C. A. Hilgartner



All western Indo-European discursive languages, and all the specialized technical sub-languages, discursive or formalized, derived from them -- logical, mathematical, scientific, philosophical, etc. -- utilize at least two KINDS of terms (at least two logico-linguistic "roles"). Traditionally we label these two KINDS of terms by means of paired substantives such as noun vs. verb, or subject vs. predicate, or quantity vs. operation, or thing (such as set) vs. relation (such as belongs to), etc.


There already exists a new viewpoint which in its logico-linguistic structuring differs from that of the western Indo-European languages, and from the familiar version of the scientific tradition based on those languages. This new viewpoint generates its own formalized notation, analogous to but structured differently from our traditional symbolic logics, set theories, etc. [Ref.]


From the very beginning, this new viewpoint (including the formalized language which it generates) stems from novel premises, the non-aristotelian premises proposed by Alfred Korzybski (1879-1950). These premises qualify as entirely non-traditional -- they do not stem from the logico-linguistic structuring of any language or family of languages, nor from the "common sense" of any culture. Thus the present viewpoint qualifies as non-Western, and also as non-Eastern.


As their central tenet, the non-aristotelian premises forbid (disallow) the construct of 'Identity' (or the binary relation of 'identical with', defined as "entire and absolute agreement or negation of difference" (Webster's (Second), 1961, p. 1236)) in any guise or form, explicit or tacit.


Thus, as I show in detail below, this new formalized language disallows the basis for distinguishing between 'noun' and 'verb': It perhaps allows terms analogous to 'verbs', but none anal

ogous to ('self-identical') 'nouns'; or terms analogous to 'operations', but none analogous to ('self-identical') 'quantities'; or terms analogous to 'relations', but none analogous to ('self-identical') 'things'. It also disallows all inflectional forms of to be (e.g., am, are, is, was, were, been, being, be, etc.) or any other grammatical means of expressing the binary relation of 'identical with'.


Consequently, in a non-aristotelian framework, we may not subscribe to the traditional "logical axiom of 'Identity'": For two different and distinguishable reasons, we may neither explicitly state nor tacitly hold that


For all x which belong to the delimited 'domain' D , x qualifies as 'identical with' x .


For not only do the non-aristotelian premises specifically negate what the traditional axiom asserts, but also they disallow the two-term grammar -- betokened by 'self-identical' "thing"-terms such as x or D and not-'self-identical' "relation"-terms such as 'identical with -- by means of which we state the traditional axiom.



Even this brief description suffices to notify linguists that the new viewpoint drastically alters our perspective on those "doings" or "happenings" which we traditionally call human language. For example, the new formalized language completely eludes the analytical "net" of the generative grammarians: In no sense does a well-formed expressing in the new formalized language "generate" two logico-linguistic "roles," such as those signified by the terms "noun-phrase" and "verb-phrase."


The above remarks which describe the new viewpoint (and the new formalized language which it yields) may on first encounter seem like conversation-stoppers. Indeed, most exponents of Western viewpoints who have gone so far afield as to question the "logical axiom of 'Identity'" have expressed themselves as believing that anyone who refuses to subscribe to it has no other alternative than to fall mute -- to cease speaking, writing, or symbolizing altogether.


Further, the above descriptive remarks, I believe, cannot fail to elicit some kind of reaction from each reader. As I understand the social institution of science, those of us humans who subscribe to its tenets require of ourselves that we hold no hypothesis -- belief -- already conclusively disconfirmed, no matter how painful the consequences. As a plausible first reaction to the above conversation-stopping assertions and claims, then, each reader may wish to examine one or more documents which present the new viewpoint, in order to convince himself as to whether or not the above remarks mis-state the case.


Those readers who convince themselves of the unavoidability of taking seriously the above-stated claims may wish to come to understand the structuring of the new viewpoint; and as a first step in that direction, they may wish to know where it comes from, and how it arose.


The new formalized language stems from a fortunate discovery made in the course of a long-term study. Convinced from an early age of the importance of the non-aristotelian premises, I had already spent some eight years exploring the more and more far-reaching of their implications (Hilgartner & Randolph,m 1969a,b,c,d). Then I chanced to disclose a previously unnoticed and unexamined assuming encoded in the grammatical structuring of western Indo-European languages, an assuming so pervasive as to have previously escaped notice. This "hidden assuming" qualifies as unmistakably untenable, for any human who relies on it thereby tacitly and unquestioningly treats as 'identical' two unmistakably different and distinguishable constructs. In the text of the paper I discuss this "hidden assuming" in detail.


After struggling for several more years -- the period needed to recover from the shock of discovery -- I managed to write a formalized language structured differently from the familiar Western ones, and thus demonstrated that I had finally found ways systematically to disallow this previously hidden untenable assuming.


Those who have convinced themselves that the (alleged) new viewpoint described above does "exist" and does merit their attention will find, I believe, that efforts spent trying to understand for themselves this (alleged) previously hidden untenable assuming encoded in the familiar western Indo-European languages will turn out to do much to make the structuring of the new viewpoint comprehensible to themselves.


To that end, I shall use the main body of this paper to explore this previously unnoticed, unexamined, and untenable assuming: I shall


a) Name the traditional explicit assumings encoded in the grammatical structuring of the western Indo-European languages, and the hidden untenable assuming which underlies them;


b) Specify their 'logical'-and-'empirical' structuring;


c) Show how they qualify as untenable; and


d) Show how these untenable assumings underlie the western Indo-European languages, discursive and formalized, and thus how they figure in the traditional Western 'World-View' which these languages presume-and-express.




As Einstein (1955) remarks,


The object of all science, whether natural science or psychology, is to co-ordinate our experiences and to bring then into a logical system. (Einstein, 1955, p. 1)


Then I can express the major purpose of this new theoretical system as that of providing an accounting for human behaving-and-experiencing (behaving as viewed from the "outside," experiencing as viewed from the "inside") free of the traditional but untenable western Indo-European assumings.




The altered perspective on what we traditionally call human language provided by the present viewpoint emphasizes as nothing else could the limited scope, the "incompleteness," of previous linguistic investigations. For the grammatical structuring of the new formalized language stems from, qualifies as a direct consequence of, the non-aristotelian premises. In other wording, the new viewpoint extends the traditional construct of "strict deductive system" so as to encompass not only what we traditionally call "argumentation" of "logical structure," but also what we traditionally call "grammatical structure." Furthermore, I see no a priori reason why we cannot, by exercizing sufficient ingenuity, treat traditional discursive and/or formalized languages similarly. Indeed, I offer a worked example: Only some years after I had succeeded in disclosing the traditional explicit and tacit assumings underlying western Indo-European languages more fully than had any previous worker, even Korzybski (1933, p. 749), did I manage to elaborate the present formalized language.


As Benjamin Lee Whorf (1897-1941) comments,


A change in language can transform our appreciation of the Cosmos. (Whorf, 1956, p. 263)


In order to throw the traditional explicit and tacit assumings encoded in western Indo-European languages into high relief, from this point on I tamper (or rather further tamper) with the grammatical structuring of my English. As noted above, the new viewpoint disallows to be in any inflectional form; and in the text down to this point I have not once used this word (except in the passage quoting from Einstein). Now I shall disallow all standard 'nouns'. Where possible, I replace them: mainly with -ing-forms, but also by rephrasing so as to substitute adjectival, adverbial, etc., termings. I also neologize moderately freely, inventing termings such as to noun, to verb, etc., so as to replace 'noun' with nouning, 'verb' with verbing, etc. Sometimes, however, I find myself insufficiently ingenious to get away with such devisings, and in order to make what I want to say intelligible, end up by nouning. Where I deem nouning unavoidable, I enclose the 'noun' between single quotings (e.g. 'word').


In order now to say what I want to, I will have to argue lengthily and carefully.




To accord with the non-aristotelian premisings, I assume that no 'human' can speak or write any uttering or expressing which does not presume-and-express certain "assumings" or "believings." As one exampling, when in the 'sentence' preceding this one I use the universalizing phrasing, no 'human', I presume-and-express that there "exist" MORE THAN ONE 'HUMAN'; viz., I suggest the "believing" that certain "happenings" which I might designate by the terming 'humans' "exist" or "occur" more or less independent of those "happenings" which I might designate by the terming myself. And this "believing" rests on a prior choosing: It presumes, and expresses, that I deny or negate that "believing" known as 'solipsism' (the "believing" that "the 'self' comprises the only existing 'thing'").


