Undefined terms

"You will know that no doctrine can, without committing the unpardonable sin of circularity, undertake to define all of the terms it employs but that every doctrine must employ one or more terms regarded as being, without definition of them, sufficiently intelligible for the purposes of clear discourse. You will know that for a like reason no doctrine can furnish proof of all its propositions but that every doctrine must contain one or more propositions which it takes for granted, using them without demonstrating them. And you will know that a doctrine can have maximum clarity and cogency when and only when it has the minimum of undefined terms and undemonstrated propositions."
— Cassius J. Keyser, TAT

"Here a semantic experiment suggests itself. I have performed this experiment repeatedly on myself and others, invariably with similar results. Imagine that we are engaged in a friendly serious discussion with some one, and that we decide to enquire into the meanings of words. For this special experiment, it is not necessary to be very exacting, as this would enormously and unnecessarily complicate the experiment. It is useful to have a piece of paper and a pencil to keep a record of the progress.

We begin by asking the 'meaning' of every word uttered, being satisfied for this purpose with the roughest definitions; then we ask the 'meaning' of the words used in the definitions, and this process is continued usually for no more than ten to fifteen minutes, until the victim begins to speak in circles—as, for instance, defining 'space' by 'length' and 'length' by 'space'. When this stage is reached, we have come usually to the undefined terms of a given individual. If we still press, no matter how gently, for definitions, a most interesting fact occurs. Sooner or later, signs of affective disturbances appear. Often the face reddens; there is a bodily restlessness; sweat appears—symptoms quite similar to those seen in a schoolboy who has forgotten his lesson, which he 'knows but cannot tell'. If the partner in the experiment is capable of self-observation, he invariably finds that he feels an internal affective pressure, connected, perhaps, with the rush of blood to the brain and probably best expressed in some such words as 'what he "knows" but cannot tell', or the like. Here we have reached the bottom and the foundation of all non-elementalistic meanings—the meanings of undefined terms, which we 'know' somehow, but cannot tell. In fact, we have reached the un-speakable level."
— Alfred Korzybski, Science and Sanity p. 21, International Non-Aristotelian Library (1933).

 Typical errors about Undefined Terms 

Mostly accustomed to dictionaries, people are convinced that one can define circularly. This is a fallacy of Circular Definition, known even in traditional Aristotelian 'logic'. It is apparent if you try for example to explain the verb "to trade" to a foreigner. To define that term, you use the verb "to exchange" that the foreigner does not know either. Then, you proceed by explaining "to exchange" using "to trade." Do you think the foreigner will understand either word after that? One can also try to explain "white color" to a born-blind person. It is quite impossible to learn a language from scratch, based only on word definitions, as all parents know when they have to point silently to objects/images for their children. One must first know some basic words, which do not need definition, which we understand somehow but cannot define at a given time, the undefined terms. These undefined terms do vary during a person's life, mostly due to education in a very general sense. One conjecture made by Korzybski about these terms is that they are all multiordinal (the converse not being true, i.e. a multiordinal term might not be undefined).

© ESGS, 2002.