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Logic. Quantification. Semantics. Pragmatic. Philosophy of Language.
Quantifying expressions have been part of the history of philosophy and logic at least since Aristotle’s creation of syllogism. Another pivotal moment in the history of these expressions is the introduction of the formal system in Frege’s Begriffsschrift, which includes axioms for quantifying individual objects and concepts. Since quantifiers are also a type of concept, Frege calls them "second-level concepts". With the advent of model theory (in the 1950s) the semantic notion of "interpretation" promotes a Copernican revolution in this field of study and in the way of defining Fregean "concepts", by emphasizing on quantifying expressions. Such a revolution does not merely consist of a new way of presenting Frege’s quantifiers but has made it possible to expand the range of quantifiers that can be implemented. This opening to new possibilities is due, basically, to the work of Mostowski (1957) and Lindström (1966) that develop the notion of generalized quantification. There are, however, limits both to this implementation and to the interpretation of certain natural language quantifiers. The dependence of an expression on a context is one of the barriers that natural language imposes on formal logic. In this sense, Grice in 1975 makes room in his ’Logic and Conversation’ for another look at the "logic of ordinary language". This thesis proposes an analysis of the various attempts to formalize quantifiers in natural languages. We start from an approach that investigates logical and pragmatic aspects of quantifiers and aim at a classification of quantifiers that we believe can elucidate problems on the limits of definitions of these expressions.