Phrased in 'logical' termings, I assume that every terming, 'proposition' or 'sentence', 'propositional or sentential function', 'doctrine', 'doctrinal function' 'system', 'system-function', etc. (cf. Korzybski, 1933, p. 437), which a 'human' "uses" or can "use," presumes-and-expresses at least one complete 'World-View' or 'metaphysics'.




As Whorf (1956) points out,


What we call "scientific thought" is a specialization of the western Indo-European type of language ... (Whorf, 1956, p. 246)


Beyond any disputing, except for the Arabic algebraists, etc., of about twelve 'centuries' ago, every 'human' who has contributed to the written 'tradition' of our 'logics', our 'mathematics', our 'sciences', etc., writes (and perhaps also speaks) in at least one of the western Indo-European languagings (e.g. Dutch, English, French, German, Greek, Latin, Polish, Russian, Spanish, etc.). And according with the non-Aristotelian premisings, I maintain that each of the various 'philosophies', 'logics', 'mathematics,' 'sciences', etc., elaborated by those who write in at least one of these closely-related languagings, presumes-and-expresses a particular 'World-View'.


Moreover, however, much these various writings may differ in detailing, they demonstrably share certain (usually unstated) assumings codified in (viz., inferable from) the logico-linguistic structuring of these closely-related languagings in which they get expressed.


What I call shared but unstated assumings Whorf (1956) apparently refers to as an implicit and unstated ... agreement:


We dissect nature along lines laid down by our native languages. The categories and types that we isolate from the world of phenomena we do not find there because they stare every observer in the face; on the contrary, the world is presented in a kaleidoscopic flux of impressions which has to be organized by our minds -- and this means largely by the linguistic systems in our minds. We cut nature up, organize it into concepts, and ascribe significances as we do, largely because we are parties to an agreement to organize it in this way -- an agreement that holds throughout our speech community and is codified in the patterns of our language. The agreement is, of course, an implicit and unstated one, BUT ITS TERMS ARE ABSOLUTELY OBLIGATORY: we cannot talk at all except by subscribing to the organization and classification of data which the agreement dictates. (Whorf, 1956, pp. 213-4)


Furthermore, as for the relationing between discursive or "natural" languagings such as 'English', etc., and the formalized, notational languagings of our 'logics' and 'mathematics', although 'logicians' (e.g. Mates, 1965) emphasize that to translate between natural-languaging expressings and the expressings of a notational 'logical' languaging qualifies as hazardous (imprecise), in my viewing, the 'World-View' codified in any (traditional) formalized languaging yet published demonstrably shares precisely those assumings common to the western Indo-European discursive languagings.


Then these shared metaphysical assumings of the western Indo-European languagings, discursive or formalized, specify what I shall call the (shared) traditional western Indo-European 'World-View'.




I can bring out and express the tacit assuming(s) codified in the logico-linguistic structuring of the western Indo-European languagings by pointing to four structural featurings of these languagings, each one of which betokens what I call an explicit assuming. Structurally speaking, each of these languagings


a) divides its termings into two main groupings, called 'nouns' and 'verbs', which its speakers treat as grammatically different;


b) admits (allows) the 'notion' of 'Identity' (the 'binary relation' of 'identical with', as traditionally defined (Webster's (Second), 1961, p. 1236);


c) uses the copula (in English, to be), or some notational equivalent of the copula, e.g. =_ ; and


d) uses the famous "Laws of Thought" attributed to Aristotle of Stagira (384-322 BC) as its "rules for naming (nouning)."


Further, as I demonstrate in later sections, with each of these structural features in turn, I can specify the explicit assuming which it betokens by using the other three structural features. But that means that each taken singly or all taken together jointly presume a single common "hidden assuming," here called tacit 'identity'. And when brought out of "hiding" and stated explicitly, e.g. stated in 'words', this assuming appears unmistakably untenable.


Actually, in what follows, I end up specifying the "Laws of Thought" by means of the other three constructings.




In approaching and dealing with those human "doings" or "happenings" which I designate as human languaging -- viz., speaking-and-listening, or writing-and-reading, etc. -- Western 'linguists' and 'logicians' restrict themselves to studying spoken and.or written expressings (e.g. "sentences") "in isolation," by which I mean that in studying the expressings, etc., they somehow manage to avoid considering the 'human organisms' who speak and/or write, listen and/or read, in "sentences."


Thus (as I see it) 'linguists' and 'logicians' have noticed and/or postulated that to those humans who speak and/or write (and listen and/or read) in a given, namable and shared languaging, certain expressings spoken or written by a 'human' (regardless of what they "say") appear somehow satisfying to the 'speaker' or 'writer' and/or to a 'hearer' or 'reader'; whereas other expressings appear somehow unsatisfying.


Then, striving to account for their observings, viz., concerning how those (human) expressings which (TO A HUMAN) appear somehow satisfying resemble each other and how these differ from those which appear somehow unsatisfying, they have postulated a 'criterion' which they label with phrasings such as "complete sentence" or "significant utterance" of "grammatically correct" or "acceptable"g or, in the wording of L/ukasiewicz, "well-formed."


Then when some 'observer' proposes some structuring for expressings which will meet this 'criterion', e.g., specifies the patterning(s) which an expressing composed of English 'words' must show (follow) in order to qualify as well-formed (in 'English'), his proposings function as 'unifying hypotheses' designed economically to account for his observings.


But in framing their 'studies' thus, our 'linguists' and 'logicians' appear to regard well-formed or not well-formed as 'characteristics' or 'attributes' of "sentences," and in so doing, they manage effectively to isolate "language" from "the languaging organism": They thereby manage to avoid making explicit WHO "applies" the (postulated) 'criterion', or HOW, or TO WHAT, or WHY.


In the new formalized languaging, one cannot isolate "language" and "languaging organism". Instead, this formalized languaging explicitly posits an 'organism' who abstracts from his environings (and a 'logician' who elaborates and uses formalized languaging in order to describe the "doings" of the 'organism' amid his environings).


Furthermore, I hypothesize that those "doings" or "happenings" betokened by the 'criterion' of well-formed tell something fundamental about 'humans' ('speaker-listeners', 'writer-readers'); and that before I can account for the logico-linguistic structuring of ANY languaging, I must disclose and make explicit this fundamental "concealed message."


Two examplings, borrowed from the findings of Whorf (1956), will suffice to highlight this "concealed message." Whorf (1956, pp. 241 ff) points out that (along with many others) those languagings of the Indo-European grouping utilize a 'type' of 'sentence' having two 'parts', each built around a grouping of 'words' -- I call them nounings and verbings -- which these languagings treat as grammatically different. For exampling, except for certain special constructings (ejaculatings, 'imperative mood', scene-settings such as That night or Meanwhile, back at the ranch ..., etc.), in a 'noun-verb' languaging such as English, no single 'noun-phrase' or 'verb-phrase' can stand alone as well-formed (a "complete sentence" or a "significant uttering"). Instead, the simplest expressing which appears well-formed requires at least one terming from each grouping. To example, in our so-called intransitive patterning, the simplest well-formed expressing consists of a verbing (of the intransitive grouping, e.g., froze) preceded by a nouning (e.g. the puddle).:


The puddle froze.


Or, in our so-called transitive patterning, the simplest well-formed expressing consists of a (transitive) verbing (e.g. froze) not only preceded by a nouning but also followed by a nouning:


The cold wind froze the puddle.


To contrast, (outside of a setting in which we "understand" the missing grammatical "parts," as when answering a direct questioning, etc.) expressings such as


The puddle.

Lake pond puddle.

Froze hardened congealed.


do not appear to us as well-formed. Neither does an expressing 'jumbled' in ordering, such as


Wind the cold the froze puddle.

The the froze cold wind puddle.


But languagings historically and geographically distant from the Indo-European grouping may follow markedly different patternings. To example, in Nootka, an Amerindian languaging of Vancouver Island, as Whorf (1956) points out,


... the sentence without subject or predicate is the only type. The term "predication" is used, but it means "sentence." Nootka has not parts of speech; the simplest utterance is a sentence, treating of some event or event-complex. Long sentences are sentences of sentences (complex sentences), not just sentences of words. In Fig. 17 we have a simple, not a complex, Nootka sentence. The translation, 'he invites people to a feast', splits into subject and predicate. Not so the native sentence. It begins with the event of 'boiling or cooking', tl'imsh; then comes -ya ('result') = 'cooked'; then -'is 'eating' = 'eating cooked food'; then -ita ('those who do') = 'eaters of cooked food'; then -itl ('going for'; then -ma, sign of third-person indicative, giving tl'imshya'isita'itlma, which answers to the crude paraphrase, "he, or somebody, goes for (invites) eaters of cooked food'. (Whorf, 1956, p. 242)


WHORF: FIG. 17 (p. 243) ABOUT HERE


By juxtaposing these two examplings, I bring out what intrigues me here. To summarize, according to Whorf,


Nootka has no parts of speech; the simplest utterance is a sentence, treating of some event or event-complex.


