Updates 14 March 2026: clarified Hayakawa’s contribution to the reconfiguration of Korzybski’s ideas and filled out the final comments re naivety of normative map concept a bit.

I’ve been quiet recently, because I’ve been obsessively reworking the introduction to Maps: Concepts and Histories (the work in progress) and from there realigning the book content so that the whole points in the right direction to launch me properly into the target: chapter 8 on the anthropogenic map concept. But once that was done, and I got into chapter 8, I immediately hit a snag… I’ve this post in just a few days, to get this all out of my system, so please forgive me (and perhaps tell me) for the problems that undoubtedly lurk here.

In reviewing works on/about the postmodernist critique of representation, trying to get a coherent handle on the phenomenon, I encountered some commentaries on Alfred Korzybski’s now famous dictum—that “the map is not the territory”—that said that Korzybski had argued that maps, and therefore language, are “self-reflexive” (notably Mitchell 2008, 3).

This made me do a double-take! I’ve always understood and taught the opposite, that Korzybski had indicated that maps are not self-reflexive. Moreover, I now realize that I don’t actually understand what Korzybski meant by self-reflexivity: what’s the significance of saying that language is self-reflexive? What does the term even mean when applied to maps?

So I went back and reread the relevant works with far greater care and attention than I ever had before, to try to discern in detail how Korzybski used “the map” to explain the character and nature of language, and to clarify what that usage implies about how Korzybski understood the nature of maps.

In rereading Korzybski (at least those parts dealing with maps: it’s just too much to read the whole darn book), I identified some internal contradictions within Korzybski’s map metaphor. Moreover, the metaphor has since been changed to remove those contradictions and to align it with other academic positions.

So I’m writing this essay—with transcriptions of the relevant parts of Korzybski’s book and other works, collected in the appendix—in an effort to work through and understand what Korzybski meant by “self-reflexivity,” how it relates to or is sustained by his map metaphor, and how to use his contradictions to reveal how Korzybski and his contemporaries understood “maps.”

While I’m at it, I was also directed by one of Peta Mitchell’s footnotes to the fact that, in the very same year that Korzybski’s magnum opus was published (1933), the mathematician Eric Thomas Bell offered a map metaphor that was very similar to Korzybski’s (Mitchell 2008, 171n5). I did not know this further metaphor, so I looked it up as well. It seems, from Korzybski’s (1933, 247) late inclusion of a pertinent quote from Bell’s book that there was some collaboration around the idea.

Overall, this mini-history of Korzybski’s map metaphor indicates that it has not been consistently deployed: what is today understood by the “map-territory relation” is not what Korzybski wrote. Beginning with Korzybski, scholars have deployed the metaphor in rhetorical rather than explanatory support of their key concepts, relying on popular and naive concepts of “the map” to do so.

Korzybski’s Map Metaphors

Alfred Korzybski (1879–1950) was an aristocratic Polish engineer who settled in the USA after World War I. He became an independent scholar and philosopher, developing a system of interpretation that he called “General Semantics.” His primary work was Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics (Korzybski 1933). The movement remained rather cultish until the 1970s, although A. E. Van Vogt did attempt to integrate General Semantics into his genre novel, The World of Ā [The World of null-A], serialized in Astounding Science Fiction in 1945 and separately published in 1948. (Van Vogt seems to have been especially influenced by Korzybski’s popularizer/competitor, the Canadian-American-Japanese English professor Samual Ichiyé Hayakawa [1906–1992], who is name checked in Van Vogt’s book: “Professor Hayakawa is today’s Mr. Null-A himself, the elected head of the International Society for General Semantics” [quoted on Hayakawa’s Wikipedia page].)

Korzybski’s vision was perpetuated by the Institute of General Semantics, which was responsible for introducing Korzybski’s map/territory dictum into wider academic use after 1970. At that time, the stirrings of postmodernist thought significantly reconfigured the dictum, dropping the further qualifications that were so important to Korzybski’s metaphor. So, let’s review the entire use to which Korzybski put maps.

December 1931 Lecture

To begin with, in December 1931, Korzybski presented a paper to the American Mathematical Society, on the “necessity” of “a Non-Aristotelian System” for “Rigour in Mathematics and Physics.” Beginning with a review of the different schools of thought about the still-problematic concept of infinity, Korzybski argued that their differences could be resolved by what he called a non-Aristotelian approach to language. Most of the paper was therefore an account of this “general semantic mechanism underlying human behavior,” a mechanism that pays conscious attention to the different philosophical implications of the multiple meanings borne by each word. To illustrate this approach, Korzybski turned to maps (transcript in appendix 1).

Korzybski used the example of the placement of three cities on a map and in the world to show how a correct map possesses a structure similar to that of the world, and that they are incorrect when they do not do so. He was not explicit in this initial moment, but he implied that even correct maps do not replicate the territory. Korzybski (1933, 750–51) accordingly gave four propositions:

A) A map may have a structure similar or dissimilar to the structure of the territory. (1)

B) Two similar structures have similar “logical” characteristics. Thus, if in a correct map, Dresden is given as between Paris and Warsaw, a similar relation is found in the actual territory. (2)

C) A map is not the territory. (3)

D) An ideal map would contain the map of the map, the map of the map of the map … endlessly. This characteristic was first discovered by Royce. We may call it self-reflexiveness. (4)

Languages, Korzybski immediately stated, have the same four characteristics: languages have structure (5) and that structure must be similar to that of both the external world and the internal human nervous system if the language is to be considered “rational” (6). Furthermore, words are not the things they represent (7) and language is used self-reflexively to speak about language, albeit with serious difficulties unless one pays close attention to the multiple meanings of words (multiordinality) (8). Korzybski then developed many more propositions about language and science from (5–8) but without further reference to the map metaphor (propositions 1–4).

