Chasing Chwistek, A Discussion of Multiordinal Terms, or Why Did Korzybski Call It “General Semantics”?


I don’t read Polish.

This fact frustrates me to an extent, because it has seemed almost certain to me that for me to understand why Alfred Korzybski called his field “general semantics,” I have to read the writings of Polish logician Leon Chwistek.  Or maybe I have to read a bit of German, because the reason for the term may be locked away in a Chwistek title written  auf Deutsch.

I can be a persistent little bugger, and my rather undying quest for solving the mystery as to why Korzybski called it “general semantics” continued recently, and I feel I may have made some progress.

First off, here is what I understand.  In some way or another, Korzybski pulled the term “general semantics” from the writings of Leon Chwistek, quite possibly his Neue Grundlagen der Logic und Mathematik.  In referencing this work in Supplement III of Science and Sanity, Korzybski writes on page 753:

Analysis finds that certain of the most important terms we use; such as, ‘yes’, ‘no’, ‘true’, ‘false’, ‘all’, ‘fact’, ‘reality’, ‘existence’, ‘definition’, ‘relation’, ‘structure’, ‘order’, ‘number’, ‘is’, ‘has’, ‘there is’, ‘variable’, ‘infinite’, ‘abstraction’, ‘property’, ‘meaning’, ‘value’, ‘love’, ‘hate’, ‘knowing’, ‘doubt’.,., may apply to all verbal levels and in each particular case may have a different content or meanings and so in general no single content or meaning. I call such terms multiordinal terms (m.o). The definition of such terms is always given in other m.o terms preserving their fundamental multiordinality. In other words, a m.o term represents a many-valued term. If the many values are identified, or disregarded, or confused, we treat a fundamentally many-valued term as one-valued, and we must have every kind of paradox through such an identification. All known paradoxes in mathematics and life can be manufactured by the disregard of this fundamental multiordinality. Vice versa, by formulating the general semantic problem of multiordinality we gain means to discriminate between the many meanings and so assign a single meaning in a given context. A m.o term represents a variable in general, and becomes constant or one-valued in a given context, its value being given by that context. Here we find the main importance of the semantic fact established by Skarzenski [accents in his name omitted] [,] that the ‘logical’ freedom from contradiction becomes a semantic problem of one-value. But for application we must have a four-dimensional, [non-elementalistic], [non-aristotelian], extensional system, based on structure., and the complete elimination of identity.

Whoa.  That’s a heapin’ handful.  Let me try to break that passage down into something more understandable.  First off, you can skip the list of terms Korzybski lists off in the beginning because they will confound you more than help you at this point.  What’s more important is Korzybski’s definition of “multiordinal terms.”

In general, it is agreed that Korzybski’s meaning for the term “multiordinal term” is a bit vague, and where it actually seems to make sense, its importance within general semantics is a bit, I don’t know, puzzling.  Ralph Kenyon has an internet-popular explanation of multiordinal terms which in my opinion misunderstands the concept by expecting the notion of multiordinal terms to be more of a logical concept than Korzybski ever wrote.  (Sorry, Ralph!  We do draw some similar conclusions about the idea, though!)  From what I’ve been able to glean to date from Korzybski, the “invention” of the concept of multiordinal terms helps to solve particular logical problems that create verbal paradoxes, or just general verbal chaos.  More frankly, it’s a newback then way of seeing words so there aren’t contradictions in what you’re saying.  I’ll see if I can create one  such paradox wherein the concept of terms-being-multiordinal clears up the paradox . . .

Let’s look at the process of abstracting as discussed in general semantics.  It is a sequence of natural steps.  First, there exists the event level.  From the event level, we perceive something in our mind (i.e., mind-body), which manifests as an object.  This object in our mind has notably fewer characteristics than its correspondent event-level existence.  With that perception in mind, we recognize it as similar to a concept we have, which we label “apple.”  This concept has fewer characteristics than the object apple in our perceptions, and far fewer characteristics than the event-level “thing.”  We also have the concept we label “fruit,” which represents far fewer characteristics than the concept apple, the perception, and the event-level “thing.”  So we are talking here in this process of abstracting about 1 “thing” plus 3 other resultant “things.”

