Dilemmas of Ambiguity and Vagueness

By Leon Felkins

Email: leonf@perspicuity.net

Copyright 1996-2003

Written December 12, 1995

Latest revision: October 10, 2009

Note: this essay remains unfinished and will be modified as time permits.

"All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally. Godel's Incompleteness Theorem, Church's Undecidability Theorem, Turing's Halting Problem, Turski's Truth Theorem -- all have the flavour of some ancient fairy tale which warns you that `To seek self-knowledge is to embark on a journey which...will always be incomplete, cannot be charted on a map, will never halt, cannot be described." - Douglas R. Hofstadter


In this essay, I shall provide an introduction to the concept of Vagueness and Ambiguity. As a convenience to the reader, the major points will be covered here and will be expanded in detail in the companion essay, "Understanding Vagueness".

Vague or Ambiguous Ideas and Concepts

"Everything you've learned in school as "obvious" becomes less and less obvious as you begin to study the universe. For example, there are no solids in the universe. There's not even a suggestion of a solid. There are no absolute continuums. There are no surfaces. There are no straight lines." - Richard Buckminster Fuller (1894-1983)

Society somehow plods on in a sea of vagueness and ambiguities! Humans routinely live, love, work, go to prison, and die based on vague or ambiguous definitions! The most amazing aspect of it is that it works so well -- in spite of the vagueness and ambiguities. It is not a trivial matter -- in fact it is a very serious matter. People rot in prison and die in wars based on vague definitions and criteria. Let us examine just a few of the vague terms we live by:

Taking Advantage of Vagueness

We all use vagueness to our advantage sometimes in dealing with other people. Our intention is not necessarily to do harm or to take advantage but maybe to avoid hurting someone or to improve communication or a situation. A humorous example is the problem most of us have to face from time to time of being forced to give a "Letter of Recommendation" on someone you may not think too highly of. Check out the link, and you will see how using a tad of vagueness can be helpful.

While in our personal and natural lives, vagueness may not be a problem and, in fact, is quite useful, when it is used in the field of governance, there are serious consequences. Following this essay is an expose of that particular subject called, "Vagueness in Governance". It is strongly recommended that you read it for it could save your life. I'm serious.

Yet, Somehow We Cope in this Vague and Ambiguous World

In a natural state, humans convey meaning even though the terms are vague. We understand "dangerous", "sexy", "wealthy", "skinny", "friendly", and "happy" without knowing the precise meaning. It is the structured society that is managed by a legal structure that has a problem with vagueness. Bureaucrats and computer programmers have a difficult time with vagueness. The rest of us have a general feeling about what the terms mean which is adequate for communications.

The directions that society is going, which is to make every term and definition precise, is a mistake. It appears that Gödel's Theorem of Incompleteness may have more general application. Complex systems seem to get more complex and more inconsistent the more we try to remove the vagueness and inconsistencies. But, sadly, that will not keep us from trying.


[Note 1] The discussion on government in this essay is on the US government in particular. Other governments, however, are probably similar.


BLACK, Max: Perplexities: Rational Choice, the Prisoner's Dilemma, Metaphor, Poetic Ambiguity, and Other Puzzles. Cornell University Press. 1990

On the net: FUZZY SYSTEMS - A TUTORIAL, James F. Brule', 1985

On the net: Otávio Bueno and Mark Colyvan, 'Just What is Vagueness?'

Connolly, William E.: Politics and Ambiguity. University of Wisconsin. 1987

George C. Christie, "Vagueness and Legal Language", 48 Minn. L. Rev. 912 (1963-1964), online at http://eprints.law.duke.edu/247/

Katz, Leo: Bad Acts and Guilty Minds. University of Chicago Press, Chicago. 1987

Keefe, Rosanna and Peter Smith, eds.: Vagueness: A Reader. MIT Press. 1996

On the net: Justin Needle has a wonderful page on Vagueness with lots of references. (Already it looks great, but I think there is much more to come!)

"Fuzzy Logic Introduction", Jeyakody Parthiban, 1996

Pilla, Daniel J.: "Why You Can't Trust the IRS", Real Money magazine, Spring, 1996

On the net: Vagueness, Bertrand Russell, 1923.

On the net: Stewart Shapiro, Primer on Vagueness, May 20, 2005

Sorensen, Roy, Vagueness and Contradiction, Oxford: Oxford University Press, 2001.

Sorensen, Roy, "Vagueness has no function in law", Legal Theory, 7/4: 385-415, 2001.

Sorensen, Roy, A Vague Demonstration, Linguistics and Philosophy(2000) 23: 507-522

Varzi, Achille C.: "Vagueness, Logic, and Ontology", (Published in The Dialogue. Yearbooks for Philosophical Hermeneutics 1 (2001), 135–154). Excellent, non-technical, introduction to the theory of vagueness.

Williamson, Timothy: Vagueness. Rutledge, London. 1994.

On the net: Williamson, Timothy: "Vagueness in Reality",

Back to "the Paradox page".
Forward to "Understanding Vagueness"
Forward to "Vagueness in Governance"
Back to my philosophy page.