But note that Korzybski played rather loose with the parallel of maps to language. He initially (propositions 5 and 6) treats maps as language (langue), the entire system that linguists study, but then shifts (propositions 7 and 8) to considering maps as individual expressions of communication (parole or texts) or even communal expressions (discourse). This is not a coherent metaphor!

Korzybski’s reference to Royce in proposition 4 requires some explanation. Josiah Royce (1855–1916) was an American pragmatist philosopher who had postulated an ideal map when trying to explain one kind of infinite mathematical sequence (Royce 1899, 502–7). The technicalities of what Royce called a “trivial illustration” are understandably labored and contrived as he struggled, like all philosophers and mathematicians at the time, with understanding and describing infinity (transcript in appendix 2). Royce began by postulating “the ideal map,” a “perfectly exact” work “involving” a “one-to-one correspondence, point for point, of the surface mapped and the representation.” He then suggested that such an ideal map might be constructed within the territory being mapped, so that if the ideal map is to be complete, it “will have to contain, as a part of itself, a representation of its own contour [shape] and contents.” Moreover, this “representation itself will have to contain once more, as a part of itself, a representation of its own contour and contents; and this representation, in order to be exact, will have once more to contain an image of itself; and so on without limit.” Before explaining the mathematical significance of such a sequence, Royce observed that creating “such an endless variety of maps within maps” was physically impossible. After all, he was working with concepts of infinity, not with the nature of representation (Edney 2019, 18; see also Dewey 1938, 363–64, re the impracticality of Royce’s paradox).

Yet Korzybski took Royce’s ideal map as having real significance and meaning, and as defining a key characteristic of representation/language:

An ideal map would contain the map of the map, the map of the map of the map … endlessly. This characteristic was first discovered by Royce. We may call it self-reflexiveness. (4)

For a system like General Semantics that is supposedly grounded in the honest recognition of reality and of carefully matching the structure of one’s speech to the structure of that reality, this seems a rather perverse move.

Indeed, this embrace of unreality and imagination breaks the parallel between the map (propositions 1–4) and language (propositions 5–8): proposition 4 appears more as a retrospective imposition made necessary to account for a key quality of language.

Science and Sanity (1933)

Korzybski evidently thought he had a great explanatory device in his map metaphor, and he used it again, early in his full explication of General Semantics in Science and Sanity (transcript in appendix 3). He did, however, reconfigure it slightly by situating it within his explanation of the structure of language, but he still slipped easily from talking about language as a system to the texts expressed through language. The need, he wrote, was to ensure structural similarity between language and the world, and he identified the language of Einstein and others as matching the four-dimensional reality of the world … not the physicists’ actual linguistic system, but rather what they described. More particularly, Einstein and company argued that space and time are inextricably interrelated as space-time, so what is needed is a language (i.e., General Semantics) that is all about clarifying the relations between things in aggregate. People might routinely “distinguish objects by certain characteristics” and therefore isolate them, but what is necessary at “a higher order of abstraction” is to consider individual objects “as members of some aggregate or collection of objects” according to their common connectivity or “relations.” It is at this point that Korzybski brings in the map metaphor.

[I’m starting to think, without having read all of Korzybski’s huge and utterly mystifying book, that Korzybski saw “language” as “creating meaning,” words as the core of meaning, so linguistic structure as the definition and regulation of meaning, so he could shift seamlessly between langue and parole and discourse.]

Korzybski again started with the idea of how the agreement or similarity of structure—of relations—between a map and territory indicates that a map is correct, and expanded on how an incorrect map will “lead us astray.” And then he offers his now famous dictum, which really requires the full paragraph:

Two important characteristics of maps should be noticed. A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness. If the map could be ideally correct, it would include, in a reduced scale, the map of the map; the map of the map, of the map; and so on, endlessly, a fact first noticed by Royce. (Korzybski 1933, 58)

That is, correct maps are useful because they have the same structure, they codify the same relations, as the territory: maps-as-texts and reality. But in the following paragraph he immediately returns to map-as-language—“If we reflect upon our languages, we find that at best they must be considered only as maps”—before once again confusing language with speech: “A word is not the object it represents.”

Beyond the conflation of language with texts—am I really the first person to notice this sloppy logic, or has everyone else been blinded by the seeming profundity that the map/text is indeed not the territory/world?—my rereading of Korzybski and subsequent commentaries has generated two points of concern: (I) the way in which the self-reflexive map contradicts the deployment of maps as being correct in their structure but specifically not ideally correct in all their details; and (II) what the supposed “self-reflexivity” of maps actually means.

Concern I: Korzybski’s Internal Contradictions

When Korzybski first brought up Royce in December 1931, in his proposition 4, he plainly took the ideal map as a legitimate philosophical concept, but nonetheless distanced its implications: “an ideal map would contain the map of the map….” In 1933, the reworked map metaphor placed the reference to Royce and the ideal map directly after the fact that maps are only correct in their structure and therefore not in all details. Moreover, the key verb has been altered:

A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness. If the map could be ideally correct, it would include, in a reduced scale, the map of the map; the map of the map, of the map; and so on, endlessly, a fact first noticed by Royce.

The if..could construction implies that in practice maps can never be ideally correct. I have therefore always read Korzybski’s 1933 reference to Royce as reinforcing the argument that maps are only ever structurally correct (else they can not be useful) and that that is the nature of representation: an image can never be perfect. Indeed, just a few years earlier in 1929, René Magritte had similarly exposed the falsity of mimesis with his painting, “La trahison des images” (The treachery of images), depicting a precisely painted tobacco pipe above the equally precisely drawn phrase, “Ceci n’est pas une pipe” (This is not a pipe).