We’ll call the product of each of these latter 3 steps “abstractions.”  That is, the perception in our mind is an abstraction, the concept labeled “apple” is an abstraction, and the concept labeled “fruit” is an abstraction.  If you take note, what the word “abstraction” represents here is three very different things.  In one case, it represents something that will seem more or less concrete to us (the object).  In another case, it represents something that is a bit more of a representation (the concept apple).  And in the last case, it represents something that seems a bit more like a class (the concept fruit).  It’s probably better not to qualitatively differentiate these abstractions like that, but instead to quantitatively differentiate them.  So we might say that the perception represents or is composed of, say, 100,000 characteristics, the concept apple 1,000 characteristics, and the concept fruit 10 characteristics.  The point is just to differentiate how different each of these things we call “abstraction” are.

If we don’t differentiate the abstractions, we can run into problems.  For example, we might try to make a blanket statement about abstractions, but find that it’s too hard to talk about perceptions in the same way as classes.  The word “abstraction” is part of the problem because we use it for both of these different things.  We practically act as if a box that contains 100,000 items is the same thing as a box that contains 10 items.  It doesn’t take much processing to figure out that 100,000 items > 10 items.  But when we talk, we often don’t make these differentiations, so we end up with confusing identifications like a box that contains 100,000 items = a box that contains 10 items.  We erroneously think, “The image in my head is (the same thing as) a fruit.”

Here is about where Korzybski’s notion of multiordinal terms comes in, in my opinion.  Note that we are talking about steps in a process.  There’s a 1st step, a 2nd step, and a 3rd step.  “1st,” “2nd,” and “3rd” are referred to in mathematics as ordinal numbers.  Keeping that in mind, a multiordinal term would be a term that stands for each step in a process.  The term “abstraction” fits that definition of “multiordinal term” well, because we call the product of the 1st step “an abstraction,” the product of the 2nd step “an abstraction,” and the product of the 3rd step “an abstraction.”  That is, we have a 1st abstraction, then a 2nd abstraction, then a 3rd abstraction.  So “abstraction” would be a multiordinal term.  The word “step” would also be a multiordinal term, because it stands for each point in the process.  “Point,” too, would be multiordinal in this context.  But returning to our example abstracting process, the abstractions are ordinally different–both in when they happen in the sequence of steps in the process of abstracting, as well as in the magnitude of characteristics they represent.

If we don’t call attention to the multiordinality of the term “abstraction,” we run into our problems when we start talking about abstractions.  We want to see all of these as “essentially the same!” when they are significantly different.  However, if we do call attention to the multiordinality of the term “abstraction,” we can avert this problem.  That is, if we cite, “The term ‘abstraction’ is multiordinal,” we are saying that “not all abstractions are the same,” that “in fact, they are different in ordinality,” that is, “they represent different orders of abstracting,” that is, “they represent different numbers of characteristics.”  The perception represents an extraordinary number of characteristics, the concept apple represents few characteristics, the concept fruit represents far fewer.  By citing upfront “The term ‘abstraction’ is multiordinal,” we make it clear that though we call each “an abstraction,” these abstractions are ordinally different.

I hope that makes some sense to you.  I’m basically giving you a new way to conceptualize some of the confusing words you hear and read.  I’m teaching you to see some of them as multiordinal.  But recognizing the multiordinality of particular terms, you realize that the things these words refer to are inequatable.  Just because I call a perception an abstraction and a word an abstraction, doesn’t mean I can equate them.  Equating multiordinal terms is like trying to equate apples and appleseeds (or applesauce).  Sure they’re all apples, but they’re ordinally different apples so they ain’t quite the same thing.

This understanding of ordinality and multiordinality becomes important in understanding where Korzybski may have been breathtaken by Chwistek.  I look now to Chwistek’s posthumously published book The Limits of Science.  The Introduction to this book, written by Helen Charlotte Brodie, talks about Chwistek’s use of the term “semantics” (even the term “general semantics”!) when talking about order, expressions, and the concepts of reality.  On page xlvi, Brodie writes:

Chwistek’s position on questions of logical theory have influenced the formulation  of his views on the problem of reality.  He requires, for example, the acceptance of a theory of types prior to the formalization of reality.  With the help of this theory he distinguishes an infinite number of meanings of the word “real” in addition to the four meanings already indicated.  For there are formalizations of higher type which take formalizations of lower type as arguments.

Here we have the setup for a discussion of the term “real,” and how it may be a multiordinal term.  Watch the next sentences Brodie writes, which spill over onto page xlvii:

However, this theory of types, which Chwistek called “metascientific”, is not formulated very precisely.  Thus while Chwistek maintains that each of the four formalizations (i.e. each of the four “concepts of reality”), are of a different order although they are or the same type,[…] he nowhere sets up a precise hierarchy of orders.  Nevertheless at very isolated points he does venture to make such comments as: the concept of physical reality is of higher order than the concept of natural reality […].

