Aristotle, Russell or Quine have thought about the theory of meaning and the philosophical applications of the notion of ambiguity for logic, but it was the German mathematician Gottlob Frege who introduced a unique understanding of meaning as sense and reference into early modern philosophy that paves the way to accurately define one type of ambiguity in particular: lexical ambiguity. This essay aims to show the nature of ambiguity, the dilemma that ambiguity as a linguistic phenomenon poses for logic and the different types of ambiguity.
Ambiguity is a phenomenon imbued in natural language where a word or phrase has more than one distinct meaning. This implies that different but equally valid interpretations are possible. How to know which interpretation is intended and what argument is being put forward? If it isn’t clear what the meaning of a proposition is, then there is no understanding of what exactly is being discussed and this might result in an error in reasoning unless the context disambiguates the argument. If sentences that constitute an argument are ambiguous, what exactly does ambiguity refer to then? When working on number theory as a logical endeavour, Frege1 had to come up with conceptual innovations to handle the difficulties that arose from the notion of equality of names, signs and objects. Therefore, he distinguished “sense” (intension) from “reference” (extension). The intension of a term denotes the internal content of a term. It encompasses the attributes, properties or the quality of a term connoted by its definition. The extension of a term is a set or classes of things to which the designated term corresponds and to which it extends to. It describes the range of applicability of a term in the world. Thus, ambiguity refers to the intensions of a word or phrase, to its necessary and sufficient conditions that define the scope of a term.
There are different types of ambiguity: structural, lexical, cross-reference, pragmatic and spoken. Structural ambiguity occurs in the way a sentence is put together. “She is an English teacher” could either mean that she teaches English or that she comes from England. Lexical ambiguity occurs when one word can be understood in different ways such as “bank” which means either river bank, financial institution or blood bank. Then there are ambiguities of cross reference when it is not clear which pronoun (reference) links back to a name. Pragmatic ambiguity occurs when a sentence can be used to do different things (speech acts) and even spoken ambiguity when the pronunciation of two words is too much alike to differentiate.
Ambiguity is a lack of clarity that hinders the assignment of a truth value to an assertion. Logical statements are unambiguous and thus, ambiguity is a real concern for logic but a real treasure for rhetoric. The uncertainty arising from ambiguity creates a void that persuasion fills.
To me she speaks; she moves me for her theme:
What, was I married to her in my dream?
Or sleep I now, and think I hear all this?
What error drives our eyes and ears amiss?
Until I know this sure uncertainty
I'll entertain the offer'd fallacy.
Shakespeare: The Comedy of Errors, II, 2.