The Semantics Of Individual Terms

Philosophers have discussed the proper names embeddedly and harvestly since Frege opened the epoch of modern logic. Frege, Russell, Kripke, etc., analyzed and explained this problem, and their views are not the same: Frege did not make the distinction between proper names and descriptions, and thought that difference in other aspects between proper names and descriptions can be tolerated as long as their references are the same; yet Russell strictly distinguished proper names from descriptions; and Kripke regarded proper names as rigid designators, and descriptions as non-rigid designators. These discussions enrich the theory of philosophy, and accelerate the research and development of philosophy. We can see that they are both philosophers and logicians, so we may find the grounds of their different kinds of analysis of proper names in first-order and modal logics. Briefly speaking, the recognition of proper names depends on the logical properties of individual terms.The logical properties of individual terms can be analyzed in both syntactical and semantic aspects. From syntactical perspective, individual terms are divided into two basic types: the first type is simple individual terms; the other is complex individual terms. Simple individual terms conclude individual variables and individual constants. We can get complex individual terms produced by combination of simple individual terms and a functional expression. The logical properties of individual variables and individual constants are different, the formulae combining with predications and quantifiers are different whether seen from the standpoint of first-order or modal logic. In semantic perspective, the interpretation of individual constants is determined if the structure used to interpret non-logical symbols is given, yet interpretation of individual variables is determined by value-assignments. The truth-conditions of quantified well-formed formulas containing individual variables can be determined only in terms of the interpretation of predications in it. That is to say, in terms of the notion of satisfaction. We can discuss the logical properties of individual terms of proper names and descriptions. While through different logical systems, such that first-order logic and model logic, we can get different ideas of proper names, so Frege, Russell and Kripke get the conclusions above. Traditional logic concerns with common terms, not individual terms, so when applying those rules about the notion of class to individual terms will lead to many difficulties. Traditional logic and modern logic have so many differences. The analysis of individual terms is the most important way of distinguishing one from the other.According to the property of individual terms and the different discussions of proper names, we can see the relations between logic and philosophy clearly. Logic is important to the philosophy.