But in an Indo-European languaging such as English, we require nouning followed by verbing to form even the simplest (intransitive) "sentence."


So I ask: How do we Westerners pull it off? What special assumings do we tacitly presume-and-express whenever we rely on the 'noun'-'verb' splitting?


Two considerings guide my inferring here: First, I believe that any "responding" of 'organism' to environings, from the 'simplest' to the 'most complex', shows the structuring of a gestalting (abstracting), viz. "it consists of a figuring or foregrounding which focally interests the 'organism', against a backgrounding which does not much interest the 'organism' just then" (cf. Perls, Hefferline & Goodman, 1951, pp. vi-xii; Polanyi, 1964, pp. 55-65). As Perls et al. (1951) put it,


Gestalt formation always accompanies awareness. We do not see three isolated points, we make a triangle of them. The formation of complete and comprehensive Gestalten is the condition of mental health and growth. Only the completed Gestalt can be organized as an automatically functioning unit (reflex) in the total organism. Any incomplete Gestalt represents an "unfinished situation" that clamors for attention and interferes with the formation of any novel, vital Gestalt. Instead of growth and development we then find stagnation and regression. (Perls, et al., 1951, ix)


Second, in according with the non-aristotelian premisings, I regard what I might call speaking as a direct "responding" of 'organism' to environings, and regard any exampling of what I might call a spoken uttering (including any well-formed uttering) as evidencing such a "responding." Further, I regard what I might call writing as another typing or classing of direct "responding," which can represent (qualify as a 'map' of) some exampling of the first type of "responding"; and I regard any exampling of what I might call a written expressing (including any well-formed written expressing) as evidencing such a "responding."


(Similarly, I regard listening-to-and-understanding a spoken uttering, or reading-and-understanding a written expressing, as two more typings of direct "responding.")


From these two considerings it follows that any single linguistic grouping ("construct," "word"), as spoken or written by a 'human', shows the logico-linguistic structuring of a gestalting; and further, any single well-formed expressing ("sentence") shows the logico-linguistic structuring of a (higher-ordered) gestalting, which structuring I label a (well-formed) linguistic gestalting.


Aligned with this hypothesizing, I can show that any single linguistic grouping in English does in fact show the logico-linguistic structuring of a gestalting. Using a proceeding* which anyone can apply _______________________________________________________________________

*In 1940, Whorf anticipated this proceeding by discussing "Gestalt Technique of Stem Composition in Shawnee" (Whorf, 1956, pp. 160-172).


to any 'word', I show this by quoting, and interpreting, two 'dictionary definitions', namely, that for puddle and for to freeze:


puddle noun 1a (1) : a shallow depression full of water and especially of muddy or dirty water <a hard rain leaves ~s in the road>


freeze verb intransitive 1a : to become congealed into ice by cold <fresh water ~s at 32o Fahrenheit>


(Webster's Third, 1961, pp. 1837 and 907)


For me this terming puddle, then, appears to refer to a structuring ("domain") which I could characterize by some phrasing such as "configurations of the 'landscape', moderately small in 'depth' (and perhaps also in 'area') as compared to a 'human body'." Further, this terming appears to background (to exclude) what I might call "roughly planar configurings," and "convex configurings," and "concave configurings devoid of 'water'"; and it appears to figure (to include) only what I might call "concave configurings containing 'water'."


Similarly, for me this terming (to) freeze appears to refer to a structuring ("domain") which I could characterize by some phrasing such as "changing the 'physical state' of a 'liquid' (e.g. 'water')." Further, this terming appears to background what I might call "boiling" (not to mention other changings of 'physical state', e.g. "melting," "condensing from 'gas' into 'liquid'," "condensing into 'solid'," and "subliming (vaporizing from 'solid')"); and it appears to figure only what I might call "changing from 'liquid' into 'solid'."


Now if I should utter (or write) a "sentence" such as


The puddle froze.


and you should ask me what I mean by puddle and froze, I might answer by specifying two gestaltings which parallel these 'dictionary definitions'. However, if (outside a setting in which we "understand" the missing "parts") I should utter expressings such as



The puddle.


neither you nor I would regard these as well-formed.


From these considerings I infer that we native speakers of a western Indo-European languaging such as English rely on usually unnoticed assumings which I have described above, including the one I might label with the phrasing the 'noun'-'verb' splitting; and these assumings effectively structure our linguistic groupings so as to make the gestalting specified by any single nouning or verbing appear somehow "incomplete," whereas they make a "sentence" composed of nouning followed by verbing appear "complete," viz. as a single (well-formed) linguistic gestalting.


If I could adduce a counter-exampling, e.g. a languaging in which even the simplest linguistic grouping also qualifies as a (well-formed) linguistic gestalting, that would show it as possible NOT to depend on the usually unnoticed assumings which underlie western Indo-European languagings. Whorf (1956) offers further commentings concerning Nootka which suggest that it provides a suitable counter-exampling:


... in Nootka, a language of Vancouver Island, all words seem to us to be verbs, but really there are no classes 1 and 2 [viz., 'nouns' and 'verbs' -- C.A.H.]; we have, as it were, a monistic view of nature that gives us only one class of word for all kinds of events. 'A house occurs' or 'it houses' is the way of saying 'house', exactly like 'a flame occurs' or 'it burns.' These terms seem to us like verbs because they are inflected for durational and temporal nuances, so that the suffixes of the word for house event make it mean long-lasting house, temporary house, future house, house that used to be, etc. (Whorf, 1956, pp. 215-6)


Hence, if there exists a Nootka expression analogous to the English 'noun-phrase'


The puddle.


it would qualify as a "complete sentence," viz., as well-formed. (We might translate such an expressing back into English as


(It) exists as a puddle.

(It) puddles.)


Or in my termings, in Nootka even the simplest linguistic grouping also qualifies as a well-formed linguistic gestalting. And indeed, considered without pre-judging, why should it not?


Granting that we must infer that hidden assumings underlying the 'noun''verb' splitting do "exist," how might I disclose and display them? To do so, I point out (after Whorf, 1956, pp. 241-2) that in our various traditional western Indo-European accountings ('philosophies', 'logics', etc.) there appear many different but equivalent constructings, each consisting of two opposed (mutually contradictory) termings (which get treated like (unacknowledged) "undefined terms"), which (I maintain) express the so-called explicit assuming I have labelled as the 'noun''verb' splitting. Traditionally, we label these constructings with paired 'substantives', which include 'subject' vs. 'predicate', 'actor' vs. 'action', 'things' vs. 'relations between things', 'objects' vs. their 'attributes' (or 'properties' or 'qualities'), 'form' vs. 'substance', 'quantities' vs. 'operations', etc.


In other wording, those who write in at least one of the western Indo-European grouping of languagings unanimously rely on one or another of these equivalent constructings. To example, below (under the heading of EXPLICIT 'IDENTITY') I present quotings from the writings of various highly respected contemporary 'logicians' and 'mathematicians' in which, in presenting what they appear to regard as their most fundamental notionings, they demonstrably rely on such two-terming constructings; and, like almost everyone else who has contributed to the western Indo-European 'World-View', they give no explicit accounting fo their doing so (nor do they appear to sense any 'need' so to account for their own constructings or the (allegedly explicit) assumings which underlie them).


To make comprehensible this puzzling unanimous relying, after Korzybski (1933), I posit that there "exists" a non-verbal, non-symbolic, non-linguistic 'event-level' (I might call this the (non-verbal, non-symbolic) 'World-Viewed', as opposed to the (symbolic or verbal) 'World-Viewed'; or, better, might call it the 'World Unviewed'). I contrast the 'event-level' against what Korzybski (1933) calls the 'object-level' (or 'linguistic isolate', "that which we designate by a 'word'"). Further, I assert that, except for Korzybski and his allies, no native speaker of western Indo-European languagings explicitly recognizes this 'World Unviewed' -- by which I mean, no one else has clearly distinguished between this 'World Unviewed' and the LINGUISTICALLY-DETERMINED 'World-Viewed' ('object-level').