To be honest, before this round of reading, I had only ever skimmed Korzybski’s further comments re self-reflexivity, other than to know that it is not possible for maps to be self-reflexive because no map can show itself, which seemed to agree with Korzybski’s comments that language is only self-reflexive with difficulty. Now, paying closer attention to Korzybski’s text, it’s plain that Korzybski wants maps to be self-reflexive, in principle and in practice, despite everything else he wrote about them.

In this respect, Korzybski’s proposition 4 in December 1931 appears more as an assertion than as an argument. Propositions 1–3 are pragmatic, referencing the character of maps in practice, but proposition 4 does not follow on from them, in the way that all the further propositions about language stem from propositions 5–8. Moreover, while propositions 1–3 about maps do metaphorically parallel propositions 5–7 about language, proposition 4 appears as a cynical deployment of Royce’s work with the goal of forcing the appearance of proper metaphorical parallel between propositions 4 and 8. That is, proposition 8 was really important to Korzybski—he later stated that self-reflexivity was one of the two pillars of General Semantics (Korzybski 1947)—but self-reflexivity is not supported by the map metaphor, so Korzybski stretched the map metaphor to make it look like it works. The self-reflexive map is metaphorical blowback.

Concern II: What Is Self-Reflexivity?

So what is “self-reflexivity” in language and maps? What is its mechanism? Why is it so important?

Annoyingly, the term is so central to General Semantics, that adherents tend to refer to in an established short-hand: “the ability to make maps of maps (the self-reflexive nature of maps)” (Lahman 2013, 113). But, speaking here as a map scholar, what the photon does it mean, “to make maps of maps”? (A map bibliography might be a map of maps, in an early interpretation of “cartography” as the description of maps, but I really don’t see Korzybski digging reasoned map listings.) It seems that in this context, Korzybski uses “map” to mean texts and not in reference to real, actual maps that are a metaphor for texts in general. That is, the metaphor has collapsed:

basic metaphor:

A is not B in the same way that C is not D, but both A and C have similar structures respectively to B and D

proposition 4:

C refers to C so A-as-C refers to A-as-C

(or something like this … I’m not into formal logic)

Also, Korzybski’s adherents have been quite comfortable to adjust the structure and meaning of Korzybski’s map metaphor in line with wider cultural trends.

In his popular and accessible presentation of General Semantics, Hayakawa (1939, 253) recast Korzybski’s four postulates of the map metaphor into just three, that now made it explicit that maps cannot show the entire territory and furthermore entirely dropped the foundational premise that maps are correct because of their structural similarity to the territory:

A map is not the territory it stands for; words are not things.

A map does not represent all of a territory; words never say all about anything.

Maps of maps, maps of maps of maps, and so on, can be made indefinitely, with or without relationship to a territory.

Hayakawa recast the map as strictly a metaphor for texts, accounts, descriptions, abstractions, etc. (also pp. 21–25), i.e., expressions using language, and no longer treated the map as a metaphor for language itself. He made Korzybski’s metaphor internally consistent. No longer a metaphor for language, Hayakawa did not refer to the “self-reflexive” character of language. But he did remove from the ideal map any hint that the ideal map was a fiction and presented it as a practical reality and, in the process, suggested that maps have no necessary relationship with the territory! This was a truly significant reconfiguration and simplification of Korzybski’s metaphor, making it far more comprehensible.

It is accordingly Hayakawa’s premises that subsequent commentators have quoted, attributing them to Korzybski and Science and Sanity, and that they have further modified. Corey Anton (2014, 29), for example, adjusted what he stated were Korzybski’s own propositions, but they were actually Hayakawa’s, to create “new corollaries for general semantics premises” (favorably quoted in manuscript by Lahman 2013, 114):

1. [AK via SIH] The map is not the territory => [CA] there is no not territory.

2. [SIH] The map cannot cover all the territory => [CA] any map is only part of the territory.

3. [AK via SIH] maps are self-reflexive => [CA] “maps” is the word used to refer to parts of the territory becoming reflexive to other parts at different levels of abstraction.

These changes remove Korzybski’s own confusion over what maps are metaphors for, whether language or texts, so as to emphasize that the map metaphor is all about texts and their non-similarity to the world. Functionality be damned; here is the dictum as deployed widely today.

However, I did encounter one specialist essay that gives some sense of what is entailed by self-reflexive maps:

We live in a world of maps and territories, of models and phenomena, of symbols and referents, of words and things. General semanticists view language as a map and the subject of the map as the territory. Presumably, the more closely the map approximates the territory, i.e., the greater the isomorphism of our language to the “real” world, the more sanely we journey through a world fraught with linguistic snares and pitfalls. Korzybski has presented the map/territory distinction in three basic premises of non-Aristotelian logic, the foundation of general semantics: (1) the map is not the territory; the symbol is not the referent, (2) the map does not represent all of the territory; symbols cannot cover everything, and (3) the map is self-reflexive; symbols can stand for other symbols at various levels of abstraction. Korzybski states that since the map clearly is not the territory, the only possible relationship between them is structural. (1) …

We begin indirectly, down an avenue suggested by the third premise: self-reflexiveness. One statement may refer to a prior one. In turn, another statement may refer to the second, and yet another, ad infinitum. One statement lies nested within another more general one. One inference may nest within another, which in turn nests within another, much like a Chinese puzzle box – maps of maps of maps of maps, etc. Where does the ultimate map lie? What meaning does the ultimate map contain? (Dallmann 1982, 65):

So, self-reflexive maps—statements—refer to others, before and after. Here, “maps” are plainly not literal maps but texts. Self-reflexivity has never been about actual maps!!