You start to get the sense that Chwistek sees with the word “real” a possible hierarchy of uses of the term.  That is, some uses of the term “real” mark a higher rank or magnitude than other uses.  Put another way, some uses of the term “real” ordinally differ from other uses.  The real similarity to korzybskian thought follows, as Brodie explains immediately after:

In spite of the lack of an explicit formulation of the “metascientific” theory of types this theory is of use in resolving some of the epistemological puzzles raised in connection with dreams.  Chwistek maintains, for example, that it is not an error for an individual to regard his dreams as “real”.  Dreams are just as “real” as are persons or things.  They are merely of a different order.

Shabam.  According to Brodie, Chwistek says that different uses of term “real”–or put another way, some concepts labeled “real”–may differ ordinally.  In this way, a dream can be real but so can something else–just as long as we recognize that “real” is a multiordinal term, that is, it stands for concepts of different orders.

Brodie continues, bolding mine:

On the other hand, it would be wrong for an indivdual to regard the sensation which he experiences when he is dreaming as sensations of the same type as those which he experiences when he is awake.  Chwistek’s contribution to philosophical theory thus rests on the method he has devised by which it is possible to obtain precision in philosophical concepts.

Or as I understand this passage, Chwistek made it possible to conceptualize hierarchically different uses of a particular term.  Just because we call two different things “abstractions” doesn’t mean we can treat them as the same.  The same with things called “real”: Just because we call two different things “real” doesn’t mean we can treat them the same.  Both dreams and perceptions are real, but though we call them “real” doesn’t mean they’re the same real, though they may be a related kind of real.  The word “real” is a multiordinal term, with each appearance potentially standing for hierarchically different ideas than in other appearances.  The same with the word “abstraction.”  Another way to think about multiordinal terms would be to look at the price tag on a toy and on a house.  Both may say “Sale” on their tags, but the magnitudes represented by each appearance of the term are extraordinarily different.  A toy sale is ordinally different from a house sale, at least in terms of the discount being offered.

All in all, Korzybski’s term “multiordinal terms” is just a nice conceptual device for realizing that not all abstractions are alike, not all yeses are alike, not all trues, falses, definitions, etc., are alike.  They may be ordinally different.  A definition of an object is not necessarily the same thing as a definition of a term–the term “definition” stands for ordinally different behaviors.  At least this is how I’ve understood multiordinal terms for a while, coming more to a head in this blog post.

While I have your attention on Brodie, I’ll include one last passage from page xlvii found in the second footnote, which deals specifically with Chwistek’s use of the term “general semantics”:

In his consideration of the problem of reality Chwistek has on occasion alluded to general semantics (as distinct from rational semantics) and seems to suggest its importance in dealing with the problem of reality.  He does not, however, specify exactly what he understands by the term “general semantics” and always returns to rational semantics, the system of semantics developed at length in this book, for hints to be applied in resolving the problem.

Brodie’s passage communicates two things to me: One, that Chwistek coined the term “general semantics” to differentiate something from rational semantics, and two, that semantics has something to do with meaning and the ordinality of terms.  (I would imagine that Korzybski was inspired by Chwistek in naming the field “general semantics,” rather than indebting himself to Chwistek as the namer of the field.)

At this point, it’s seeming to me that the term “general semantics” means something really quite specific: that some words, though they seem similar, are ordinally different, and it is this fact that we are driving home in the field of general semantics.  Put another way: though two things are called the same thing, the meanings of those words may be different, because what they represent may differ ordinally (in sequence or in magnitude).  Saying the term “general semantics” is almost like saying “general insights related to the meaning of terms, especially in terms of multiordinality.”  General semantics is general commentary on meaning, or general commentary with respect to meaning, or general commentary related to meaning.

As a brief sidebar before continuing, it should be noted that multiordinality and multi-meaning are different concepts that are often confused.  Multi-meaning is just the concept of having more than one possible meaning for a term.  The term “pen” would be a good example of that, when you think of the writing implement and the place where a pig lives.  Multiordinality is the concept of a term’s representational magnitude.  One use of the word “abstraction” may represent a higher magnitude of characteristics than another use of the word “abstraction.”  The word “abstraction” is said to be a multiordinal term for that reason (I argue).  In some places in general semantics literature you’ll find a basic confusion (equation) of multiordinality and multi-meaning.  Myself and others would disagree with that characterization.

