ABSTRACT
This chapter shows clear understanding and careful application of recent results in logical analysis—extending the traditional syllogism to cover intermediate quantifiers —will confirm one hypothesis in recent grammatical analysis (from McCawley) and (b) disconfirm two others (also from McCawley). Propositions are the entities that possess truth-values, stand in logical relationships (such as entailment), and are the (so-called) objects of some central varieties of knowledge and belief relations (where the subjects of these relations are knowers and believers). Data for semantic analysis and theory (of natural languages and their uses) consists, to start with, of immediate intuitions on word, phrase, and sentence meanings. Rather, the traditional syllogism is low-level description of basic semantic relationships between universal and particular quantifier words and phrases for very simple subject-predicate sentences in light of the simplest basic alternatives for negation.
