IGS Discussion Forums: Learning GS Topics: Understanding multiordinality
Author: Ralph E. Kenyon, Jr. (diogenes) Monday, July 10, 2006 - 11:32 am Link to this messageView profile or send e-mail

You all may find multiordinal of possible interest.

Author: Ralph E. Kenyon, Jr. (diogenes) Wednesday, July 12, 2006 - 12:31 am Link to this messageView profile or send e-mail

Thomas Johnson offered the following to illustrate his understanding of multiordinal.


Person1; I am hungry.
Person2; What do you mean?
Person1; I need to eat something.
Person2; What do you mean?
Person1; I haven't eaten anything since breakfast.
Person2; When was that?
Person1; That was 5 hours ago.

These statements do not exhibit the form that Korzybski specified. The form requires that the prospective multi-ordinal term be applied to a sentence. Here is a structuring of the conversation to put it in the form of a statement applied to a sentence. In the first two sentences the restructuring is direct.

What does, "I am hungry." mean?
What does, "I need to eat." mean?

The proposed multiordinal term can only be 'mean', and here it is applied to the two sentence in the conversation. This rendition fails to satisfy Korzybski's structural description because the second sentence, "I need to eat.", is not about the first sentence, "I am hungry." It is another parallel abstraction by self observation from non-verbal observations. To get the form of a sentence about a sentence it would have to be "I need to eat, because I am hungry." With a lot of contrivance, one can say that the sentence "I need to eat." is about the sentence "I am hungry." The sentence, "I am hungry." is actually a lower level of abstraction, but it is really not the subject of the second sentence.

I am hungry = low level report of self observation that could be better expressed as "I feel hungry."
I need to eat is an inference that presumably is built on feeling hungry, but they could actually be unrelated, such as by taking it out of context and talking about the chemistry involved in our scientific model that purports to explain what is going on "beneath" the feelings. In any event, it is clear that the second sentence is not a sentence that is about the first sentence. For that to be true, one could safely put quotation marks about the sentence within a sentence, and that does not work here. They are different levels of abstraction formulations about the body of person1.

Person2's third sentence does not even use the term that is the candidate for multiordinality.

So, the three sentences are.
1. an observation of condition.
2. an inference about the condition.
3. a factual report about past events.

Statements 1 and 3 are both at the same lower level of abstraction, differing only in tense (present and past). Both describe the activity of person1 (present and past).
Statement 2 is an inference., but it is not about statement 1, it is about the state described by statement 1.

There is NO sign of any multiordinalty in this example at all.

You need
a statement.
A proposed multiordinal term applied to the statement.
A second statement about the first statement.
The same proposed multiordinal term applied to the second statement.

That structure is missing in Thomas Johnson's example.

Here is my illustration that shows the structure Korzybski described.


s1. John: "It's bad."
m1. Larry: "I agree that it's bad".
s2. Moe: "You shouldn't say, 'It's bad.'"
m2. Larry: "I agree that you shouldn't say, 'It's bad'".
s3. Curley: "It's stupid to say, 'You shouldn't say, "It's bad."'"
m3. Larry: "I agree that it's stupid to say, 'You shouldn't say, "It's bad."'"

Sentence s2 is about sentence s1.
The multiordinal term 'agree' is applied to both sentence s1 and s2. Moreover, s3 is about s2, and m3 is applying 'agree' at a third level of abstraction.

This is precisely Korzybski's structural defining of multiordinal terms illustrating the term agree.

The meaning of the utterance gets more and more complicated as the abstraction level gets higher.

But John and Larry both think something is bad.
Moe and Larry both think something should not be said.
And, Curley and Larry both think something is stupid.

In all three cases, two people have the same attitude about the same thing.

The structural meaning of the term is the same at all three levels of abstraction.

The relationship of one person to some thing or act is the same as that same relationship is of another person to the same thing.


