Lexicalizing and Combining

ing away from the specific content of CAESAR yields the monadic concept ARRIVED(X).Starting with SAW(CAESAR, BRUTUS) and abstracting away from the contents of both saturatingconcepts yields the dyadic concept SAW(X, Y). I assume that concepts have contents, which neednot be linguistic meanings. I follow the usual conventions of using small capitals to indicateconcepts, with variables (‘x’, ‘y’, ...) indicating the number and logical order of saturaters:SAW(CAESAR, BRUTUS) implies that Caesar saw Brutus; SAW(X, BRUTUS) is a monadic concept that applies to anything that saw Brutus, while SAW(CAESAR, Y) is a monadic concept that appliesto any entity that Caesar saw. But as discussed below, I do not assume that the contents ofunsaturated concepts are functions, or that ARRIVED(CAESAR) denotes the value of some functionwith Caesar in its domain. 3 I assume that talk of lexical items expressing concepts is to be understood, eventually, in termsof how concepts are indicated in speech and/or accessed in comprehension. But I do not assumethat each lexical item λ is paired with a single concept C: if only because of polysemy, and thepossibility of different perspectives on the things thinkers think about, a speaker might indicateone concept with a word that fetches a related but distinct concept in a hearer. For me, sayingthat λ expresses C is a simple of saying that λ is linked, in a special indicating/fetching way, toone or more concepts that share a certain form and perhaps a common root; see section two. 4 This divergence can be described in terms of “covert” movement or type-adjustment; see, e.g.,May (1985) and Jacobson (1999). 5 But if events of arriving are not independent of arrivers, no value of the variable inARRIVE(E, BRUTUS) is independent of Brutus, and so ARRIVE(E, X) is not a concept of a genuinerelation. Compare AFTER(E, F), ABOVE(X, Y), and ARRIVE-AT(T, X), whose first variable rangesover times, which are independent of arrivers. Likewise, while SEE(E, X, Y) is formally triadic, the corresponding relation does not hold among three independent entities. In this sense,hypothesizing that verbs indicate concepts like ARRIVE(E, X) and SEE(E, X, Y)—as opposed toARRIVED(X) and SAW(X, Y)—adds one to the posited adicities, allowing for adverbialmodification of event variables, without changing much else. 6 If the adverbial phrases correspond to conjuncts of a complex monadic concept, closed byexistential quantification, the valid inferences are instances of conjunction reduction:∃E[Φ(E) & Ψ(E) & Δ(E)] implies ∃E[Φ(E) & Ψ(E)], which implies ∃E[Φ(E)]. But an instance of ∃E[Φ(E) & Ψ(E) & Δ(E)] & ∃E[Φ(E) & Γ(E) & Θ(E)] need not imply ∃E[Φ(E) & Ψ(E) & Θ(E)] or ∃E[Φ(E) & Δ(E) & Γ(E)]. See Taylor (1985), expounding an argument due to Gareth Evans. The example also shows that values of event variables are not ordered n-tuples consisting ofparticipants and a moment in time; a sharp hit (of y by x) with a red stick can occur at the sametime as a soft hit with blue stick.