The insistence that maps are self-reflexive is an obfuscation caused by the metaphorical blowback of intertextuality.

There is, on top of all this, the fact that self-reflexivity literally means referencing oneself. In this respect, “maps” have been turned back on their creators. The preface to the fifth edition of Science and Sanity expanded the already-shrunken metaphor accordingly:

13. Languages, formulational systems, etc., as maps and only maps of what they purport to represent. This awareness led to the three premises (popularly expressed) of general semantics:

the map is not the territory

no map represents all of ‘its’ presumed territory

maps are self-reflexive, i.e., we can map our maps indefinitely. Also, every map is at least, whatever else it may claim to map, a map of the map-maker: her/his assumptions, skills, world-view, etc.

By ‘maps’ we should understand everything and anything that humans formulate—including this book and my present contributions, but also including (to take a few in alphabetical order), biology, Buddhism, Catholicism, chemistry, Evangelism, Freudianism, Hinduism, Islam, Judaism, Lutheranism, physics, Taoism, etc., etc. …! (Pula 1995, xvii)

So, maps are at once language but also texts as well as entire belief systems. All that is certain is that none are actually the territory.

Isomorphism and Numerology

The presumption that maps are the territory leads to fundamental problems. This was made clear by the mathematician Eric Temple Bell (1883–1960) in the same year that Korzybski’s Science and Sanity appeared. Bell was a mathematician specializing in number theory—about which I know nothing other than it’s a major subfield within mathematics—who then taught at the California Institute of Technology (CalTech). Bell was on the list of philosophers, mathematicians, and scientists that Korzybski (1933, [5]) identified as having been of great influence on the formation of General Semantics. His doctoral supervisor at Columbia (PhD 1912) was Cassius Keyser, another of Korzybski’s acknowledged influences. Korzyski (1933, 247) inserted a quote from Bell’s book as one of the epigrams for chapter 18; the crammed typesetting and the listing of Bell’s book as a late addition made after the citations had all been numbered in alphabetical order, indicate that Korzybski learned of the quote after he had written Science and Sanity, and well after the 1931 paper, but it does suggest some correspondence or other connection around the idea between Bell and Korzybski. Perhaps Bell had attended the New Orleans meeting where Korzybski had presented in December 1931.

Given Bell’s specialty, it seems appropriate that a chance encounter with a radio show about numerology and astrology led him to research and write a critique, simply entitled Numerology, that is effectively an easy introduction to a wide range of mathematical topics (Bell 1933). A second edition in 1946 bore the wittily suggestive subtitle: Numerology: The Magic of Numbers.

To explain mathematical (as opposed to biological) isomorphism, Bell turned to his map metaphor (transcript in appendix 4). Isomorphism is possessing the same structure, not identity; correct maps are isomorphic with reality. Bell illustrated this by talking about how maps show three points along a road as they occur in reality. He stressed however that maps are plainly and obviously not the same as the territory (unless you are in a Muppets movie and one “travels by map”):

Now did anyone ever hear of even the drunkenest driver mistaking his map for the countryside, and trying to get anywhere by crawling like a fly from A to B on the paper? I do not say that it cannot be done, by slipping into the fourth dimension at A, for instance, and oozing out to the third again at B and C, but I have never seen it done. (Bell 1933, 135)

For Bell, much modern numerology was grounded in “just this sort of magic,” in which “the thing mapped is identified with the map” and also “the map is not the thing mapped.” I like the idea of the mythical ideal map being magic.

Explaining the Confusions and Conflations: Naive Presumptions about the Nature of Maps

I think, by this late stage in this essay, that I’m just insulted by the looseness of thought about maps in a work that has generated such a large following and that claims to be a mathematically inspired work of philosophy. But, then, I really should not be surprised, because Korzybski’s original formulations of his map metaphor and subsequent commentary about his premises have all been written from a naive understanding of what maps are.

By naive I mean unsophisticated and unexamined. This is not the understanding of maps held by scholars and practitioners, but by the general public. It has taken me a long time to realize that many of the intellectual problems and inconsistencies in discussions of maps stem neither from intellectual conservatism nor from the paradoxical failure by specialists to recognize the intricacies and complexities of mapping, but from the overwhelming dominance of an understanding of the nature of maps that initially arose within the public, not among scholars. That understanding is the belief that maps are properly—normatively—containers of metrical fact and mimetic images. It is this normativity, this idealism, that propels people to take maps to all be mimetic and therefore logically perfectible images. They can readily imagine the ideal map—half the General Semantics map metaphor requires that this be so—and they can accept the idea of maps mapping itself or other maps, regardless of the humorous satires on the idea of a map at 1:1, and regardless of the meaningless of the statement.

Korzybski’s map metaphor perpetuated mimesis even as it denied it. The practical impossibility of making the ideal map is irrelevant; maps should be so, they are so. This tension has only been exacerbated by later modifications to the metaphor and to the eventual stripping it down to the simple dictum, “the map is not the territory.” Thus the light-bulb moment of pause and insight when one encounters the realization that maps are not territories. The power of that insight relies for effect on the commitment to maps as ideal, perfectible, normative statements.

As long as people don’t look too closely at maps, they can be treated in line with these presumptions, even when close examination conflicts with normativity. This is why I call normativity naive: map specialists have their own, particular, precise understandings of maps (at least the particular kinds of maps that they study or make), but map normativity developed within public and non-specialist discourses and does not entail examination and reflection. Normativity emerged in the early twentieth century and slowly infected precise, specialized map discourses through writings such as those of Korzybski and his followers/adherents (especially after 1945).

