18 Logical interpretation of Cinque’s table: preliminaries
Several notes are needed in advance.
1. The following logical interpretation does not cover the very fact of the hierarchy existing between the functional heads. Thus, we will consider the rows of Cinque’s table in an arbitrary order.
2. Our interpretation will miss the first row (the area of speech act distinction: declarative [indicative], interrogative, imperative, and so on). We are interested in the internal modal structure only, which is the same regardless to this kind of grammatical distinction.
3. In the original Cinque’s table, there are four rows which are repeated twice with the only distinction in number, either “I” or “II”: repetitive, frequentative, celerative, and completive aspects (“completive I” is meant for both completive-sg and completive-pl). The I-rows and the II-rows differ in the area of quantification only, over either acts (I-rows) or events (II-rows). For both series, the logical structure is the same, and so, we do not differ between them.
4. Thus, the following interpretation is referring to a simplified Cinque’s table: without the first and the four last rows and with an arbitrary rows’ order.
пока что напишу сюда и такое: ))
5. I am very sorry to acknowledge that right now, I don’t know what to do with the Voice row, either. Very probably, it will be not fitting my system, alike the first Cinque’s row. But I will ponder when writing the following stuff, and so, let’s see.
19 Logical interpretation of Cinque’s table: binary oppositions
Cinque follows the structuralist tradition, especially Roman Jacobson, in discerning between “default” and “marked” values of each operator (“functional head,” in his terms). These binary oppositions proved to be useful in various kinds of linguistic analysis, but they were never “deduced” from any logical abstraction.
Seeing from logic’s corner, we are prepared to encounter, in these binary oppositions, some confusion between generalized quantifiers. Indeed, we have seen that for a large branch of logic, the logic of preferences, the quantifiers of ‹1, 1, 1› type form binary oppositions. Moreover, the triplet structures formed by ‹1, 1› type quantifiers look sometime as binary oppositions, too (not to say that these triplets belong to the complete squares of the quantifiers, and we know a priori nothing about the possible linguistic role of the internal negation). The “true” binary opposition looks as A vs B; a binary opposition that is a fragment of the triplet ABC looks as either A vs B or B vs C, that is very similar, but with an important implication of being a part of the triplet structure as a whole.
Such considerations we need to have in mind when approaching empirical binary oppositions of Cinque with a theoretical tool of logical analysis.