The multiordinal term has the same meaning at all levels of abstraction, but that meaning is structural, like a propositional function.
When the values are provided for a propositional function, a specific meaning is produced, but without the values, we cannot produce a meaning.
In the formulation R(p1,x)=R(p2,x) we have a relationship between a person and something that is the same for two people.

Just for fun, here is a fifth person agreeing with himself: R(p5,x)=R(p5,x).

What might be something for the Institute to consider is calling for and/or funding reasearch to determine corresponding propositional function structures of other proposed multiordinal terms.
This could be the subject of graduate student research thesis and credit towards a degree in general semantics.

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, July 14, 2006 - 08:08 am Link to this messageView profile or send e-mail

Thomas Johnson wrote:


Person1; I hate going on boats.
Person2; (alarm goes off, 'hate' is ambiguous)What do you mean? Person1; I went on a boat when I was little and fell off and almost drowned.
Person2; (trying to establish the order of abstraction)Interesting, you hate going on boats because you had one bad experience when you were young. Perhaps you hate 'the idea' of going on boats because of trauma you suffered as a child.
Person1; Hey, I never thought of it that way!
Person2 (gee, this GS really works!)

In this example the word 'hate' is used in the first sentence. It is not applied to an existing sentence. In the third sentence, by person2, the first sentence is indirectly quoted, but the rest of the sentence is not about the first sentence. This structural use is not multiordinal, because the term that is offered as being used multiordinally is not being applied to a sentence, and it is also not being applied to another sentence about the first sentence. Moreover, the word hate depicts an attitude relation between a person and an action or object. It is used in exactly the same way in both sentences, although the object in once instance is an abstraction from the prior event. It has the same precise structural meaning in all shown instances. The example illustrates consciousness of abstracting, but it does NOT illustrate multiordinality in any way. It fails to meet Korzybski's structural description of multiordinal use of terms. See multiordinal.

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, July 14, 2006 - 09:13 am Link to this messageView profile or send e-mail

Milton writes:


Some examples of “multiordinality” from my point of viewing. (We can think of multiordinality as a special case of multimeaning.)

... in love with love. ...
... I hate myself ... (I hate I)
... fear of showing fear. ...
... statement about a statement. ...
... Learning about learning ...
... Teaching teaching: ...
... knowing about knowing. ...
... questioning our questions. ...
... thinking about the way we think ...

These constructions all illustrate self-reflexivity of terms. It illustrates the problem and the necessity of differentiating levels of abstraction. It is an application of Russell's theory of types as the solution to Frege's contradiction by allowing self-reflexivity.

However, this too fails to satify Korzybski's explanation of multiordinal.

Make a statement 1.

Apply a proposed multiordinal term to that statement to form statement 1a. Statement 1a contains a multiordinal term AND statement 1.

Now make a second statement about statement 1.

Statement 2 must be a more complex statement contains a direct or indirect quote of statement 1 such that this new statement is about statement 1.

Apply the same proposed multiordinal term to statement 2 to form statement 2a. Statement 2a contains a multiordinal term AND statement 2.

The self-reflexive examples supplied by Nora do not meet Korzybski's criteria.

Self-reflexivity is not a simple matter. Neither is multiordinal. Many words that may be used self-reflexively may be use in a non-multiordinal way, as is the case in Nora's examples.

Nora says: "(I feel fear (statement (1)). I feel fear, that I will show that I feel fear...Statement (2) about statement (1)."

Contrary to her labeling, statement (2) does not have statement (1) as its referent. It has the referent of statement (1), and these are two totally different levels of abstraction.
Statement (1) is a (limited) map of the person feeling state.
Statement (2) is another (limited) map of a different feeling state of the person.

The "territory" can be mapped as follows:
The person has a feeling state of fear in war.
The person is aware of that feeling state. (Consciousness of abstracting).
The person has a second order feeling state of fear with a different object - showing his first order fear to other soldiers.

