Bertil Rolf

In a seminal paper of 1923 on vagueness, Bertrand Russell discussed some of the most important problems concerning the nature of vagueness, its extension within the language, and its relation to truth and logic. The present paper inquires into Russell's theory. The following topics will be analysed and discussed in turn in sections 1?5: Russell's definition of vagueness; his claim that all phrases are vague; his theory of the source of the vagueness in our language; his principles for the transmission of vagueness; and his claim that logic is incompatible with vagueness. This paper is an attempt to give a rational reconstruction of Russell's position as expressed in his paper. Compatible passages in other of his works are also studied.

Körner's notion of vagueness, its relation to ostension and the alledged gulf between logic and experience are examined. Ostension is seen not to cause vagueness ~ there are precise concepts of mathematics which can be ostensively introduced. A distinction is drawn between classical logic not applying to the vague world and not applying to the vague language. The claims about logic and the vague world are unverifiable claims about existence. Körner's attempt to elimmate the seeming incompatibility between vague language and logic leads to a Protagorean relativism which is rejected. It is denied that the incompatibility between vagueness and classical logic causes a gulf between two sublanguages; instead, ordinary language is held to contain both and so to be inconsistent