But (to anticipate what I develop in detail below) to fail to distinguish between two discernably different "happenings," e.g. between 'World Viewed' and 'World Unviewed', appears precisely equivalent to tacitly (and erroneously) assuming that the two qualify as 'identical' (viz., "absolutely the same in all respects"). Thus I attribute to these native speakers the parochial, preposterous (tacit) assuming that in its presumed non-verbal structuring, this (inferred) non-verbal, non-linguistic 'World Unviewed' exactly matches the linguistic structuring of western Indo-European languagings; or in other wording, that the 'World Unviewed' somehow consists of two "kinds" (classings) of "happenings" or "occurrings," and so exactly "corresponds to" or "matches" (shows a 'one-to-one relation' to) the two-term constructings of western Indo-European 'philosophies', 'logics', etc.


(But to posit "kinds" of classings in the 'World Unviewed' already contradicts in termings.)


Corollary to this (tacit) assuming, then, we western Indo-European 'provincials' presume that for any human to represent these supposed (non-linguistic) "happenings" or "occurrings" which make up what I have called the 'World Unviewed' without relying on the 'noun-'verb' splitting -- as native 'speakers' of Nootka apparently routinely do -- would qualify as infeasible.



From the above considerings I conclude that, if I would disclose the "metaphysical theory" tacitly assumed (viz., the structuring tacitly attributed to the 'World Unviewed') by native 'speakers' of western Indo-European languagings, I need first to disclose the logico-linguistic structuring of the 'noun'-'verb' splitting. This I can do by proposing a single 'criterion' which serves to distinguish 'noun' from 'verb', and then using this 'criterion' to examine at least one linguistic exampling.


I suggest that the notioning of "selfsame" or "self-identical" or "identical with itself expresses the 'criterion' which distinguishes 'noun' from 'verb'. Stated in termings of 'things' and 'relations between things', this notioning (as displayed, and made more or less explicit, in the first of the "Laws of Thought," the so-called "Law of Identity") holds that:


Every 'thing' qualifies as 'identical with itself'. Using A to signify any nouning and = to signify 'identical with', I could state this "Law" perspicuously by


A = A .


Crucially, the "Law of Identity" does not EXPLICITLY distinguish between 'World Viewed' and 'World Unviewed'. Indeed, as I detail below, I interpret the "Law of Identity" as (tacitly) asserting that 'World Unviewed' qualifies as 'identical with' the 'World Viewed' (or that the 'empirical' aspecting of any uttering qualifies as 'identical with' the 'logical' aspecting, where the terming 'empirical' designates the relationing between the uttering and whatever it refers to, and the terming 'logical' designates the relationing between the uttering and other utterings).


Mapping these explicit distinguishings onto the traditional "Law of Identity," I maintain that, on 'logical' levelings, we traditionally regard any linguistic grouping ('word') as a nouning if and only if we regard this linguistic grouping as "selfsame" or "identical with itself," viz., if and only if to substitute it for A in the "Law of Identity" seems to us "proper." And on 'empirical' levelings, when "choosings" or "assigning" a 'word' to "represent" or "refer to" or "name" some 'linguistic isolate' ("that which we designate by a 'word'"), we "choose" a nouning if and only if we regard the 'linguistic isolate' as "identical with itself."


As a simple exampling, assume that you and I both see some (non-verbal) "happening" which we agree to describe by the 'sentence':


The cat leaped.


To paraphrase Alice in Wonderland, traditionally speaking, we would agree that we could have seen that (non-verbal) "cat" ("that selfsame cat") without that "leaped," but that we could never have seen that "leaped" without that "cat." In other wording, as native 'speakers' of a western Indo-European languaging (English), we would probably agree that (speaking traditionally) it "makes sense" to us to discuss "that selfsame cat", but somehow it does not "make sense" to us to discuss "that selfsame leaped."


And when I go on to question what the notioning of 'selfsame' or 'self-identical', etc., signifies, the most obvious interpreting comes out as "permanent" or "persisting" or "really existing" or (as little as we may like to admit it) "unchanging." As Whorf (1956) puts it,


... pursuant again to grammar, the notion became ingrained that one of these classes of entities cannot exist without an entity of the other class, the "thing" class, as a peg to hang on. (Whorf, 1956, p. 2


To summarize and overview, in an Indo-European languaging such as English, we native 'speakers' observably use each of our linguistic groupings ("words") in rigidly-delimited 'ways'; and when accounting for our observings, we 'observers' say that we native 'speakers' tacitly and/or explicitly "assign" each of our "words" to one or another of a few logico-linguistic 'roles', e.g. 'noun', 'verb', 'adjective', 'adverb', 'preposition', 'conjunction', etc. Further, I maintain that these logico-linguistic 'roles' specify a 'World-View' or 'metaphysical theory'. As Sapir (1921) puts it,


It is almost as though at some period in the past the unconscious mind of the race had made a hasty inventory of experience, committed itself to a premature classification that allowed of no revision, and saddled the inheritors of its language with a science that they no longer quite believed in nor had the strength to overthrow. Dogma, rigidly prescribed by tradition, stiffens into formalism. Linguistic categories make up a system of surviving dogma -- dogma of the unconscious. (Sapir, 1949, p. 100)


Specifically, the 'role' of 'noun' designates that restrictive structuring I could describe by some phrasing such as "more or less permanent, static, unchanging ('self-identical')," viz., for short, a "thing" (instead of a "happening" or "occurring").


noun noun 1 : a word that is the name of a subject of discourse (as a person, animal, plant, place, thing, substance, quality, idea, action, or state) and that in languages with grammatical number, case and gender is inflected for number and case but has inherent gender (Webster's Third, 1961, p. 1545)


Further, the 'role' of 'verb' designates that restrictive structuring I could describe by some phrasing such as "more or less transient, dynamic and/or static ('not-self-identical') 'relations (between 'things')'."


verb noun : a word belonging to that part of speech that characteristically is the grammatical center of a predicate and expresses an act, occurrence, or mode of being and that in various languages is inflected for agreement with the person and number of the subject, for tense, for voice, for mood, or for aspect and that typically has rather full descriptive meaning and characterizing quality but is in some instances nearly devoid of such meaning and quality especially in use as an auxiliary or copula (Webster's Third, 1961, p. 2542)


Hence, whenever we employ the paired contrasting 'roles' of 'noun' vs. 'verb', we tacitly, unavoidably presume-and-express this 'metaphysical theory': To that 'linguistic isolate' designated by the 'noun', we attribute the ("incomplete") structuring of a static, 'self-identical' "person, animal, plant, place, thing, substance, quality, idea, action, or state"; and to that 'linguistic isolate' designated by the 'verb', we attribute the ("incomplete," complementary) structuring of a more or less transient ('not-self-identical') "act, occurrence, or mode of being."


Then it follows that in order to specify a single well-formed linguistic gestalting, we require at least one terming from each of these "incomplete," complementary logico-linguistic groupings.





Meanwhile, I must point out a fundamental failing of the 'noun''verb' splitting: If I left off after having contrasted linguistic grouping with 'linguistic isolate', most 'readers' would translate into some rendering of the traditional constrasting of 'Name' vs. 'Thing Named' (both of which termings, incidentally, occupy the logico-linguistic 'role' of 'noun'). Furthermore, most 'readers' would probably regard the two termings as sufficient, viz., would probably not expect me to introduce any other crucial distinguishings. But contrary to this expecting, a non-aristotelian systeming requires explicit mentioning of at least one more terming, which, after Korzybski (1933), I could render as 'event' of 'event-level'. (I could also render 'linguistic isolate' as 'object' or 'object-level', and linguistic grouping as occupying one or more of Korzybski's (1933) 'verbal levels'.) Then in the termings of the 'map'-'territory' analogizing, the 'verbal levels' occupy the 'role' of 'map' and the 'object-level' occupies the role of 'territory' supposedly "represented" or "referred to" by that 'map'; and taken in ordering, the 'object-level' occupies the role of 'map' which (allegedly) "represents" or "refers to" the 'territory' known as 'event-level'. (Please note that according to the non-aristotelian premisings, the 'territory' (e.g. 'event-level') remains fundamentally unknown, by which I mean, "known" only inferentially, as by projecting from the 'map', and therefore "known" at best INCOMPLETELY and INACCURATELY.)


In other wording, the traditional western Indo-European 'World-View', as inferred from the 'noun'-'verb' splitting, does not EXPLICITLY distinguish between 'linguistic isolate' ('object-level', "that which we designate by means of a 'word'") and 'event-level' (the INFERRED 'territory' of which the 'linguistic isolate' provides a 'map').