Feeling1: fear of unknown possibilities.
Feeling2: fear of showing fear.

In both cases, the structure of fear depicts an attitude relation between the person and some event (different events). Those events happen to be related by both levels of abstraction and consciousness of abstraction, with the second order fear being about his own actions resulting from his consciousness of abstracting regarding the first order fear.

Now, the map, in our language uses the word fear to say that he fears showing fear.

This illustrates self-reflexivity of terms, consciousness of abstracting, and levels of abstraction, but it does not illustrate multiordinality.

Multiordinaly has been confused with self-reflexivity for decades. Even at the institute sessions I attended, "never say never" was being used as the paradigm case explanation of multiordinality. But multiordinaly is more complex, and it may or may not involve self-reflexivity.

Look at the quote from Korzybski that Nora supplies:


By multiordinality is meant the possibility of applying a given term to different levels or orders of abstractions. Somebody makes [a statement, and then somebody makes] a statement about that statement,

(1) By multiordinality is meant the possibility of applying a given term to different levels or orders of abstractions.
(2) Somebody makes [a statement, and then somebody makes] a statement about that statement,

Start with (2) and get two statements, the second about the first.
Then apply the given term of (1) to both sentences from (2).
It does not mean that the given term is USED IN both sentences of (2), nor that it is used twice in one sentence.

For the usage of a term to be multiordinal it must be applied to a prior sentence not contanining the term, and it must be applied to a higher level abstraction about the first sentence, also not containing the supposed multiordinal term.)

S1 = sentence 1.
S2(S1) = Sentence 2.

Now apply multiordinal term M to both sentences.
If this can be done successfully, then M is being used multiordinally.

In symbols:
IF M(S1) AND M(S2(S1)) THEN M is a multiordinal use.

(Message edited by nora on July 14, 2006)

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, July 14, 2006 - 09:32 am Link to this messageView profile or send e-mail

Milton wrote with respect to thinking about thinking:


From a gs. perspective, the second thinking usually reflects an Aristotelian orientation --

From my "general semantics" perspective, I find that many novice general semanticists are continually projecting that others are exhibiting an "Aristotelian orientation". (Don't ask me if I have counted them, it's my subjective experince abstraction.) I do not think that to be a mature general semantics perspective. I object to Milton's formulation. Let's NOT suggest to beginners and novices that this is "the state of affairs" as they are likely to take it as "gospel". It can color their seeing and encourage them to see thinking about thinking in a parochial and pejorative way.

As non-Aristotelian thinking is an extension of Aristotelian logic, it includes Aristotelian logic as a proper subset. The problem is not that there is something "wrong" with so-called "Aristotelian logic"; the problem is that it gets misapplied in circumstances where it cannot resolve the issue.

Far too much "anti-Aristotelian" rhetoric has been circulated by supposed general semanticists in the name of "non-Aristotelian". Let's be more carefull with such proclamations.

An extensional orientation would dictate that someone research a sufficient sampling of literature and, using prepared criteria, count the instances of case where the distinction matches. (Subjective perceptions aside.)

(Message edited by nora on July 14, 2006)

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, July 14, 2006 - 09:42 am Link to this messageView profile or send e-mail

Your statement reduces to
I hate my hating that I hate going on boats.
This is not multiordinal. It is using a term with the same structural meaning self-reflexively at three successive levels of abstraction.

The sentences that a multiordinally used term applies to do not include the term itself.

If you said:
It's true that I hate going on boats.
It's true that I hate my hating going ot boats.
It's true that I hate my hating my hating going on boats.

The term 'true' is the multiordinal term used about a sentence, a sentence about the sentence, and a bonus sentence about the sentence about a sentence, but the term hate is merely use self-reflexively.

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, July 14, 2006 - 10:08 am Link to this messageView profile or send e-mail

Sorry Nora,

I sometimes miss which posting belongs to which person due to the way the posting is presented by the message board. I've made this mistake in the past too.

