NAMING AND NECESSITY (Harvard University Press, 1980)
(Copyright © 2000 Piero Scaruffi | Legal restrictions - Termini d'uso )
|
Kripke developed a model-theoretic interpretation of various axiom sets for
modal logic. Modality can be represented by recurring to the notion of
possible worlds. In Kripke's semantics a property is necessary if it is true in
all worlds, a property is possible if there is at least a world in which it
is true.
The extensional analysis of language cannot account for sentences that are very common such as those that employ opaque contexts (to know, to believe, to think) and those that employ modal operators (all words that can be reduced to "it is possible that" and "it is necessary that"). These senteces are not extensional, meaning that they do not satisfy Leibniz's law. These sentences can be interpreted in Kripke's model-theoretic semantics. A statement that is false in this universe can be true in another universe. The truth values of a sentence are always relative to a particular world. Tarski's theory is purely extensional (for each model the truth of a predicate is determined by the list of objects for which it is true), Kripke's modal logic is intensional. An extensional definition would actually be impossible, as the set of objects is infinite. Proper names and definite descriptions are designators. Proper names are rigid designators, i.e. in every possible world they designate the same object. Kripke (unlike Frege) carefully distinguishes the meaning of a designator and the way its reference is determined (which are both "sense" in Frege). Then he puts forth his causal theory of naming: initially, the reference of a name is fixed by some operation (e.g., by description), then the name is passed from link to link. A name is not identified by a set of unique properties satisfied by the referent: the speaker may have erronous beliefs about those properties or they may not be unique. The name is passed to the speaker by tradition from link to link. Terms for natural kinds behave in a similar way to proper names. Kripke rejects the view that either proper or common nouns are associated with properties that serve to select their referents. Names are just "rigid designators". Both proper and common names have a referent, but non a Fregean sense. The property cannot determine the reference as the object might not have that property in all worlds. For example, gold might not be yellow in all worlds. Kripke's causal theory of names assumes that names are linked to their referents through a casual chain. A term applies directly to an object via a connection that was set in place by the initial naming of the object. A nonrigid designator is a term that changes its referent across possible worlds. Mental states cannot be identical to physical states because both are rigid designators and they might designate different objects in different worlds. |
| 
| 
| 
|