As I suggest above, the four structural featurings which I examine (namely, the 'noun'-'verb' splitting, explicit 'Identity', the 'copula', and the "Laws of Thought") betoken the "explicit assumings" underlying any western Indo-European languaging. Further, any one of these featurings appears definable by the other three. But that means that they jointly presume a single common "hidden assuming," which I call tacit 'Identity'


Here I first bring out and state in words the usually wordless (tacit) assuming which I call tacit "Identity', and criticize this construct; and then I examine, and criticize, explicit 'Identity'.




The construct of tacit 'Identity' signifies that some 'human' TREATS two discernably different "doings" or "happenings" as 'identical'.


To example, I point out above that the traditional western Indo-European 'World-View' does not explicitly distinguish between 'linguistic isolate' and 'event-level'.


Some verbal substituting makes it plain that this observing means that the traditional Western 'World-View' encodes tacit 'Identity': For the "neglecting" phrasing, does not explicitly distinguish between (them), I could substitute some obversed expressing addressed from another leveling, some "tacitly assuming" phrasing such as, tacitly assumes that (they) qualify as 'the same in all respects', or tacitly assumes that (they) show 'entire and absolute agreement or negation of difference', or tacitly assumes that (each) qualifies as apoint-for-point perfect replica of (the other)', or tacitly assumes that there exists an 'exhaustive and entirely accurate one-to-one relation between (them).


To summarize, each of these phrasings, "neglecting" or "assuming," explicitly and verbally replaces that wordless "assuming" which I call the postulating of tacit 'Identity'.




Any human who wordlessly TREATS two discernably different "happenings" or "doings" as 'identical' has, by definition, made a 'mistake'.


In a non-aristotelian languaging, the postulating of tacit 'Identity' occupies one and only one "role": as a labelling for fundamental erring


Over the past three or four 'centuries', human experiencing -- especially in our 'sciences' -- has reached at least one secure concluding: that "my picture of what exists" does not qualify as 'identical with' "what exists (as inferred from scientific inquiring)."


But by wordlessly equating these two levelings, one linguistic and the other (supposedly) non-linguistic, the postulating of tacit 'Identity' silently attributes a (fictitious) "Cosmic Validity" to the accidental linguistic structuring of the languaging involved.


Otherwise stated, since all available evidencing contradicts (indeed, no evidencing could possibly support) that assuming I have labelled the postulating of tacit 'Identity', I regard this assuming as delusional (a "believing" held REGARDLESS OF EVIDENCING).



'Dictionaries' leave little doubting concerning the explicit and overt meaning (using) of the 'noun-form' 'identity' or the adjectival 'form' identical'. Webster's Third (1961) defines the first using of the 'noun-form' 'identity' as follows:


identity noun 1a : sameness of essential or generic character in different examples or instances : the limit approached by increasing similarity <the ~ of the red in the rug with the red of a brick> b: sameness in all that constitutes the objective reality of a thing: SELFSAMENESS, ONENESS: sameness of that which is distinguishable only in some accidental fashion (as being designated by different names, or the object of different perceptions, or different in time and place) <the ~ of Scott with the author of Waverly> <the sense of ~ arising in shared experiences> c: an instance of such sameness (Webster's Third, 1961, p. 1123)


As for the adjectival 'form', in contrasting the using of the roughly synonymous termings identical, same, equivalent, equal, tantamount, Webster's (Second) (1961) states that


IDENTICAL is the strictest term for entire and absolute agreement or negation of difference. (Webster's (Second), 1961, p. 1236)


Other 'dictionaries' treat these various termings similarly.


The notioning of "sameness" depends upon some kind of "comparing." Plainly, the 'dictionaries' specify this "comparing" in termings of one rendering of the 'noun'-'verb' splitting, viz., a "comparing" of "THINGS": 'Identity' stands as the 'name' of a relationing between an "entity" we would designate by means of a nouning and an "entity" we would designate by means of a nouning. Specifically, 'Identity' names the relationing which holds when the implied "comparing" yields the finding that the "entities" ('linguistic isolates') compared show entire and absolute agreement or negation of difference. (In another sensing, 'Identity' names a linguistic or mathematical 'sentence' (composed of a symboling for a nouning, followed by a symboling for the 'relation' of 'identical with', followed by a symboling for a nouning) which asserts the relationing of entire and absolute agreement or negation of difference (between the nounings).


But this seems like hopelessly circular reasoning: We define the 'noun'-'verb' splitting by means of the notioning of 'Identity', and we define 'Identity' by means of the 'noun'-'verb' splitting.


In our traditional 'logics', this hopelessly circular reasoning becomes diagrammatically obvious. To example, using as key constructings the terming "objects" (e.g., x, y ) and their "properties" (one rendering of the 'noun'-'verb' splitting), Tarski (1965) writes,


Among the logical laws concerning the concept of identity the most fundamental is the following:


I. x = y if, and only if, x has every property which y has, and y has every property which x has ...


Law I was first stated by LEIBNIZ (although in somewhat different terms) and hence may be called LEIBNIZ'S LAW. It has the form of an equivalence, and enables us to replace the formula


x =_ y ,


which is the left side of the equivalence, by its right side, that is by an expression no longer containing the symbol of identity. With respect to its form this law may, therefore, be considered as the definition of the symbol '=_' , and so it was considered by LEIBNIZ himself. (Of course, to regard LEIBNIZ'S law here as a definition would make sense only if the meaning of the symbol '=_' seemed to us less evident than that of the expressions on the right side of the law, such as " x has every property which y has; cf. Section 11). (Tarski, 1965, p. 55)


This 'passage', to my eyes, does indeed display circular reasoning: For, as I show above, to distinguish between "objects" and "properties" necessitates utilizing the notioning of 'Identity', and yet Tarski utilizes this distinguishing to "define" the notioning of 'Identity'.


'Logicians' distinguish between two main usings of the relationing of 'Identity': In one the two nounings involved appear differently shaped, e.g. A =_ B , and in the other, the nounings do not appear differently shaped, e.g. A =_ A .


Although Heraclitus (c. 535-c. 475 BC) almost surely would not have concurred in this*, since his 'day' western Indo-European 'logicians'


Popper (1967) interprets the "message" of Heraclitus as follows: There was no stability left in the world of Heraclitus. 'Everything is in flux, and nothing is at rest.' EVERYTHING is in flux, even the beams, the timber, the building material of which the world is made: earth and rocks, or a bronze cauldron -- they are all in flux. The beams are rotting, the earth is washed away and blown away, the very rocks split and wither, the bronze cauldron turns into green patina, or into verdigris: "All things are in motion all the time, even though ... this escapes our senses," as Aristotle expressed it. Those who do not know and do not think, believe that only the fuel is burned, while the bowl remains unchanged; for we do not see the bowl burning. And yet, it burns; it may be eaten up by the fire it holds. We do not SEE our children grow up, and change, and grow old, but they do.


appear to have generally agreed to regard 'sentences' of the 'form'


A = A


as 'universally true' and 'sentences' of the 'form'


A ¹ A


as 'universally false'. For exampling, using the termings of the 'mathematical theory of sets', Mates (1965) writes,


There is a set having as members all objects that satisfy the sentence-form


x is different from x .


Obviously this set has no members; it is called the empty set and will be denoted by ' '. Since sets are uniquely determined by their membership, there is only one such set and we are justified in speaking of the empty set. Correspondingly the universal set, symbolized by 'V', is the set of all objects satisfying the sentence-form


x is identical with x .


(Mates, 1965, p. 29)


Similar formulatings appear in Tarski (1965, pp. 72-3), Halmos (1960, p. 8), etc.