There is no way to talk about maps as normative works without being naive. Normativity is the non-expert’s view of what maps should be. I have ended up devoting much of the work-in-progress to working through the idea of normativity as a naive and unexamined approach to maps, and the reactions thereto.

The confusions in Korzybski’s ideas and in those of his followers all stem from a commitment to normativity. Korzubski’s map metaphor only works if one presumes—in accordance with normativity–that all maps are essentially the same, regardless of scale, being reductions and simplifications of the earth’s geography, and that maps are all instrumental, intended to guide human action and travel. Korzybski’s metaphor of structure begins with geographical maps and segues to the ideal, territorial map; in fact, all of the twentieth-century map metaphors are grounded in this presumed unity of maps, or in reactions thereto. Also, Hayakawa (1939, 21–25) imbued his discussion of the map/territory relationship with allusions to the art-to-science narrative of the history of cartography, itself a creation of twentieth-century normativity.

It does not seem to be much of an extension of normativity’s naivety to conflate maps as a practice (map making) and as a thing, as a process (language) and as an image, or even as an entire discourse, and not to worry about the classificatory error involved. (And don’t get me going on the conflation of map/territory with word/thing … maps are texts, not individual words/signs.) The failures in Korzybski’s map metaphor are barely noticeable when one is already ignoring the differences between kinds of maps and their intellectual (rather than strictly instrumental) character.

I’m not sure where I’ve ended up in this essay. Korzybski’s map metaphor was originally much more complex than allowed by the now drastically abbreviated dictum. His confusions and conceptual flexibility enabled his successors to modify and recast the metaphor and its implications in line with bigger intellectual trends. His successors have deployed the metaphor in rhetorical rather than explanatory support of their key concepts. Ultimately, as much as Korzybski’s dictum has become the watchword for postmodernist and counter-mapping, like other twentieth-century map metaphors, it was grounded in naive, modernist normativity.

Appendices: Transcripts of Key Portions of Texts re Maps and Territories

To make the narrative a bit easier to follow, I’ve decided to put full transcriptions of the various passages into this appendix.

Appendix 1. Korzybski, December 1931

Korzybski published the text of his lecture, “A Non-Aristotelian System and Its Necessity for Rigour in Mathematics and Physics,” presented to the New Orleans meeting of the American Mathematical Society on 28 December 1931 as Supplement III of Science and Sanity (Korzybski 1933, 747–62). The relevant portion of the presentation reads (with original emphasis):

750/

The scientific problems involved are very extensive and can be dealt with only in a large volume. Here I am able to give only a very sketchy summary without empirical data, omitting niceties and technicalities.

(a) Paris Dresden Warsaw

* ------------- * ------------- *

(b) Dresden Paris Warsaw

* ------------- * ------------- *

If we consider an actual territory (a) say, Paris, Dresden, Warsaw, and build up a map (b) in which the order of these cities would be represented as Dresden, Paris, Warsaw; to travel by such a map would be misguiding, wasteful of effort, … In case of emergencies, it might be seriously harmful. We could say that such a map was “not true,” or that the map had a structure not similar to the territory, structure to be defined in terms of relations and multidimensional order. We should notice that:

A) A map may have a structure similar or dissimilar to the structure of the territory. (1)

B) Two similar structures have similar “logical” characteristics. Thus, if in a correct map, Dresden is given as between Paris and Warsaw, a similar relation is found in the actual territory. (2)

C) A map is not the territory. (3)

751/

D) An ideal map would contain the map of the map, the map of the map of the map … endlessly. This characteristic was first discovered by Royce. We may call it self-reflexiveness. (4)

Languages share with the map the above four characteristics.

A) Languages have structure, thus we may have languages of elementalistic structure such as “space” and “time,” “observer” and “observed,” “body” and “soul,” “sense” and “mind,” “intellect” and “emotions,” “thinking” and “feeling,” “thought” and “intuition,” which allow verbal division or separation. Or we may have languages of non-elementalistic structure such as, “space-time,” the new quantum languages, “time-binding,” “different order abstractions,” “semantic reactions,” which do not involve verbal division or separation; also mathematical languages of “order,” “relation,” “structure,” “function,” “variable,” “invariant,” “difference,” “addition,” “division,” which apply to “sense” and “mind,” that is, can be “seen” and “thought of.” (5)

B) If we use languages of a structure non-similar to the world and our nervous system, our verbal predictions are not verified empirically, we cannot be “rational” or adjusted. We would have to copy the animals in their wasteful and painful “trial and error” performances, as we have done all through human history. In science we would be handicapped by semantic blockages, lack of creativeness, lack of understanding, lack of vision, disturbed by inconsistencies, paradoxes. (6)

C) Words are not the things they represent. (7)

D) Language also has self-reflexive characteristics. We use language to speak about language, which fact introduces serious verbal and semantic difficulties, solved by the theory of multiordinality. (8)

Appendix 2. Josiah Royce on the Ideal Map

Josiah Royce (1899, 502–7) reads as follows (with original emphasis):

502/ I. First Illustration of a Self-Representative System.

The basis for the first illustration of the development of an Infinite Multitude out of the expression of a Single Purpose,

503/ . . .