The attribution panels are all the same color, and your name immediately followed Milton's post - like a signature below the message. It would be much more helpful if the heading and the post had the same color, as that would visually tie the two together. The message board alternates colors of text, but it does not alternate colors for the header.

As board moderator, can you change your name to Milton's in the erroneous post?

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, July 14, 2006 - 10:18 am Link to this messageView profile or send e-mail

I have argued in the past that the terms that Korzybski identifies specifically as multiordinal can only be considered multiordinal in their use. Korzybski presents a structural usage definition for multiordinal. Many, if not most, of the terms he lists can be used in simple ways that fail his defining structure. I will stick to "multiordinal use" rather than "identifying" such terms as "multiordinal" simpliciter. If you want to show how such a term causes confusion, I think you need to show it in a multiordinal usage context, not in a simple univocal use context.

Even if you have "assumed" the term "hate" to be one of the terms identified as having a multiordinal use, you have not shown it used in such a way, although you have illustrated some of the problems of using any terms in multi-level abstraction contexts - not the same as multiordinal.

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, July 14, 2006 - 08:17 pm Link to this messageView profile or send e-mail

How is "firstgradelist" being applied to a statement about a statement? It is merely a higher order abstraction that names the class. This is not multiordinality, because none of the "sentences" (names of individuals together with their position) talks about another such "sentence".

In "computer lingo", if X is an array and Y is an array of arrays, one of which is the array X, then a term that applies to array X that also applies to array Y may be multiordinally used, the criteria being that array Y can be said to be "about" array X, but the array Y, by itself is not an illustration of multiordinality.

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, July 14, 2006 - 08:22 pm Link to this messageView profile or send e-mail


In post you write I would tend to avoid making a statement like "It is used in exactly the same way in both sentences." To me, this shows an elementalistic preference for word definitions over experience, rather than allowing experience to define words.

Would you, perhaps, be satisfied with "It is used in structurally the same way in both sentences."

How are "preferences" "elementalistic"? I understood that "elementalistic" applied to the use of terms that "split" that which cannot be split in the territory such as using time and space instead of time-space, or body and mind instead of body-mind.

How does one infer "preference", and how does it become "elementalistic", from this statement? Please explain this reasoning or abstracting process.

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, July 14, 2006 - 08:50 pm Link to this messageView profile or send e-mail

Ben asks, How is a multiordinal term different from a variable, as in a math equation?

A variable takes on a number of possible values.
The multiordinal use of a term works more like a function that can operate on both objects and functions.


In object oriented programming, a function is just another object - one that returns a value, so the multiordinally used fuctor m operates on an object at one level and it also operates on a function that operates on the first object.

Let P be a functor that takes an argument that can be (1) x an individual item for sale, or (2) A() a function that returns the average sale price of an object, given an object.

Then P(x) is the price of that object, and P(A(x)) is the average sale price of that class of objects.
x is a variable which can have individual items.
A(x) is a function which takes a variable argument or paramater.
P(x) is multiordinal functor because it can return either the price of the individual item or the average price of the class of which the individual item is an instance.

In computer implementations, the functor P must first determine the class (level of abstraction) of its argument. It then branches to two different routines depending on at what level of abstraction it is being executed. The general term for this in the industry is "overloading". The functor has multiple meanings (routines to be executed) depending on the type of arguments it is passed.

If I say A + B and both A and B are numbers we get a sum, but if both A and B are strings, we get the concatenation.

Example 1: A=25 and B=45: Result 70.
Example 2: C='Ad' and D='am': Result 'Adam'.
Example 3: E='25' and F='45': Result '2545'.

The "+" operation is "overloaded".

This is a good example of multiordinality in use in computer science contexts. The "meaning" depends on the context,

Here's a proper illustration.

What is A + B + C ? (Left to right presidence).

It is ((A + B) + C) which is (70 + 'Ad') which is '70Ad'.