But as the discoverings of modern 'logicians' and 'set theorists' have forced them to introduce and strictly to delimit the notioning of the (specified or clearly understood) 'universe of discourse' or 'domain' or 'universal set', for them to regard the relationing of 'self-identical' as 'universally true' has begun to appear troublesome. As Mates (1965) puts it,


The identity relation for a given domain is a relation that holds only between each element of the domain and itself ... it must be pointed out that our own intuitive account of the identity relation is not free of objectionable features. For instance, we have no right to speak of THE identity relation; by our analysis the identity relation among the elements of one domain will be different from that among the elements of another. Also, we have explicated the term 'relation' in such a way that whatever cannot be a member of a set cannot be related by any relation. Thus insofar as identity is a relation in this sense, such a thing cannot even stand in this relation to itself. This would hold not only of the set of all objects that are not members of themselves, but also of sets described by phrases that give no hint of impending difficulties. The problem is closely related to Russell's Antinomy, and once again every way out seems unintuitive. (Mates, 1965, pp. 148-50)


In this 'passage', Mates (1965) appears to me to have uncomprehendingly "discovered" what I call the 'noun'-'verb' splitting. Unlike 'sets' (and 'elements'), which qualify as 'self-identical' and therefore clearly occupy the logico-linguistic 'role' of 'noun', what he calls "the identity relation" clearly occupies some other logico-linguistic 'role'*: Since the notioning of 'identical with' "cannot be _______________________________________________________________________

*In modern 'symbolic logic' and 'set theory', we may treat 'predicates' or 'relations' themselves as 'sets' -- which often turns out handy. This does not, however, invalidate the generalizings spelled out here. Instead, it means that certain of our 'logicians' and 'mathematicians' found admissible 'ways' to "promote" a mathematical "entity" from the logico-linguistic 'role' of 'verb' to that of 'noun' -- and, usually, thereafter to ignore the 'operation' of "promoting." Certain fo the western Indo-European discursive languagings fairly freely allow a similar 'trick'. As Whorf (1956) puts it,


In English we divide most of our words into two classes, which have different grammatical and logical properties. Class 1 we call nouns, e.g., 'house, man'; class 2, verbs, e.g., 'hit, run'. Many words of one class can act secondarily as of the other class, e.g., 'a hit, a run', or 'to man (the boat)', but, on the primary level, the division between the classes is absolute. (Whorf, 1956, p. 215)


a member of a set" and so "cannot e related by any relation," therefore it "cannot even stand in this relation to itself," viz., it qualifies as "not 'self-identical'" or "not-noun."


(In other wording, according to Mates (1965), traditional 'logics' may not admit 'sentences' of the 'form'


=_ =_ =_ .)


To name this second, apparently unsuspected logico-linguistic 'role', I nominate the terming 'verb'.




The quotings from or citings of 'dictionaries', of Halmos (1960), of Mates (1965), of Tarski (1965), etc., support the inferring that western Indo-European 'logicians', 'mathematicians', etc., have over the 'centuries' concurred in admitting into their systemings the explicit notioning of 'Identity'; and that by now the notioning of 'Identity', even as viewed from within western Indo-European 'logics', 'mathematics', etc., appears to involve some thorny 'issues'.


But to return to the beginning of the section headed C. EXPLICIT 'IDENTITY' (where I mention that the notioning of "sameness" (or 'Identity') depends upon some kind of "comparing"), the using of explicit 'Identity' appears patently absurd. Even if for the moment I pretend NOT to concern myself with distinguishing between 'object-level' and 'event-level', I can show that the relationing of explicit 'Identity' holds under no circumstancings whatsoever. This I can do by bringing up a practical questioning with epistemological 'overtones': By what operating or operatings might we go about establishing whether or not two (non-verbal) "things" (which we agree upon) qualify as "absolutely the same in all respects"?


Clearly, no finite 'number' of "measurings" or "comparings" would suffice to establish the finding of "entire and absolute agreement or negation of difference." And no 'human' can perform an 'infinite' 'number' of "measurings" ("comparings").


Since no 'amount' of evidencing would suffice to establish even one 'instance' of 'Identity', I conclude that to admit into a 'logic' or other formal 'system' even one 'sentence' of the 'form'


A =_ B


qualifies as delusional (a "believing" held regardless of evidencing).


(But even to question thus, without pre-judging in favor of 'Identity', suggests that I have already abandoned the traditional western Indo-European assumings.)


And if, without pre-judging, I ask what operating(s) would suffice to establish whether or not any single (non-verbal) "thing" qualifies as "absolutely the same in all respects as itself," I make inescapably obvious that the notioning of 'self-identity' addresses no answerable questioning: for what do we "measure" or "compare" with what to establish or reject any given 'instance' of 'self-identity'? And in trying to determine what a given 'sentence', formalized or discursive, which asserts 'self-identity', e.g.


A =_ A ,


signifies, I can no longer even pretend to avoid the 'issue' of distinguishing between 'object-level- and 'event-level': For now I must somehow interpret at least two nounings which do not appear differently-shaped, viz., the left-hand A (which I could represent as A.) and the right-hand A (which I could represent as .A ), or discursively, "the thing" and itself."


Having at least two nounings and at least two levelings, e.g. 'event-level' and 'object-level', I find it plausible to assign one nouning to each leveling. In that 'case', the explicit notioning of 'self-identity' conceals-and-expresses the postulating of tacit 'Identity', namely, that 'event-level' qualifies as 'identical with' 'object-level'. But as I pointed out above, no "measurings" or "comparings" whatsoever would suffice to establish the relationing of 'identical with' between the two nounings, an no possible evidencing would support the inferring that 'object-level' (that 'map' which I could call "my picturing of the 'thing'") shows "entire and absolute agreement or negation of difference" with the 'event-level' (the (inferred) 'territory' which my 'map' (allegedly) "represents").


In that 'case', it follows that to regard 'sentences' of the 'form'


A =_ A


as 'universally true' qualifies as delusional (a "believing" held regardless of evidencing).



In the next section, I develop this arguing strictly, so as not to depend on the notioning of plausible.



In 'English', the terming to be has at least four main groupings of usings:


(1) To express the notioning of 'existence':


This paper is.


(2) As an auxiliary verbing, used to form progressive or perfect 'tenses' of passive 'voice':


a. He is writing a paper.


b. The paper was typed by him.


(3) As a 'copula" between a nouning and an adjectival 'form' or 'phrase', to express 'predication':


This leaf is green.


(4) As a 'copula' between a nouning and a nouning, to express 'identity':


A leaf is a natural product.


I find no grounds for objecting to usings belonging to the second grouping, and perhaps none to those of the first grouping. But neither do I find them necessary or unavoidable: Alternative expressings or synonymous 'forms' already exist in the languaging.


But the 'is of predication' appears seriously misleading. As Korzybski (1951) comments, the notioning of 'predication'


... resulted from the ascribing of "properties" or "qualities" to "nature," whereas the "qualities," etc., are actually manufactured by our nervous system. The perpetuation of such projections tends to keep mankind on the archaic levels of anthropomorphism and animism in their evaluation of their surroundings and themselves. (Korzybski, 1951, p. 183)


In other wording, I could describe a specific "human experiencing" to which 'test-sentence' (3) refers in the following termings: (non-verbal, event-leveled) 'light' strikes the (non-verbal, event-leveled) 'leaf', and some of it gets absorbed by the (non-verbal, event-leveled) 'chlorophyll'; and some of it bounces off and reaches my (non-verbal, event-leveled) 'eye', where it gets absorbed by and so stimulates the (non-verbal, event-leveled) 'retinal receptors', thereby initiating (non-verbal, event-leveled) neuro-biological "happenings" which I might describe by some phrasing such as the (non-verbal, object-leveled) visual experiencing that I call "green"; and perhaps in turn initiating other (non-verbal, event-leveled) neuro-biological "happenings" which I might describe by some phrasing such as saying the 'word' "green."


But the 'is of predication' structuring of (3) specifies none of these "happenings" on various levelings. Instead, by failing EXPLICITLY to distinguish between the "happenings" on these various levelings, (3) allows -- no, expresses -- the inferring that the 'quality' or 'property' ("green," unspecified as to leveling) exists "in" the 'referent' ("leaf," unspecified as to leveling). Thus (3) serves by its linguistic structuring alone tacitly to assert the 'Identity' of "happenings" which (in my analyzing) occupy at least three different levelings, namely, event-leveled, object-leveled, and verbal-leveled "happenings." And as I showed above, no evidencing could possibly support this postulating of tacit 'Identity'.


Otherwise stated, the 'is of predication' using qualifies as inevitably and intrinsically NEVER VALID (viz., delusional).


Similarly, the 'is of identity' using expresses the (explicit) relationing of 'identical with', which (as I showed above) holds under no circumstancings whatsoever.



But even if I pretend to start out by NOT categorically rejecting the notioning of 'Identity', I can show the 'is of identity' as necessarily inadmissible, by which I mean, as inevitably and intrinsically NEVER VALID. To show this perspicuously, I extend my simple notating, using roman lower case and capital letterings to signify "elements" and "sets" respectively (and I point out that "elements" and "sets" occupy the 'role' of 'noun'); and using =_ to signify 'identical with', and (epsilon) to signify 'element of' or belongs to, and / to signify not; and finally, I quote from Webster's (Second) and from Russell (1903).