We are familiar with maps, and with similar constructions, such as representative diagrams, in which the elements of which a certain artificial or ideal object is composed, are intended to correspond, one to one, to certain elements in an external object. A map is usually intended to resemble the contour of the region mapped in ways which seem convenient, and which have a decidedly manifold sensuous interest to the user of the map; but, in the nature of the case, there is no limit to the outward diversity of form which would be consistent with a perfectly exact and mathematically definable correspondence between map and region mapped. If our power to draw map contours were conceived as perfectly exact, the ideal map, made in accordance with a given system of projection, could be defined as involving absolutely the aforesaid one-to-one correspondence, point for point, of the surface mapped and the representation. And even if one conceived space or matter as made up of indivisible parts, still an ideally perfect map upon some scale could be conceived, if one supposed it made up of ultimate space units, or of the ultimate material corpuscles, so arranged as to correspond, one by one, to the ultimate parts of that a perfect observation would then distinguish in the surface mapped. In general, if A be the object mapped, and A′ be the map, the latter could be conceived as perfect if, while always possessing the desired degree of visible similarity of contours, it actually stood in such correspondence to A that for every elementary detail of A, namely a, b, c, d (be these details conceived as points or merely as physically smallest parts; as relations amongst the 504/ parts of a continuum, or as the relations amongst the units of a mere aggregate of particles), some corresponding detail, a′, b′, c′, d′, could be identified in A′, in accordance with the system of projection used.

All this being understood, let us undertake to define a map that shall in this sense be perfect, but that shall be drawn subject to one special condition. It would seem as if, in case our map-drawing powers were perfect, we could draw our map wherever we chose to draw it. Let us, then, choose, for once, to draw it within and upon a part of the surface of the very region that is to be mapped. What would be the result of trying to carry out this one purpose? To fix our ideas, let us suppose, if you please, that a portion of the surface of England is very perfectly levelled and smoothed, and is then devoted to the production of our precise map of England. That in general, then, should be found upon the surface of England, map constructions which more or less roughly represent the whole of England,—all this has nothing puzzling about it. Any ordinary map of England spread out upon English ground would illustrate, in a way, such possession, by a part of the surface of England, of a resemblance to the whole. But now suppose that this our resemblance is to be made absolutely exact, in the sense previously defined. A map of England, contained within England, is to represent, down to the minutest detail, every contour and marking, natural or artificial, that occurs upon the surface of England. At once our imaginary case involves a new problem. This is now no longer the general problem of map making, but the nature of the internal meaning of our new purpose.

Absolute exactness of the representation of one object by another, with respect to contour, this, indeed, involves, as Mr. Bradley would say to us, the problem of identity in diversity; but it involves that problem only in a general way. Our map of England, contained in a portion of the surface of England, involves, however, a peculiar and infinite development of a special type of diversity within our map. For the map, in order to be complete, according to the rule given, will have to contain, as a part of itself, a representation of its own contour 505/ and contents. In order that this representation should be constructed, the representation itself will have to contain once more, as a part of itself, a representation of its own contour and contents; and this representation, in order to be exact, will have once more to contain an image of itself; and so on without limit. We should now, indeed, have to suppose the space occupied by our perfect map to be infinitely divisible, even if not a continuum.

One who, with absolute exactness of perception, looked down upon the ideal map thus supposed to be constructed, would see lying upon the surface of England, and at a definite place thereon, a representation of England on as large or small a scale as you please. This representation would agree in contour with the real England, but at a place within this map of England, there would appear, upon a smaller scale, a new representation of the contour of England. This representation, which would repeat in the outer portions the details of the former, but upon a smaller space, would be seen to contain yet another England, and this another, and so on without limit.

That such an endless variety of maps within maps could not physically be constructed by men, and that ideally such a map, if viewed as a finished construction, would involve us in all the problems about the infinite divisibility of matter and of space, I freely recognize. What I point out is that if my supposed exact observer, looking down upon the map, saw any where in the series of maps within maps, a last map, such that it contained within itself no further representation of the original object, he would know at once that the rule in question had not been carried out, that the resources of the map-maker had failed, and that the required map of England was imperfect. On the other hand, this endless variety of maps within maps, while its existence as a fact in the world might 506/ be as mysterious as you please, would, in one respect, present to an observer who understood the one purpose of the whole series, no mystery at all. For one who understood the purpose of the making within England a map of England, and the purpose of making this map absolutely accurate, would see precisely why the map must be contained within the map, and why, in the series of maps within maps, there could be no end consistently with the original requirement. Mathematically regarded, the endless series of maps within maps, if made according to such a projection as we have indicated, would cluster about a limiting point whose position could be exactly determined. Logically speaking, their variety would be a mere expression of the single plan, “Let us make within England, and upon the surface thereof, a precise map, with all the details of the contour of its surface.” Then the One and the Many would become, in one respect, clear as to their relations, even when all else was involved in mystery. We should see, namely, why the one purpose, if it could be carried out, would involve the endless series of maps.

But so far we have dealt with our illustration as involving a certain progressive process of map making, occurring in stages. We have seen that this process never could be ended without a confession that the original purpose had failed. But now suppose that we change our manner of speech. Whatever our theory of the meaning of the verb to be, suppose that some one, depending upon any authority you please,—say upon the authority of a revelation,—assured us of this as a truth about existence, viz., “Upon and within the surface of England there exists somehow (no matter how or when made) an absolutely perfect map of the whole of England.” Suppose that, for an instance, we had accepted this assertion as true. Suppose that we then attempted to discover the meaning implied in this one assertion. We should at once observe that in this one assertion, “A part of England perfectly maps all England, on a smaller scale,” there would be implied the assertion, not now of a process of trying to draw maps, but of the contemporaneous presence, in England, of an infinite number of 507/ maps, of the type just described. The whole infinite series, possessing no last member, would be asserted as a fact of existence. I need not observe that Mr. Bradley would at once reject such an assertion as a self-contradiction. It would be a typical instance of the sort of endlessness of structure that makes him reject Space, Time, and the rest, as mere Appearance. But I am still interested in pointing out that whether we continued faithful to our supposed revelation, or, upon second thought, followed Mr. Bradley in rejecting it as impossible, our faith, or our doubt, would equally involve seeing that the one plan of mapping in question necessarily implies just this infinite variety of internal constitution. We should, moreover, see how and why the one and the infinitely many are here, at least within thought's realm, conceptually linked. Our map and England, taken as mere physical existences, would indeed belong to that realm of “bare external conjunctions.” Yet the one thing not externally given, but internally self-evident, would be that the one plan or purpose in question, namely, the plan fulfilled by the perfect map of England, drawn within the limits of England, and upon a part of its surface, would, if really expressed, involve, in its necessary structure, the series of maps within maps such that no one of the maps was the last in the series.

