Quantification - Natural Language

Natural Language

All known human languages make use of quantification (Wiese 2004). For example, in English:

• Every glass in my recent order was chipped.
• Some of the people standing across the river have white armbands.
• Most of the people I talked to didn't have a clue who the candidates were.
• A lot of people are smart.

The words in italics are quantifiers. There exists no simple way of reformulating any one of these expressions as a conjunction or disjunction of sentences, each a simple predicate of an individual such as That wine glass was chipped. These examples also suggest that the construction of quantified expressions in natural language can be syntactically very complicated. Fortunately, for mathematical assertions, the quantification process is syntactically more straightforward.

The study of quantification in natural languages is much more difficult than the corresponding problem for formal languages. This comes in part from the fact that the grammatical structure of natural language sentences may conceal the logical structure. Moreover, mathematical conventions strictly specify the range of validity for formal language quantifiers; for natural language, specifying the range of validity requires dealing with non-trivial semantic problems. For example the sentence ″Someone gets mugged in New York every 10 minutes″ does not identify whether it is the same person getting mugged every 10 minutes.

Montague grammar gives a novel formal semantics of natural languages. Its proponents argue that it provides a much more natural formal rendering of natural language than the traditional treatments of Frege, Russell and Quine.