I point out that 'mathematicians' and 'logicians' generally regard 'identical with' as reflexive, symmetric, and transitive:


Reflexive: A = A .


Symmetric: If A = B then B = A .


Transitive: If A = B and B = C then A = C .


Furthermore, they generally regard belongs to as asymmetric and intransitive:


Asymmetric: If A (epsilon) B then B /(epsilon) A .


Intransitive: If A (epsilon) B and B (epsilon) C then A /(epsilon) C .


(According to current axiom-schemes, belongs to qualifies also as irreflexive:


Irreflexive: A /(epsilon) A .


But without special 'provisions', even to CONSIDER questioning whether or not belongs to qualifies as reflexive involves us in "the set of all objects which do not belong to themselves," and so leads us into Russell's paradox (antinomy).

Therefore, by no stretch of imagining may we defend the interchanging of

the notioning of 'identical with' and that of belongs to.


Discussing the terming to be, Webster's (Second) (1961) does not explicitly distinguish between the 'is of predication' and the 'is of identity'; and it "philosophizes" to the extent of pointing out that to be, where it functions as the 'copula' in a 'sentence' or 'clause',


... asserts a relation between subject and predicate noun, adjective, or the like. Strictly, the copula does not imply or specify any particular kind of relationship, but, in usage, it has commonly one of the following meanings:


a) To equal in meaning, purport, nature, or the like; to have identity with; to constitute the same idea or object as; as, to be good is to be happy; the only person in sight is my brother.


b) To signify, either symbolically or in effect; to represent; to mean, as, let x be ten.


c)To belong to the class of; to have the class or type characteristics; to come under the general designation of; as, this fish is a trout; apples are fruit; red is a color.


d) To bear or carry a (specified) qualification, characterization, or attribution; as, man is rational; this book is heavy.


(Webster's (Second), 1961, p. 236)


Structurally speaking, meanings (a) through (c) qualify as 'is of identity' usings, and (d) qualifies as the 'is of predication'.


Apropos of the claiming that the 'is of identity' does not imply or specify any particular kind of relationship, Russell (1903), who does not here explicitly and categorically reject the notioning of 'Identity' (and who did not do so up till the end of his very long life), comments,


When a term is given, the assertion of its identity with itself, though true, is perfectly futile, and is never made outside the logic-books; but where denoting concepts [such as 'the King' in the 'statement', Edward VII is the King -- C.A.H] are introduced, identity is at once seen to be significant. In this case, of course, there is involved, though not asserted, a relation of the denoting concept to the term, or of the two denoting concepts to each other. But the is which occurs in such propositions does not itself state this further relation, but states pure identity. (Russell, 1903, p. 64)


In other wording, according to Russell (1903), whenever we juxtapose one nouning to another, we can find some definite relationing between them; but when we join them with the 'is of identity', we do NOT assert this further definite relationing between them, but rather we assert that the relationing of 'identical with' holds between them.


And, I add, by asserting relationing B when we mean relationing A , we may or may not get ourselves into trouble. I offer it as a hypothesizing, for testing, that we will get ourselves into trouble thus.


To test this hypothesizing, I take, in turn, 'test-sentences' which belong to usings (c), (b), and (a). To example,


c. This fish is a trout.


The relationing between the left-hand and right-hand nouning goes by the 'name' of 'left-to-right class-inclusion', where the left-hand nouning stands in the 'role' of "element" (e.g., x ) which "belongs" (signified by (epsilon)) to the "set" (e.g., A ) specified by the right-hand nouning:


x (epsilon) A .


However, as Russell (1903) intimates, the presence of the is between these two nounings implies that they qualify as 'identical' (signified by =_ ):


x = A .


And if they qualify as 'identical', then the relationing between them qualifies as symmetric:


If x = A then A = x ;


and therefore we may freely interchange them. However, as we know from the 'mathematical theory of sets', the relationing of belongs to qualifies as asymmetric:


If x (epsilon) A then A /(epsilon) x .


Hence we may NOT, without erring, interchange the left-hand and right-hand nounings. And therefore, in this recognized using of to be, the implicating of the 'is of identity' turns INADMISSIBLE.


b. Let x be ten.


The left-hand nouning (x) comprises a 'variable', and the right-hand nouning comprises a 'constant' which qualifies as an admissible 'substituent' for the 'variable' -- in other wording, the relationing between them goes by the 'name' of 'right-to-left class-inclusion:


x (reversed-epsilon) 10 .


And again, the 'is' implies the symmetric relationing of 'identical with' between them, which implicating turns out INADMISSIBLE.


a. The only person in sight is my brother.


Here again, as in (c), the actual relationing between the two nounings consists of 'left-to-right class-inclusion', with the notioning of my brother occupying the 'role' of an abstract relationing ("set"). Here the is', however, implies the symmetric relationing of 'Identity' between them, which implicating turns out INADMISSIBLE.


Hence, even if I do not start out by categorically rejecting the notioning of 'Identity', I find that invariably the nounings which I would join by the 'copula' belong to different logical 'orders' (levelings), precisely as "element" and "set" belong to different logical 'orders'. Consequently every listed using of to be as a 'copula' joining two nounings turns out as DEMONSTRABLY AND ONLY ERRONEOUS.


I can apply this concluding even for a 'case' of 'self-identity' which actually occurs outside the 'logic-books':


"Boys will be boys!"


as stated to the neighbor by the father, making 'excuses' for the boy whose 'baseball' broke the neighbor's 'window'. Here the left-hand nouning refers to "element," namely the 'culprit'; while the right-hand nouning refers to a "set," a cultural stereotyping of 'male children' as "robust, vigorous, active, noisy, and often in trouble."


Even in the abstract 'case' of 'self-identity', viz., in the asserting that


A = A ,


of which Russell (1903) says,


... though true, is perfectly futile, and is never made outside the logic-books,


I may apply this insighting: Here let us regard the right-hand nouning as somehow more generic, abstract, inclusive, etc., than the left-hand one. I can achieve this by taking the asserting of 'self-identity' to mean that "Independent of any 'observer', the right-hand nouning signifies a 'member' of the 'class' of 'nouns' (a 'construct' at the 'level' 'World-View', viz., verbal-leveled), while the left-hand nouning signifies a "corresponding" "entity" at the 'level' of 'World Viewed' (viz., object-leveled)." Or, alternatively, I can take it to mean that "Independent of any observer, the right-hand nouning signifies an "entity" at the 'level' of 'World Viewed' (viz., object-leveled), while the left-hand nouning signifies a (supposedly) "corresponding" "entity" at the 'level' of 'World Unviewed' (viz., event-leveled)."


In either 'case', the asserting of 'self-identity' tacitly makes the preposterous claiming that two of these 'levels' show ENTIRE AND ABSOLUTE AGREEMENT. (And since 'Identity' qualifies as transitive, the asserting of 'self-identity' also implicitly claims that event-leveled "happenings" qualify as 'identical with' verbal-leveled "happenings," e.g. 'World-View'.)


But that does not exhaust my criticizing. To my viewing, and according to the non-aristotelian postulatings, any 'map' elaborated by an 'organism' -- including any specific exampling of the asserting of 'self-identity' -- unavoidably consists of two components, one of which I could label 'hetero-referential', in that it "tells" about the 'territory', and the other 'self-referential', in that it "tells" about the 'organism'. In other wording, despite Russell's (1903) opining that it appears futile, to assert 'self-identity' serves (non-trivially) to SPARE THE 'ASSERTER' THE 'TROUBLE' OF ACCURATELY SPECIFYING THE (hetero-referential) RELATIONING HE ALLEGEDLY DISCUSSES (including the relationing between 'map' and 'territory'); and serves (non-trivially) to AFFIRM (self-referentially) THAT THE 'ASSERTER' SUBSCRIBES TO PECULIAR BUT TRADITIONAL METAPHYSICAL ASSUMINGS such as those underlying the western Indo-European languagings.


To summarize, even if I pretend to start out by NOT categorically rejecting the notioning of 'Identity', on examining I find that the linguistic 'means' for asserting 'Identity', namely, the 'is of identity', serves only to confer the 'privilege' of keeping one's expressings (formulatings) logically imprecise, by "replacing" and so concealing some more interesting relationing, and in so doing, yielding 'sentences' which qualify as DEMONSTRABLY AND ONLY ERRONEOUS.




