a) A grammatical category (like aspect) and a value of a grammatical category (like perfective) of a specific language are significative units (“signs”). They have a significatum, viz. whatever is shared, at the semantic level, by the aspects of the language, and the significatum of the perfective aspect, say telicity of the situation designated, resp. The difference between a grammatical category and its significatum is in their theoretical status: a sign comprises a significans and a significatum and, consequently, formal (or “structural”) properties, while a significatum does not do this. They do not, however, differ in one being language-specific and the other language-independent (let alone, universal); both are language-specific.

b) A possible complication arises if one assumes grammatical categories at a language-independent level, “cross-linguistic grammatical categories” like “the perfective aspect” as something shared or instantiated by various languages (Lehmann 2018). Such concepts are generally conceived as prototypical concepts. Observe that this language-independent category is not a purely semantic object; it still has some formal properties, e.g. as being the marker of some grammatical process (rather than being a lexeme) and as being a verbal or clausal (rather than a nominal) category.

In typological comparison at the level of grammar, the objects to be compared are commonly grammatical categories and constructions. The issue is what kind of tertium comparationis can or should be used in such a comparison. In principle, this must be some specific parameter constituted independently from the objects compared. The significata of the two categories compared cannot serve as a tertium comparationis because they differ depending on the particular language.

a) Instead, the perfective aspect of language L1 and the perfective aspect of language L2 can be compared, e.g., with respect to their limitation (yes or no) to temporally anterior events. In such cases, the tertium comparationis is neither itself a grammatical category nor the significatum of one, but rather a cognitive function that may be fulfilled by grammatical categories. So far, this corresponds to generally accepted scientific methodology.

b) The methodological situation becomes less straightforward if instantiations of a language-independent grammatical category are compared with regard to how close they come to the prototype (or the focal instance). Since the prototype is constituted by a set of features, the tertium comparationis is, in such cases, not a single parameter but rather a certain combination of values of various parameters.