While Korzybski described the growth of knowledge as following an exponential curve, no general semanticist has ever, to my knowledge, attempted to quantify that growth rate. There is, and has been, such a measure that is closely related to the growth of knowledge itself, and that is growth in the capacity to handle knowledge. This measure, from the computing industry, is known as Moore's law.
In 1965 Gordon E. Moore, who co-founded Intel, noticed that each new computer chip contained roughly twice the capacity of its predecessor. Computing power seemed to be doubling approximately every two years.
This relationship or prediction is now known as Moore's Law. It has held true for over three decades. If anything, the rate of increased computing power is accelerating so that computing power is now doubling each year. **
Since 1965, the capacity to handle knowledge, and consequently our best measure of the quantity of knowledge in the world, has been doubling every two years. So the amount of knowledge handling capacity in 1967 was twice that in 1965, which was twice that in 1963, etc, etc.. From 1949, the last year that Korzybski actively published, to 1965 was 16 years, or 8 doublings of the knowledge handling capacity in our world that was available to Korzybski shortly prior to his death. Backing that up to 1933, the year of publication of Science and Sanity, the difference is (1965-1933)/2 = 32/2 = 16. So between 1933 and 1965, the publication date of Korzybski's tome, and the discovery of Moore's law, knowledge handling capacity doubled 16 times. That means that in 1965 there was approximately 65,536 times as much knowledge handling capacity in the world as there had been in 1933. How much more has developed between 1965 and 2003? (2003-1965)/2 = 38/2 = 19, which computes to 524,288 times as much knowledge handling capacity in 2003 as in 1965. This makes the growth in knowledge handling capacity between 1933 and 2003 a phenomenally large number - 2,147,483,648 - over two billion times as much knowledge handling capacity in the world as there had been in 1933.
|A measure of the capacity to handle knowledge is not the same as a
measure of knowledge itself. The knowledge of how to practically
measure knowledge was only first developed in 1994. By April of 2003,
a more reasonable estimate of the growth of knowledge itself was
available, which just happens to provide the precise date range we are
interested in. . In April 2003, Leot
Leydesdorff showed that knowledge increased from 1933 to 2001 by a
factor of approximately 27 million times. A little mathematical
analysis shows that this represents a doubling of knowledge itself about
every 2.75 years. In the two years since 2001, knowledge will have
nearly doubled again to over 44 million times the amount of knowledge we
had in 1933.
Science and Sanity was written with only a miniscule fraction of the knowledge we had as of 2003 being available to Korzybski - one forty-four millionth part, to be precise. Vast areas of material presented in Science and Sanity have been superseded by more recently gained knowledge. Korzybski was aware that this would happen, and he predicted it. The amount of knowledge change is so great that even major premises of general semantics need to be revised. The formulations as written in Science and Sanity and Korzybski's other writings are way out of date. Even general semanticists who routinely quote from Science and Sanity get embarrassed when Korzybski's remarks on colloids and life are remembered. Levels and orders of abstraction is another area that has seen much development. The formal definitions of recursion theory were developed post Korzybski. The majority of the work done in the areas of linguistics, artificial intelligence, the philosophy of language, natural language processing, formal semantics, denotational semantics, and closely related fields has all been done since Korzybski wrote Science and Sanity. Most of these fields did not even exist until after Korzybski's death. Even a cursory knowledge of these fields provides clarification and distinctions that cannot be inferred from Science and Sanity.
As early as 1975 Andy Hilgartner attempted to apply some of the concepts from formal languages to general semantics, but it was very clear that he was not up to the task. (See A Non-Formalized Non-Language) Prior to my analysis, no active members of the general semantics community exhibited the technical expertise to provide the required review, and there was apparently no significant interest outside the community. **
The "liar's paradox" has long been a topic of philosophical discussion, and Korzybski doesn't hesitate to add his own two cents worth. Korzybski accepts Bertrand Russell's theory of types as the basis for his approach. In the theory of types, any statement that is about another statement must be indexed higher than the statement it is about. Korzybski applies this indexing to the terms themselves and to the order of the statements.
