# Plural To Thesis For instance, (2) can be formalized as $\tag\label \Exists \Forall (u\prec xx \rightarrow Au \amp Tu)$ And the Geach-Kaplan sentence (3) can be formalized as $\tag\label \Exists [\Forall(u\prec xx \rightarrow Cu) \amp \Forall\Forall(u\prec xx \amp \textit \rightarrow v\prec xx \amp u\ne v)].$ However, the language $$L_$$ has one severe limitation.In two important articles from the 1980s George Boolos challenges this traditional view (Boolos 19a).

A predicate $$P$$ that isn’t distributive is said to be For instance, the predicate “form a circle” is non-distributive, since it is not analytic that whenever some things $$xx$$ form a circle, each of $$xx$$ forms a circle.

Another example of non-distributive plural predication is the second argument-place of the logical predicate $$\prec$$: for it is not true (let alone analytic) that whenever $$u$$ is one of $$xx, u$$ is one of each of $$xx$$.

This translation allows us to interpret all sentences of $$L_$$ and $$L_$$, relying on our intuitive understanding of English. Applying $$\Tr$$ to (\ref), say, yields: of plural first-order quantification based on the language $$L_$$.

Let’s begin with an axiomatization of ordinary first-order logic with identity.

But in recent decades it has been argued that we have good reason to admit among our primitive logical notions also the plural quantifiers $$\forall$$ and $$\exists$$ (Boolos 19a).

More controversially, it has been argued that the resulting formal system with plural as well as singular quantification qualifies as “pure logic”; in particular, that it is universally applicable, ontologically innocent, and perfectly well understood.

But the existence of two or more objects may not be semantically required; for instance, “The students who register for this class will learn a lot” seems capable of being true even if only one student registers.

It is therefore both reasonable and convenient to demand only that there be at least one object satisfying $$\phi(x)$$.

The traditional view, defended for instance by Quine, is that all paraphrases must be given in classical first-order logic, if necessary supplemented with set theory.

In particular, Quine suggests that (3) should be formalized as $\tag\label \kern-5pt\Exists(\Exists\mstop u \in S \amp \Forall(u\in S \rightarrow Cu) \amp \Forall\Forall(u\in S \amp \textit \rightarrow v\in S \amp u\ne v))$ (1973: 1: 293).

• ###### Plural Quantification Stanford Encyclopedia of Philosophy

We will refer to this admittedly vague claim as the Logicality Thesis. Since the corresponding languages are interpreted.…

• ###### From Plurals to Superplurals In Defence of Higher. - UTIA

In this thesis, after introducing the debate on plurals in Chapters 1 and 2, I turn to de- fending the legitimacy of the notion of higher-level plural reference. To this.…

• ###### Irregular Plural Nouns—Word Patterns and Tips Grammarly

Plurals of irregular nouns can trip up even native English speakers. To make a plural of a word ending in -f, change the f to a v and add es. thesis, theses.…

• ###### Irregular plural nouns Grammar & Punctuation Rules.

Confused on Irregular plural nouns? Learn the definition of Irregular plural nouns, usage, examples & grammatical rules. ✓ Learn more. thesis, theses.…

• ###### Plural vs. Possessive 'S' - University of Manitoba

Nouns that end in an -is are replaced by -es in the plural. Thesis singular becomes theses plural. Count nouns that end in -f pluralize by changing to a –ves.…

• ###### ABSTRACT DISTRIBUTIVITY AND PLURAL ANAPHORA.

This dissertation is an investigation of the semantics of sentences exhibiting plural. issues about distributivity and plurality that arise in cases of plural De Se.…