Types of Predicates and the Representation of Existential Readings (original) (raw)
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On the Existential Import of General Terms
In his book Logic and How It Gets That Way Jacquette (2010) presents 'the formalization paradox' which emerges from the attempt to formalize a sentence like 'some monkey devours every craisins', where craisins are imaginary non-existent fruits. From this paradox Jacquette concludes the expressive inadequacy of classical predicate quantificational logic. In this paper I analyse the three assumptions supposed in the emergence of the paradox, viz.: (i) colloquial expressions of the same logical form can and should be formally symbolized by applying the same symbolization schema); (ii) 'Some monkeys devours every raisin' is correctly translated as ∃x[Mx & ∀y[Ry → Dxy]]; (iii) uninstantiated predicates can legitimately enter into (meaningful, true or false) predicates-quantificational symbolizations. I fully accept (iii), but reject both (i) and (ii). I argue, firstly, that (i) has at the first glance two possible interpretations, a trivial and a false one. So, I try to establish a third and more reasonable interpretation. Based on this interpretation I argue that ∃x[Mx & ∀y[Ry → Dxy]] is not the adequate formalization of 'some monkeys devours every raisin'. My basic claim is based on a generalisation of Russell's theory of description: just like most sentences of natural language which contain definite descriptions are viewed as entailing existential force which must be made explicit in formaliza-tion, so do we also consider many, although not all, sentences which contain general terms. A criterion for deciding in each possible case if the sentence entails existential force will be presented and defended.
The main goal of this paper is to develop a formal analysis which accounts for both the strong similarities, as well as a number of unexpected differences between two types of generic sentences in English, which minimally contrast in the type of subject: those with indefinite singular subjects, as in (1) (IS sentences, henceforth), and those with bare plural subjects, as in (2) (BP sentences, henceforth): (1) A grizzly bear snores very loudly (- An IS sentence) (2) Grizzly bears snore very loudly (- A BP sentence) I start by reviewing the uniform quantificational-modal representation traditionally assigned to minimal pairs like (1) and (2), and its advantages, and by presenting the problem for the uniform representation, namely a number of old, as well as newly observed differences between such minimal pairs. After reviewing several attempts in the literature to characterize and explain these differences, I propose an alternative account of both the similarities and differences between the two types of sentences which takes them, on the one hand, to have the same basic semantic structure (headed by a modalized generic quantifier, Gen), but to differ in the type of modality, i.e. the type of accessibility relation restricting Gen.
The (information) structure of existentials
Linguistic Variation: Structure and Interpretation, 2019
proper, as they are characterized by different interpretive and formal properties. Results are summarized in section 4. 1.2 Background 1.2.1 Copular constructions The term "copular construction" is generally used in the literature to indicate a structure in which two phrases of any category are linked by means of a copula: 1 (2) XPcopula-YP This structure is related to various types of copular constructions, which allow for different phrasal categories in the positions indicated in (2) as XP and YP (cf. Den Dikken 2006a). Limiting our attention to structures featuring two (major) nominal constituents, at least two types of copular constructions can be distinguished on the basis of their semantic and syntactic properties. In particular, many scholars have proposed a typology of these structures based on the referential quality of the post-copular phrase (i.e., YP in [2]). 2 In order to illustrate this twofold classification, consider the following example (taken from Den Dikken 2006a): (3) [ XP His supper] is [ YP food for the dog] This sentence is ambiguous because the post-copular constituent can be interpreted as either referential or not. 3 In the latter case, it is interpreted as 'his supper serves as food for the dog', whereas in the former the sentence can be
On the Interpretation of Common Nouns: Types Versus Predicates
Studies in Linguistics and Philosophy, 2017
When type theories are used for formal semantics, different approaches to the interpretation of common nouns (CNs) become available w.r.t whether a CN is interpreted as a predicate or a type. In this paper, we shall first summarise and analyse several approaches as found in the literature and then study a particularly interesting and potentially challenging issue in a semantics where some CNs are interpreted as types-how to deal with some of the negated sentences and conditionals. When some CNs are interpreted as types (e.g., Man : Type), a sentence like John is a man can be given a judgemental interpretation j : Man, rather than the traditional Montagovian interpretation man(j). In such a setting, the question is then how to interpret negated sentences like John is not a man (or more complicated sentences like conditionals). A theory for predicational forms of judgemental interpretations is introduced and is shown to be able to deal with negated sentences and conditionals appropriately. A number of examples are considered to show that the theory provides an adequate treatment in various situations. Furthermore, experiments in the proof assistant Coq are performed in order to provide more supporting evidence for this adequacy. Besides the above, we also briefly study the use of indexed types in order to deal with CNs exhibiting temporal sensitivity and gradability.
The structure of criterion predicates
Instrumental by adjuncts have remained ill-understood. So have criterion predicates, one of the types of predicates that can be modified by instrumental by adjuncts. There is also no consensus on the proper analysis of manner-neutral causative predicates, the other major type of predicates that can be modified by instrumental by adjuncts. I propose an analysis of the by locution where both criterion predicates and mannerneutral causatives involve reference to an indefinite predicate and where the function of the instrumental by adjunct is to fill that predicate with content by unification. In this way, long-standing intuitions can be accounted for while well-known problems are solved; in particular, the thesis that the by locution offers two descriptions of one event is vindicated without predicting a symmetry between the two descriptions.