"multiordinal"

"[Multiordinal terms] are such that if they can be applied to a statement they can also be applied to a statement about the first statement, and so, ultimately, to all statements, no matter what their order of abstraction is. Terms of such character I call multiordinal terms. The main characteristic of these terms consists of the fact that on different levels of orders of abstractions they may have different meanings, with the result that they have no general meaning; for their meanings are determined solely by the given context, which establishes the different orders of abstractions." (S&S, 4th. Ed., p. 14.)

Please note that Korzybski said that they "may" have different meaning, and the result in these cases when they do have different meanings on different levels, is that they then have no general meaning.

If a term is to be a multiordinal term, then it must be able to be used about a statement in such a fashion that it can also be used in another statement about the statement it was just used in, and so forth.

As this was explained at some seminars, where S stands for a statement and M stands for a statement with a particular multiordinal term, the expression in general would have the form M(S), and it would immediately be possible to say M(M(S)), as well as M(M(M(S))). A paradigm case is the term 'never', where S="It's bad." and M(x)="Never Say, 'x'."

John:  "It's bad."   S    
Larry:  "Never say, 'It's bad.'"   M(S)   
Moe:  "Never say, 'Never say, "It's bad."'"   M(M(S))  
Curley:  "Never say, 'Never say, "Never say, 'It's bad.'"'"   M(M(M(S))) 

Multiordinal terms are terms that are applied to statements and can be applied to statements about these statements, etc., and the meaning differs at each level. In the example above, one contradicts the other - "reversing" in some sense the overall value of the admonition to John. At each level the "prescription" for John differs. 

A more careful reading of Korzybski ["if they can be applied to a statement they can also be applied to a statement about the first statement"] would be that if S(T) stands for a general statement about some thing, and M(S(T)) is a valid statement, then so is M(S'(S(T))), and M(S"(S'(S(T)))). He does not say that the statement about the first statement must be one using the multiordinal term.

Using the term "agreement" (a word that Korzybski explicitly includes in his list of multiordinal terms), where S="It's bad.", S'(x)="You shouldn't say, 'x'.", S''(y)="It's stupid to say, 'y'.", and M(z)="I agree that 'z'."

The character of what is being agreed to differs at every level.

In the first reading the term never is both multiordinal and used self-reflexively. In the second reading the term agree is multiordinal but is not used self-reflexively.

While knowledge can be put into the following form:

It does not have a different meaning at each level. It means building a model of a process at every stage. The process being modeled is different by increasing orders of complexity, but not in kind. It is applied here self-reflexively.

Korzybski went on to write an entire section on multiordinal terms Section B. Multiordinal terms. (433-442)

A look at that section in the light of modern developments in formal semantic, linguistics, natural language processing, etc., shows that Korzybski was confusing some levels of abstracting.  Later developments in computational grammar show that the meanings that Korzybski attributed to the terms he called multiordinal are actually composite meanings of utterances generated by combining the effects of the meanings of the terms.  Korzybski thought the meanings of the utterances, which can change significantly, were to be found in the terms he called multiordinal.  He appears to have been trying to associate the composite (and therefore changed) meaning of an utterance to the words in the utterance.  Compositional grammar and formal semantics allows us to illustrate very clearly a structural meaning of these words that does not change from level of abstraction to level of abstraction.  It is the overall meaning of the utterance that varies much - primarily due to structural complexity. So in this regard, the term "multiordinal", as Korzybski defined it, is essentially incoherent.  There is no doubt that the structural complexity of the terms Korzybski lists as "multiordinal" is more involved that simpler terms, but the "meanings" of the terms themselves can be diagrammed structurally, and this structure is "the same" for any level of abstraction.  It is only the context of the term that changes, and therefore, the meaning of the utterance.

For example, the term "agree" requires two actors and a subject and a relation or attitude between the actors and the subject.

For actors a, and b; relation R; and subject s - Actor a agrees with actor b if R(a,s) = R(b,s).

In the above example, we have actors J - John, L - Larry, M - Moe, and C - Curley, and subjects b - is bad, s - shouldn't say, and j - judged to be stupid.

Statement formalism
John: "It's bad."
Larry: "I agree that it's bad". 1. R(L,b)=R(J,b)
Moe: "You shouldn't say, 'It's bad.'"
Larry: "I agree that you shouldn't say, 'It's bad'". 2. R(L,s)=R(M,s)
Curley: "It's stupid to say, 'You shouldn't say, "It's bad."'"
Larry: "I agree that it's stupid to say, 'You shouldn't say, "It's bad."'" 3. R(L,j)=R(C,j)
  1. Larry's relationship to something being bad is the same as John's relationship to that same thing being bad.
  2. Larry's relationship to saying something is the same as Moe's relationship to saying the same thing.
  3. Larry's relationship to stupid judgement is the same as Curley's relationship to stupid judgement.

The complexity comes in when the clauses are expanded.  Pay particular attention to the "[]" and "{}" pairs, as they mark the level of abstraction boundaries. I'll colorize them for you, so that they become visually apparent.

  1. s = [R(L,b)=R(J,b)]
    (Now substitute for "s" in 2.)
  2. j = {R(L,s)=R(M,s)} = {R(L,[R(L,b)=R(J,b)])=R(M,[R(L,b)=R(J,b)])}
    (Now substitute for "j" in 3.)
  3. R(L,{R(L,[R(L,b)=R(J,b)])=R(M,[R(L,b)=R(J,b)])}) = R(C,{R(L,[R(L,b)=R(J,b)])=R(M,[R(L,b)=R(J,b)])})

The structural meaning of "agree" has the same form at all three levels, although the complexity varies, and the subsequent meaning of the utterance also varies.  Korzybski claimed that the "meaning" of a "multiordinal" term (for example, 'agree') was different at each level, and hence the term had no general meaning. Clearly he was identifying the "meaning" of the overall utterance, and because it changed, he was claiming that the term itself had no general meaning. Had he known of the later developments in computational grammar and formal semantics, he could have seen that he was confusing different levels of abstraction. Obviously the complexity of 3 makes it more difficult to understand what is agreed to.  Korzybski's rudimentary awareness that "something was different" in the resulting meaning of the utterances at different levels of abstraction was not enough to allow him to distinguish carefully between levels or see that the different structures involved a similar structure at all levels.

As Korzybski was fond of saying, general semantics will need to be revised and will eventually be superseded. In the light of more modern theory, Korzybski's special term, 'multiordinal' has fallen into the category of obsolete.  By modern distinctions the definition Korzybski gives is now incoherent. As late as 1948, Korzybski did not understand these distinctions.  In the preface to the third edition he states, " ... as my work has progressed it has become obvious that a theory of 'meaning' is impossible (page xv ff.), and 'significs', etc., are unworkable."  Claiming that something "is impossible" is one of the things general semantics teaches us not to do. Had he begun to "harden his categories"? Many things have been invented since Science and Sanity was published  How much out of date has Korzybski become? 

Korzybski's term 'multiordinal' can be salvaged simply by recognizing that the terms have the "same" dictionary meaning at all levels of abstraction, but when applied to statements and statements about statements, they significantly alter the meaning of the utterance or sentence they are applied to from level to level.  Perhaps a student might be interested in looking at each of the terms that Korzybski listed and produce structural models using modern linguistic techniques.


Annotated bibliography of general semantics papers
General Semantics and Related Topics

This page was updated by Ralph Kenyon on 2009/11/16 at 00:27 and has been accessed 9445 times at 54 hits per month.