This way of viewing the case suggests that, as a mere matter of definition, we are not obliged to deal solely with processes of construction as successive, in order to define endless series. A recurrent operation of thought can be characterized as one that, if once finally expressed, would involve, in the region where it had received expression, an infinite variety of serially arranged facts, corresponding to the purpose in question. This consideration leads us back from our trivial illustration to the realm of general theory.

Appendix 3. Korzybski, 1933

The usually quoted map metaphor comes from Korzybski’s Science and Sanity, in Part II, “General on Structure,” Chapter 4, “On Structure” (Korzybski 1933, 55–65). The relevant portion reads (with original emphasis):

56/

One of the fundamental functions of “mental” processes is to distinguish. We distinguish objects by certain characteristics, which are usually expressed by adjectives. If, by a higher order of abstraction, we consider individual objects, not in some perfectly fictitious “isolation,” but as they appear empirically, as members of some aggregate or collection of objects, we find characteristics which belong to the collection 57/ and not to an “isolated” object. Such characteristics as arise from the fact that the object belongs to a collection are called “relations.” …

When two relations are similar, we say that they have a similar structure, which is defined as the class of all relations similar to the given relation.

We see that the terms “collection,” “aggregate,” “class,” “order,” “relations,” “structure” are interconnected, each implying the others. If we decide to face empirical “reality” boldly, we must accept the Einstein-Minkowski four-dimensional language, for “space” and “time” cannot be separated empirically, and so we must have a language of similar structure and consider the facts of the world as series of interrelated ordered events, to which, as above explained, we must ascribe “structure.” 58/ Einstein’s theory, in contrast to Newton’s theory, gives us such a language, similar in structure to the empirical facts as revealed by science 1933 and common experience.

The above definitions are not entirely satisfactory for our purpose. To begin with, let us give an illustration, and indicate in what direction some reformulation could be made.

Let us take some actual territory in which cities appear in the following order: Paris, Dresden, Warsaw, when taken from the West to the East. If we were to build a map of the territory and place Paris between Dresden and Warsaw thus:

Actual territory * -------------------------- * ----------------------- *

Paris Dresden Warsaw

Map * -------------------------- * -—-------------------- *

Dresden Paris Warsaw

we should say that the map was wrong, or that it was an incorrect map, or that the map has a different structure from the territory. If, speaking roughly, we should try, in our travels, to orient ourselves by such a map, we should find it misleading. It would lead us astray, and we might waste a great deal of unnecessary effort. In some cases, even, a map of wrong structure would bring actual suffering and disaster, as, for instance, in a war, or in the case of an urgent call for a physician.

If we reflect upon our languages, we find that at best they must be considered only as maps. A word is not the object it represents; and languages exhibit also this peculiar self-reflexiveness, that we can analyse languages by linguistic means. This self-reflexiveness of languages introduces serious complexities, which can only be solved by the theory of multiordinality, given as Part VII. The disregard of these complexities is tragically disastrous in daily life and science.

Appendix 4. Bell’s Critique of Numerology and His Map Metaphor

A very similar map metaphor to Korzybski’s was deployed by Eric Temple Bell. It is found in Chapter 8 (of 9), “A Great Dream,” of his Numerology (1933) (original emphasis, throughout):

135/

One of the commonest instances of isomorphism is seen on looking at any faithful map. If the map tells us that town B lies between towns A and C on a particular road R, and if we wish to go from A to C and pass through B on the way, we can follow the road R. The real towns A, B, C and the real road R are related in precisely the same way as are the points A, B, C and the line R on the map. The story told by the spots and lines of printers ink is isomorphic (it is not the same) with that told by the real countryside in its purely geometrical relations of connection and betweeness.

Numerology is just this sort of magic when it is applied to scientific speculations. The thing mapped is identified with the map. For example, if someone says that things are numbers, he probably has a four-dimensional vision denied alike to mathematicians, scientists, and people of reasonable common sense. This however does not prove that the mystics may not be right and all the rest wrong. Proof in these matters is impossible.

136/ …

But to get back on the road after this bad spill into the ditch of metaphysics. Isomorphism applies the idea of mapping to other things besides country roads. Suppose we have a collection of “things” A, B, C, …, Z, before us for contemplation. These things may be any whatever—words, mathematical symbols, human beings, physical “facts,” bricks, historical occurrences, or anything else imaginable. The problem is to construct some sort of intelligible description of the ‘‘relations”’ between them. This presupposes that there are relations between them.

137/ [then explores a specific example of a (metaphorical) map of the ages of a group of men, as defined by the operator “greater than,” so eldest man is listed first, A, then the next eldest, B, etc.]

Where have we seen anything like this before? Any numerologist will cite scores of numerical relations which map this exactly. …

138/ …

What has been done? We have made a one-one correspondence between the men A, B, …, Z and the numbers a, b, …, z of the following kind: if P, Q are any two of the men for which it is true that (P, Q) (P is older than Q), and if p, q are their corresponding numbers, then it ts true that [p, q] (p is greater than q). Conversely, if |p, g], then (P, Q). Having made this one-one correspondence, we can study the relation of ‘‘seniority in age’’ by attending only to the relation of ‘‘greater than” for the corresponding numbers.

