On "Similarity of Structure"

AUG 21, 1992

© Copyright 1992 by Ralph E. Kenyon, Jr.

Korzybski pointed out that we use language to create verbal maps and that the map is not the territory. He often comments on the dissimilarity in the structure between language (map) and "reality" (territory). He has further stated that mathematics is a language which constructs maps which are similar in structure to the territory.

Modern general semanticists have interpreted this, along with other Korzybskian formulations, as a prescription for us to attempt to construct our linguistic maps with a structure more similar to the structure of the territory.

I have heard various general semanticists argue that the term 'structure', along with the terms 'order' and 'relation', can be taken as an undefined term in Korzybski's system. If this is so, what can the phrase 'similarity of structure' possibly mean? Obviously, everyone who advocates the prescription has something in mind, but I doubt any two can have the "same" thing in mind.

General semanticists also generally eschew identification, that is, they deny that any two things can be the same -- in particular, any map and the territory it represents. They claim that no two things can ever be the same.

I see something potentially inconsistent about combining the prescription and the claim. It has to do with what we generally mean by the term 'similar'. The term 'similar' derives from the term 'same'. What do we mean when we say that two things are similar (absolute perspective) or that two things are more similar (relative perspective) than two other things?

• In geometry two objects are similar if they have the same number of each kind of part, arranged in the same relation to each other, but the sizes of the parts of one are all smaller (or larger) than the corresponding parts of the other by the same proportion. An object is thought of as composed of a number of parts bearing spatial relationships to each other.
• In philosophy two objects are more similar to each other than two other objects if they share a greater number of properties. An object is thought of as composed of a number of properties, some of which could be called meta-properties -- properties of properties. Two objects are one object if they have all the same and only the same properties. The number or proportion of properties they have which are the same is a measure of their similarity.
• In general semantics I know of no definitional formulation which attempts to quantify or qualify what 'similar' means. It seems to be taken for granted that we will know what each other means by the use of the term. We have lots of claims, some rather vociferous, that the term 'same' is not operational in general semantics. 'The map is not the territory' is often paraphrased as: 'The map is not the same as the territory'. This would suggest that the word 'same' is indeed cashed out in general semantics as it is in common usage as meaning identical, (an eschewed activity or concept).

It seems inconsistent to me that the proscription against identity presupposes and uses that very identity.

Well, let us presume that we have a working understanding of the term 'same'. "These are the same keys that started my car before." "This is the same house I left this morning." In a temporal sense, the term 'same' is used to refer to what one previously referred to. Something is the same if I can see it again. I re-cognize the same thing I cognized before. 'Same' gets cashed out in terms of the nervous system's ability to abstract and "recognize" events, places, things, etc. Even the word 'recognize' presumes that one "cognizes the same thing again".

'Similar', on the other hand, is almost the same. (Pun intended.) We usually cash out 'similar' by changing the level of abstraction of our view. We look in terms of the "structure" of something and compare it to the structure of the other thing compared. By 'structure' we usually mean a contextually determined way of breaking the thing down into parts, properties, characteristics, etc. The same method of breaking down must be used on both comparands. Geometric plane figures are broken down into line segments which, when intersecting, relate to each other by angles. Physical objects are broken down into physical parts, if they can be, otherwise into surface geometric configurations, or substance, or into properties, or etc. Words are broken down into letters, or syllables, or "definitions" -- arrangements of other words --, or etc. Two things are similar if they have a sufficient number of parts which are the same and which bear the same relation to each other -- and the sufficiency is in the "mind" of the beholder.

Postscript, March 22, 1997.
This paper was intended to ask a very serious question about the foundations of general semantics. A fundamental formulation of general semantics is based upon and uses Aristotelian identity. To date no one in general semantics has offered any significant response to this paper. It was submitted to both the Institute and to the International Society; neither has chosen to publish it - thereby denying the possibility of appropriate time-binding analysis. I began to think that the general semanticists in power" do not want to look carefully at their own system.

October 27, 2000 - Additional discussions