What is the theory of types? It is an attempt to solve, by purely logical methods, the inconsistency of self reflection. Gotlob Frege provided a formal definition of set theory which Bertrand Russell showed to be inconsistent. The problem was specifically, that the is a member of definition for a set allowed a set to be a member of itself. Russell proposed that the element appearing on the super set side of the symbol must be indexed higher than the "same" element on the subset side of the symbol. In short, the is a member of symbol must be a non-commutative relation. Of course, this lead to an infinitely ascending sequence of indices, which Korzybski expressed as higher and higher levels of abstraction. It was Tarski's work that provided for a resolution to the problem in a most satisfactory way. Tarski provided a formal way of defining semantics using correspondence theory. The liar's paradox cannot be resolved by logic alone when self-reflexivity is allowed, but when each instance or use of a term is deemed to be distinct and different, no contradiction or paradox can arise, because there is no transitivity of meaning. In formal semantics a language of tokens is paired with a set of objects, and rules of language interaction are corresponded with ways the objects may relate to each other. Korzybski's approach did not consider this, as he had not assimilated Tarski's model of truth. Moreover, Korzybski was caught up in the theory of types approach, which he matched up with levels of abstraction. Problems that require semantics to solve them can't be solved by logic alone. The formal system that can shed light on these types of problems is model theory, the development of which was enabled by Tarski's formal theory of truth.
Korzybski invented the term 'multiordinal' to refer to words which could, when un-indexed, be used at multiple levels of abstraction. He was attempting to apply Russell's theory of types to ordinary natural language. One problem that shows up in Korzybski's analysis is his failure to distinguish the structural use of such terms from the effect on the overall meaning of the resulting statement. Korzybski attributes the differences in meaning to the terms themselves, not to the combined interaction of the components of the sentence, a later development in formal semantics.
In "never say never say x", he suggests that the meaning of the multi-ordinal term 'never' differs from its use in ,"never say x".
There is a most important semantic characteristic of these m.o terms; namely, that they are ambiguous, or ∞-valued, in general, and that each has a definite meaning, or one value, only and exclusively in a given context, when the order of abstraction can be definitely indicated.
Approaching the statement more formally, the correct depiction, "Never say 'never say x.'.", can be translated as an instruction not to prohibit the saying of x. In both cases the structural use of the term 'never' applies as an imperative directed at a person related to a potential act of the person. The structural meaning of the word 'never' is not different in each context, even though its contexts differ in level of abstraction. It is the meanings of the individual clauses that are different, and each contributes to an overall, complex, meaning. Korzybski goes on to specify an extensional test for multiordinal terms.
These issues appear extremely simple and general, a part and parcel of the structure of 'human knowledge' and of our language. We cannot avoid these semantic issues, and, therefore, the only way left is to face them explicitly. The test for the multiordinality of a term is simple. Let us make any statement and see if a given term applies to it ('true', 'false', 'yes', 'no', 'fact', 'reality', 'to think', 'to love',.). If it does, let us deliberately make another statement about the former statement and test if the given term may be used again. If so, it is a safe assertion that this term should be considered as m.o. Anyone can test such a m.o term by himself without any difficulty. The main point about all such m.o terms is that, in general, they are ambiguous, and that all arguments about them, 'in general', lead only to identification of orders of abstractions and semantic disturbances, and nowhere else. Multiordinal terms have only definite meanings on a given level and in a given context.
The meaning of "Don't say X." is clearly different from the meaning of "Don't say Y.", especially when Y is "Don't say X.". While the meaning of the utterance changes, the structural meaning of the candidate "multiordinal" terms 'never' does not. Korzybski mistakenly attributes the meaning of the utterance to the meaning of the terms themselves as altering depending upon the level of abstraction. Since the distinctions available to us since the development of the field of formal semantics and other development in many fields, such as linguistics, the philosophy of language, natural language processing, and many more young fields, were not available to Korzybski, he could not have been expected to "get it all right" from the beginning.
To formalize Korzybski's test, we have the following.
Let's consider whether some of Korzybski list of terms can be applied to the above statements.
'True'. - cannot be applied to both sentences. The first sentence may be true, but the second sentence is an imperative, and as such, cannot have a truth value. Truth values can only apply to propositions. The same applies to the term 'false'. Another word from Korzybski's list, 'to speak', as in "I said", can be applied, but it means exactly the same thing, structurally, in both cases. Many of the others words he explicitly identifies as "multiordinal" either cannot be applied to one or both of the above statement, or they mean exactly the same, structurally, at both levels.
So it's clear that, in this context, some of the specific terms that Korzybski identifies as multiordinal fail his very own test for multiordinality. The main reason for this is that Korzybski is attempting to account for a great deal of structural complexity in a single concept, which he gives the name 'multiordinality' to. Advances in language understanding, especially in the area of formal semantics and compositional grammar have identified significantly more structure than Korzybski allows.