Now back to Korzybski.  We return to Science and Sanity to see how some of the above notions match up.  For now we’ll look for other mentions of Chwistek in the book.  We find a passage on page 748 which seems to be about sorting out issues in mathematics a little better.  It reads:

The restricted semantic school represented by Chwistek and his pupils, which is characterized mostly by the semantic approach, and by paying special attention to the number of values, establishing the thesis that the older ‘freedom from contradictions’ depends on one-valued formulations, as discovered by Skarzenski [accents in his name omitted] and quoted by Chwistek.

I’m not sure if I know what Korzybski is talking about here.  In The Limits of Science, Chwistek has one reference to Skarzenski as the prover of a theorem (see page 87), but The Limits of Science wasn’t even published by the time Science and Sanity was published.  I’m left at a bit of a dead end here about Skarzenski but I’ll just assume based on Korzybski’s phraseology, he didn’t look at any Skarzenski.  (I can’t validate or invalidate that claim right now.)

So I guess I have to do some guessing about what Korzybski meant in that passage.  I suppose “the semantic approach” is just an approach at looking at what something might mean as opposed to looking at something else.  Why Korzybski decided to name his field “general semantics” is a little beyond me still, but my hypothesis based on all of the above blog entry is that he felt his insights were related to the meanings of words, a general structural commentary on how people use language, that just because they use the same word for different things doesn’t mean those things are equatable.  Korzybski is conceptualizing meaning, talking about the structure of our meanings or the framework in which it lives, rather than talking about the content of our meanings (the subject of historical semantics).

Wait.  Aha.  I think I just figured out something.  The index of subjects for Chwistek’s The Limits of Science has the entry “‘Semantics’ (syntax),” suggesting that within the discourse of Chwistek, the word “semantics” refers to syntax.  This is interesting because traditionally, “semantics” does not refer to syntax.  Very generally, syntax may be thought of as the structure of a particular expression.  This is to say, could it be?, that Korzybski’s term “general semantics” has a similarly different use of the term “semantics”?

If so, this is what I’ll argue for why Korzybski called it “general semantics”: For Korzybski–from Chwistek–the word “semantics” refers not to the content of language, but to the structure of language.  Both the content and the structure of language are meaningful; that is, they can communicate to the listener.  But rather than paying attention to what was said in an expression, Korzybski was interested more in the structure of the expression and what that structure communicates.  Using our box with 100,000 items example, let’s imagine hearing an expression like receiving this box full of items.  Instead of being interested in the items he received, Korzybski was interested in the box he received.  How was the box put together?  What was its shape?  What is the design of the box?  How does the design of the box affect the recipient?  Does it hold the items well?  Etc.  (Given these questions, terms of a multiordinal character might be said to be designed poorly when their multiordinality is not called out because otherwise they make discourse confusing, with rampant, inappropriate identifications.)

The box analogy is not Korzybski’s, but mine.  It is seems to gel well with what I know of general semantics.  Korzybski chants in Science and Sanity about the importance of structure, but it never occurred to me that the word “semantics” could be referring specifically to the structure of language.  “Semantics” only ever seemed to me to refer to the content of language.  In seeing how Chwistek uses the term “semantics,” and in noting Korzybski’s citation of Chwistek as one of the main reasons for his use of the term “general semantics,” I see a coincident interest in structure between the two authors, and from this, it seems to me that Korzybski called his field “general semantics” in the sense of “general commentary on the structure of language (as opposed to the content of language).”  This reasoning spells almost exactly why Korzybski was so interested in perception, abstracting, orders of abstraction, the map-territory analogy for understanding language and its relationship with reality (actuality), the subject-predicate form, multiordinal terms, extensional devices, etc.  They were all related to the structure of language in some way or another.

We connect this all back to human engineering and the notion of time-binding Korzybski presents in his book Manhood of Humanity.  With the refinements of the concept that Cassius Keyser and Walter Polakov present in their respective works, time-binding is understood as the cooperation between dead people and living people for the purpose of production.  That cooperation is facilitated almost primarily via the language the dead people produce for the living people to later read or listen to.  The content of those communications is important, but so is the structure of those communications.  In fact, the structure of those communications may be more important than the content, Korzybski might argue.  It might be that the structure of language is a greater threat to production than the content of language, because the structure of language tends  to, or up until Korzybski has tended to, go unscrutinized.

And this is the concern of general semantics: the structure of language, for the fear that it may hinder human production if we don’t address it.  General semantics is the study of the structure of language and its effects on human production.

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