From an ontological point of view, the object area of some scientific discipline like general comparative linguistics consists of entities of different kinds. It is, however, not the case that there is one kind of entity which are prima and secunda comparationis and another kind which are tertia comparationis. Instead, being a tertium comparationis is a use in linguistic method that some entity is being put to. Consequently, the question ‘what is a tertium comparationis in language comparison’ is not answered by identifying a particular kind of linguistic object. Instead, suitability of an entity as tertium comparationis depends on the nature of the primum and secundum comparationis and on the research question.
There was, roughly between 2010 and 2020, extensive discussion on the nature of ‘comparative concepts’ in general comparative linguistics. The expressions comparative concept and tertium comparationis were often used as synonyms, as if there was, in linguistics, a specific kind of concept which was by its nature “comparative” and therefore the born tertium comparationis. However, a tertium comparationis is not a particular kind of thing or (scientific) concept. Apparently, some things are being mixed up there:
- There are sets of extralinguistic entities which bear certain relations to language and which a linguistic investigation may consider as stable and thus take for granted. Some of these come under the concept of (pre-)linguistic substance, i.e. that (cognitive-communicative and phonetic) matter which is structured in terms of significata and significantia of language signs (including constructions). With a suitable degree of abstraction, these entities can be considered as universal, i.e. as matter underlying all language systems. In more concrete terms, these may be concepts like ‘girl’ and ‘water’ and communicative functions and operations like ‘referring’ and ‘asking’.
- Every language systems consists of sets of significative units (language signs) which combine paradigmatically into categories and syntagmatically into constructions. Although this structuring is done inside each language, there are cross-linguistic similarities to such an extent that categories and constructions of different languages can be viewed as instantiating more abstract interlingual categories and constructions. Their locus is at the typological level. I.e., a language may or may not have such a category or construction, or may have a category or construction that bears a certain degree of similarity to the interlingual entity. Examples are categories like the personal pronoun or the preposition and constructions like the complement-clause construction or the possessive (or nominal) attribute construction.
None of the entities characterized is per se a “comparative concept” or a tertium comparationis. Leaving the (never explicated) term ‘comparative concept’ alone, they may, however, be turned into tertia comparationis as follows:
- A generic property may be conceived that consists in coding a given concept in one of a set of conceivable ways, or in coding a given operation in one of a set of conceivable constructions. Languages may then differ in the ways that they code the concept or the operation. In this case, the tertium comparationis is not something that a language may have or lack, but instead something that a language codes by a means that can be located on some (possibly multidimensional) parameter. The tertium comparationis is then this parameter.
- A generic property may be conceived that consists in having or lacking the linguistic category or construction in question. In a more complicated theory, this may not be a yes-or-no question. Instead, a category or construction of a particular language may come more or less close to the interlingual concept. In this set of cases, the tertium comparationis consists in having a value of this generic property.
As for the purpose of such a comparison, it was said above that one may use the tertium comparationis to establish an order of some epistemic interest in the field of such objects. However, as usual in an empirical science like linguistics, the methodology is not unidirectionally deductive. In gathering data to be compared, one always finds categories and constructions that defy the comparison because the tertium comparationis does not apply to them in a straightforward way. If they are not to be discarded as irrelevant to the problem at hand, they will lead to a refinement of the underlying theory. In case #1 above, they will lead to a richer or modified understanding of interlingual notions and communicative functions and operations. In case #2 above, they will lead us to reconceive the set of interlingual categories and constructions.
References
Lehmann, Christian 2005, “Zum Tertium Comparationis im Sprachvergleich”. Schmitt, Christian & Wotjak, Barbara (eds.), Beiträge zum romanisch-deutschen und innerromanischen Sprachvergleich. Akten der gleichnamigen internationalen Arbeitstagung (Leipzig, 4.10.-6.10.2003. 2 Bde. Bonn: Romanistischer Verlag; 1:157-168. 
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