and case in nouns, person, number, and tense in verbs) can be packed into a single morpheme. Low on the index of fusion would be an agglutinative language like Turkish, where each morpheme carries only one inflectional concept (for example, case or number, but not both together).
There is no reason why we could not look at the derivational and inflectional morphologies of a language separately and see where they fit on these two scales. In terms of inflection, English would be low on the index of synthesis, but we might place it higher on that scale if we’re looking at English derivation, since many words in the language are formed by compounding, prefixation, or suffixation. Similarly, we might class English higher on the index of fusion if we’re looking at verbal inflection (the suffix -s carries the meanings ‘third person’, ‘present’, and ‘singular’ packed together in a form like walks) than if we’re looking at derivation, where each morpheme typically has one distinct meaning