But who would say that because [p, q], therefore P is a number, not a man, and that he is greater than the man (or the number, if you prefer) Q?

The map is not the thing mapped. When the map is identified with the thing mapped we have one of the vast melting pots of numerology. Notice also that the relation considered in the map 139/ does not (in this instance at least) make sense if it is supposed to hold for the things mapped. …

That is, we set up a one-one correspondence (if we can) between the collections and map one on the other so that the relations between the things in the first are imaged exactly in relations between the things in the second. In this narrow and extremely special kind of mapping either collection can be viewed as a map of the other. But neither is the other, unless they are the same collection to start with, and the relations ( ), [ ] are the same.

The advantages of carrying a map rather than a county are so well known that the object of the 140/ highly practical kind of mapping we have just described should be plain enough.

The map metaphor returned a bit later in the chapter when Bell turned to the matter of extrapolation:

143/

If isomorphism is the Schemhamphoras of numerology, extrapolation is its Mesopotamia—that blessed word which gave unspeakable comfort to the poor tired charwoman. [ref to the lady who introduced him to numerology]

Imagine any good map you like. No matter how detailed the map is there will be certain features of the countryside which it does not portray; not every pebble can be charted on the map. But if the map is really good, we can guess from what it does give. This process of guessing is called interpolation, if we apply it to forecast some detail of the landscape which, if it had been mapped, would have been—we believe—mapped between two points on the map. This sounds much more mystical than it is, but anyone who has used a map knows intuitively what is meant.

Suppose now that the cartographer had been careless, and had omitted to mark a precipice crossing the highway on his map. Anyone interpolating over this precipice would probably break his neck if he drove the road in the dark.

144/

Extrapolation almost always, sooner or later, leads to broken theories, if not broken bones. For it is practically all driving in the dark.

Suppose our map is that of a “‘white’’ (known) spot on a ‘‘dark’’ (not wholly explored) continent. A plateau on the white looks as if it should continue uniformly into the dark. There is a river down the middle of the plateau, so we confidently head our canoes downstream toward the dark. More than one daring man has lost his life that way by going down the rapids or over the falls, swept along between precipitous cliffs. It almost happened to Major Powell several times in the Grand Canyon. But he had better luck than more scientists, even if he did have only one arm while most of them have two.

Extrapolation is guessing beyond the map.

Now, in mapping the cosmos, or any part of it, on pure mathematics, the things mapped have to be ideally simplified before any reasonably intelligible map can be drawn at all. The colorful rocks, the shapely hillocks, the winding gullies and hundreds of other more interesting details of the real landscape are omitted entirely from the map. One thing at a time is the rule.

Thus, by sufficiently abstracting, or idealizing the reality, we may be able to make a serviceable map of the physics of electricity, or of gravitation, or of the behaviour of atoms, or of the metaphysics of radiation. If it is painstakingly drawn the 145/ map will give more than was put into it, but sooner or later it will need revision. Finally so many corrections have been smeared over the map that it is no longer legible and it is discarded, to be snatched up eagerly by—never mind whom.

I do not wish to push this analogy beyond all limits, but one more aspect of it must be glanced at. Many maps are made for one and the same territory—road maps, geological maps, sociological maps, and dozens more. Each has its special purpose, for which the others are useless. Who but a fanatical unitarian would ever dream of plastering all the geology, sociology, topography, and the rest onto one and the same piece of paper? It could be done, but what use would it be? If a simple map for all could be made, the story would be different.

Here now comes a curious thing. The dream of physical science is just this, to unify electromagnetism, gravitation, radiation, in fact all physical phenomena, by mapping them on one grand, unified theory. At present fashion favors a purely mathematical unification. This is the vision which Pythagoras saw, only he went farther. He would have included humanity and all that human nature means. Then he would have joined some of the moderns by saying the map is the cosmos.

Works Cited

Anton, Corey. 2014. “A Thumbnail Sketch of General Semantics.” In General Semantics: A Critical Companion, ed. Deepa Mishra, 20–36. Delhi: Pencraft International.

Bell, Eric Temple. 1933. Numerology. Baltimore: Williams & Watkins Co.

Dallmann, William. 1982. “Of Maps, Territories, and Quanta.” ETC: A Review of General Semantics 39, no. 1: 65–70.

Dewey, John. 1938. Logic: The Theory of Inquiry. New York: Henry Holt.

Edney, Matthew H. 2019. Cartography: The Ideal and Its History. Chicago: University of Chicago Press.

Hayakawa, S. I. 1939. Language in Action. New York: Harcourt Brace Jovanovich.

Korzybski, Alfred. 1933. Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics. Lakeville, CT: The International Non-Aristotelian Library Publishing Company.

———. 1947. “General Semantics: An Introduction to Non-Aristotelian Systems.” Institute of General Semantics. August 1947. https://web.archive.org/web/20060827225535/time-binding.org/about/ak-intro.htm.

Lahman, Mary P. 2013. “General Semantics: Understanding Korzybski’s Formulations.” ETC: A Review of General Semantics 70, no. 2: 111–19.

Mitchell, Peta. 2008. Cartographic Strategies of Postmodernity: The Figure of the Map in Contemporary Theory and Fiction. London: Routledge.

Pula, Robert P. 1995. “Preface to the 5th Edition, 1993.” In Alfred Korzybski, Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics, xiii–xxii. 5th ed ed. Brooklyn: Institute of General Semantics.

Royce, Josiah. 1899–1901. “Supplementary Essay: The One, the Many, and the Infinite.” In The World and the Individual: Gifford Lectures Delivered before the University of Aberdeen, 1:471–588. 2 vols. London: Macmillan.