For Korzybski's definition to be even possible it must be the case that "if there exists a context and sentences P and Q, such that" must apply to the terms. Consequently, whether a term satisfies the definition given by Korzybski now depends upon the context of the usage of the term. The only reasonable interpretation that can come out of this is that Korzybski's definition of multiordinality cannot apply to the terms themselves, but to the effect of the use of the candidate terms and its effect on the context. It is not the terms that are multiordinal, it is the utterance of the term in certain contexts that is multiordinal. Here again "multiordinality" is not a characteristic of the term, but of the utterance of which the term is a part. Once again Korzybski misapplies the "meaning" of an utterance and attributes it to the terms used in the utterance. (Again it should be noted that the language understanding developments were post Korzybski.)
It does not require an understanding of the these disciplines to grasp the difficulty. A simple nostalgic trip down memory lane, back to grammar and high school, to our English grammar classes diagramming sentences. There is a reason our teachers never diagrammed more than a simple sentence or a sentence with a single dependent clause. The diagram had too many branches. If you remember those lessons, and retained any of it, try diagramming a sentence with two subordinate dependencies, especially one using the same word in multiple clauses. Accounting for this complexity by "blaming" the meaning shifts on the individual words oversimplifies the structural complexity.
There is a common thread to this misunderstanding that is elucidated by Korzybski himself. It is in the identification of orders of abstraction. The common mistake has been understood in Philosophy for literally millennia. It is known as simple equivocation, or the confusing of different meanings or definitions. In Korzybski's case, the distinctions from computational grammar were not yet developed; distinguishing clearly among the component meanings of individual terms and the composite meaning of an utterance had simply not been made in his time. Several levels of abstraction and multiple complex structures were all being "explained" by Korzybski as attributable to variable meanings of multiordinal terms. None of the distinctions or structural components had been elucidated by him (or anyone else) at the time.
Once the distinctions not made by Korzybski became apparent, the usefulness of the term 'multiordinal', as Korzybski defined it, became marginal, obsolete, etc. I'm aware that this proclamation will cause an uproar within the "traditional" general semantics community, but those who scream the loudest will be the very ones least capable of applying Korzybski's own directive, that general semantics will be updated and eventually even superseded.
Korzybski also failed to clearly distinguish between probability theory and multi-valued logics. On page 92 he can be seen suggesting, "∞-valued logics, which merge with the theory of probability". Obviously, he thought that multi-valued logics, as the number of possible values approaches infinity, become indistinguishable from probability theory. Logic in general and multi-valued logics in particular deal with determining the (truth) value of complex statements from the (truth) values of the component statements. Probability theory deals with likelihood of events for statements and statistical frequencies for events. Multi-valued logics, like two-valued logic deals with the values of statements, and not with what the statements might refer to. The distinction is not unlike the distinction between logic and semantics. See Levels or perspectives on the use of language for more details. Again, Korzybski identifies across levels of abstraction, in this case failing to distinguish between logic and semantic levels. This is understandable, as the theory of types is an attempt to solve semantic problems using only logical levels, and Korzybski was committed to his own personal view that levels of abstraction, multi-ordinal terms, and consciousness of abstracting would "do the job". A clear, formal, distinction between logic and semantic levels was not readily available at the time. General semantics took note of the distinction as early as 1962, ten years after Korzybski's death. Korzybski was somewhat aware of the distinction, as is evidenced by his constant reiteration that "the word is not the thing", however it was later developments based on Tarski's definition of truth that enabled the clear and precise distinctions between logic and semantics. Logic involves relations between sentences, whereas semantics involves relations betweens words and referents. Multivalued logic expresses the relations between sentences formally, while probability theory expresses the relations between some sentences and objects or events. So probability theory deals with semantic levels of structure while multivalued logic deals with logical levels of structure, and they are very clearly and distinctly different in character. Korzybski was wrong to claim that they merge as the number of logical values approaches infinity.
To summarize, Korzybski was strongly influenced by relatively recent (1933) developments in geometry and axiomatic approaches to logic and geometry, and he took Bertrand Russell's theory of types as his fundamental paradigm for understanding language and human behavior. All these views deal with language from the logic level of structure. Consequently, Korzybski significantly confused (understandably) what are later well distinguished into logical and semantic levels of structure.
|This page was updated by Ralph Kenyon on 2009/11/16 at 00:27 and has been accessed 3243 times at 0 hits per month.|