Quantification and Second-Order Monadicity

The first part of this paper reviews some developments regarding the apparent mismatch between the logical and grammatical forms of quantificational constructions like 'Pat kicked every bottle'. I suggest that (even given quantifier-raising) many current theories still posit an undesirable mismatch. But all is well if we can treat determiners (words like 'every', 'no', and 'most') as second-order monadic predicates without treating them as predicates satisfied by ordered pairs of sets. Drawing on George Boolos's construal of second-order quantification as plural quantification, I argue that we can and should view determiners as predicates satisfied (plurally) by ordered pairs each of which associates an entity with a truth-value (t or f). The idea is 'every' is satisfied by some pairs iff every one of them associates its entity with t. It turns out that this provides a kind of explanation for the "conservativity" of determiners. And it lets us say that concatenation signifies predicate-conjunction even in phrases like 'every bottle' and 'no brown dog'

Kvantifikacijski vidiki logične oblike v minimalistični teoriji jezika

The monograph ('Quantificational Aspects of Logical Form in Minimalist Program') argues that it is possible to view the Logical Form (LF) of the Minimalist Program and Semantic Form (SF), (implicitly) introduced by virtually all semantic theories, as identical. It does this by (i) defining language L*, a plural-logic extension of the first-order predicate logic, which is rich enough to express the meaning of English superlative determiner (SD) ‘most’, and (ii) constructing an isomorphism between LF and L*-encoded SF.Empirically, the introduction of L* is supported by an original cross-linguistic prediction claiming that a language having an English-like SD also has a definite determiner (DD), like English ‘the’. The prediction is most strongly corroborated by Macedonian/Bulgarian, which is the only Slavic language having the DD.The main features of the constructed isomorphism are the following. Variables of L* correspond to sequences of functional projections in head-complement relation. Predicates of L* correspond to (conceptual and) formal features of LF. Feature projection in LF is predication in L*. There are no explicit quantifiers in LF/L*: the scope of quantifiers is predictable from the occurrences of variables.Finally, the monograph provides the syntactic/semantic analysis of a wide range of constructions, the emphasis being on superlative and comparative constructions, and focus.Monografija dokazuje, da sta skladenjska ravnina minimalistične teorije jezika, imenovana logična oblika (LF), in pomenska ravnina, ki jo (implicitno) uvajajo skoraj vse pomenoslovne teorije, ena in ista ravnina. To stori tako, da (i) definira logični jezik L*, pluralno razširitev predikatne logike prvega reda, ki ima dovolj izrazne moči za zapis pomena angleškega presežniškega določilnika ‘most’, ter (ii) izdela izomorfizem med LF in pomensko ravnino, temelječo na jeziku L*.Empirično je uvedba jezika L* podprta z izvirno medjezikovno napovedjo, ki trdi, da vsak jezik s presežniškim določilnikom angleškega tipa pozna tudi določni določilnik (v angleščini ‘the’). Napoved najmočneje podkrepita makedonščina in bolgarščina, ki sta edina slovanska jezika z določnim določilnikom.Glavne značilnosti izdelanega izomorfizma so naslednje. Spremenljivke jezika L* ustrezajo zaporedjem funkcijskih projekcij v razmerju jedro – dopolnilo. Predikati jezika L* ustrezajo (pojmovnim in) formalnim oznakam LF. Projekcijo oznak v LF enačimo s predikacijo v jeziku L*. Monografija prinaša razčlembe širokega obsega jezikovnih zgradb, s poudarkom na presežniških in primerniških zgradbah ter žariščenju