The "Laws of Thought" attributed to Aristotle express one rendering of a relationing fundamental to any human symbolizing, which I have elsewhere called 'the logic of opposites' (Hilgartner, 1970d). Aristotle's rendering generalizes the 'rules for naming (nouning)' in western Indo-European languagings.


Even though eventually I insist on abandoning 'set theory', here I state the relationings of the 'logic of opposites' in the termings of the simplest constructings of the 'mathematical theory of sets'; and in order to compare, I quote another stating of the 'logic of opposites', one which apparently first got transcribed somewhere around the 'period' Aristotle lived, and which came out of a Chinese 'culture' and so got framed in a Sino-Tibetan languaging, one distant from the western Indo-European grouping. Finally, I state Aristotle's "Laws of Thought" in 'words' and in a very simple notating, and discuss them.



I start by pointing out that every expressing in 'set theory' implies-and-assumes some defined or clearly understood 'universe of discourse' or 'context', which I designate as the 'universal set' U. Furthermore, the termings 'set', 'element', and belongs (to) comprise the undefined termings of 'set theory', where the 'criterion' of correct using requires that for any 'element' we can unambiguously determine whether or not it belongs to a given 'set'. If the 'element' x belongs to the 'set' Z , I write x (epsilon) Z ; if not, I write x /(epsilon) Z .


Furthermore, although traditional Western 'logicians' and 'mathematicians' generally concur in insisting that the constructings of 'set theory' do not "represent" or "refer to" any non-symbolic, non-verbal 'domain' (but rather constitute an 'isolated' 'domain' sui generis, viz., a 'manifestation of "the mind"'), I dissent from that opining. Instead, in according with the non-aristotelian postulatings, I attribute to any formal constructings, including those of 'set theory', both 'logical' and 'empirical' relationings. In other wording, I specify relationings between (verbal-leveled or symbolic) 'elements' and (verbal-leveled) 'sets', and I also specify relationings between (verbal-leveled or symbolic) 'elements' and (non-verbal, non-symbolic) "happenings." Furthermore, I specify 'self-referential' relationings between any constructings and the 'organism' which elaborates the constructings, by which they "tell" about the 'organism'.


Then I can display the 'logic of opposites' by referring to some 'universal set' U which contains one 'proper subset' Z . (In 'set theory', we may regard a 'set' as a 'subset' of itself, an 'improper subset' of itself. A 'proper subset' of a 'superset', then, does not contain all the 'elements' which belong to the 'superset'.) For exampling, analogizing to 'point-sets' on a 'plane', I can show these relationings by using the venerable 'device' of 'Venn diagrams':




Here every 'element' of the 'point-set' U either belongs to the 'set' Z or else it does not belong to Z , in which 'case' it belongs to its 'complement' (overbar)Z (not-Z).


Thus, according to the 'logic of opposites', any "classifying" an 'organism' may do, as by means of a 'set' or nouning, symbolically splits the (verbal-leveled) "universe" into two mutually-exclusive 'parts', which I could represent as {x|x (epsilon) Z} and {y|y (epsilon) (overbar)Z}.


But in order to "classify" non-verbal, non-symbolic "happenings," the 'organism' must define or clearly assume SOME PARTICULAR 'context' or 'universe of discourse', which effectively specifies a relationing between non-verbal "happenings" and (verbal-leveled or at least symbolic) abstract 'elements'. For exampling, if Z stands for the 'set' designated by the English nouning dog, before I can classify non-verbal "happenings" as belonging or not belonging to this 'set', I need to know whether the 'context' or setting involves 'the edible', or 'domesticated mammals', or 'humans whose behaving I disapprove of', or 'constellations of stars', or 'mechanical devices', or 'meterological haloes', or whatever. And given that my setting involves 'the edible', I still need to know whose dietary 'customs' we refer to: e.g., the tribal 'customs' of the United States, where 'dog' might refer to "small skinless sausages,' or those of China, where (I understand) canine 'meat' qualifies as a 'delicacy'.


Finally, 'constructs' self-referentially "tell" about the 'organism' who elaborates them. The 'complements' of many of our common terms themselves have common 'names', e.g. 'night' vs. 'day'. In the 'context' of nomad hunters roaming about on an allegedly non-spheroidal 'Earth', this pair of termings might appear "perfectly natural," with no specific assumed 'context'. But for the 'crew' of 'Apollo 12' en route to the 'moon', this pair of 'opposites' becomes utterly irrelevant, and so its specific assumed 'context' becomes fully apparent.


For me one of the most beautiful expressings of the 'logic of opposites' comes from the Tao Teh Ching:


Whenever the most beautiful is perceived, ugliness arises, the least beautiful. Whenever good is perceived, evil exists, its natural opposite.


Thus perception involves opposites: reality and fantasy are opposing thoughts; difficult and simple oppose in degree; long and short oppose in distance; high and low oppose in height; shrill and deep oppose in tone; before and after oppose in sequence.


The truly wise accept this and they work diligently without allegiance to words. They teach by doing, not by saying; are genuinely helpful, not discriminating; are positive, not possessive; do not proclaim their accomplishments, and because they do not proclaim them, credit for them can never be taken away. (MacHovec, translator, 1962, p. 33)


I take both this excerpting from the Tao and what I said above to indicate that the 'logic of opposites' specifies one 'basis' for systematic symbolizing, by which I mean, for the "doings" by which an 'organism' makes verbal-leveled 'maps' of the (non-verbal) 'territory' which I could characterize by some phrasing such as 'himself-and-his-environings-at-some-previous-instant'. The Tao and my commentings specify distinguishings similar in 'number', and similar in structuring: The Tao specifies the necessary relationing between a constructing and its 'opposite' (e.g. 'the beautiful' vs. 'ugliness'); it explicitly points out that this opposing presumes a setting (long and short oppose in distance); it explicitly mentions 'words', and so presumes 'not-words', and similarly opposes doing vs. saying; and it explicitly mentions 'organisms' ('the truly wise', which also presumes 'the not-wise'). Finally, by explicitly mentioning one possible relationing between 'organisms' and their 'words', namely, by negating 'allegiance to words', the Tao seems to me to recognize both explicit and tacit 'Identity', and to reject both.


Now I turn to deal with some special aspectings of the 'rules for naming (nouning)' in western Indo-European languagings such as ancient 'Greek' or modern 'English'.




Korzybski (1933) writes,


Let me recall the 'philosophical grammar' of our language which we solemnly call the 'laws of thought', as given by Jevons (1883):


1. The law of identity. Whatever is, is.


2. The law of contradiction. Nothing can both be, and not be.


3. The law of excluded third. Everything must either be, or not be.


These 'laws' have different 'philosophical' interpretations which help very little and for my purposes it is enough to emphasize that:


(1) The second 'law' represents a negative statement of the first, and the third represents a corollary of the former two; namely, no third possible between two contradictories.


(2) The verb 'to be', or 'is', and 'identity' play a most fundamental role in these formulations. (Korzybski, 1933, p. 749)


Besides the notioning of 'Identity' and the terming to be, I point out that these formulatings also depend on the 'noun'-'verb' splitting, as betokened by the nounings 'whatever', 'nothing', and 'everything'.


Please note that the linguistic rendering of the "Laws of Thought" does not explicitly mention any setting or 'context' or 'universe of discourse'. When I state the "Laws of Thought" in a set theory notating, perforce I refer to a 'universal set' U which contains one 'proper subset' Z: Then they become


Identity Z = Z or


Z + Z = Æ (where the symboling 0/ signifies the 'empty set', and the symboling + signifies 'symmetric difference', viz., A + B = [(A-B) (union) (B-A)], which contains all 'elements' of (A (union) B) outside the 'intersection' (A (intersect) B).


Contradiction Z (intersect) (overbar)Z = 0/


Excluded middle For all x: x (epsilon) Z (union) (overbar)Z


(Translated into 'words', these 'sentences' say:


Identity: The 'set' Z identically equals the 'set' Z (where identically equals signifies, "not only consists of the same elements as, but also has the same name as"); or, the 'symmetric difference' between the 'set' Z and the 'set' Z proves equivalent to the 'empty set'.


Contradiction: The 'set' Z and the 'set' (overbar)Z have no 'elements' in common (the 'intersection' of Z with (overbar)Z proves equivalent to the 'empty set'.


Excluded middle: All elements x (which belong to the 'universal set' U) exist such that x belongs to the 'union' of Z with (overbar)Z .)


From these considerings, I infer that both the linguistic and the set theory renderings of the "Laws of Thought" do express the 'logic of opposites' (namely, the relationings between any nouning and its 'opposite' or 'contradictory' or 'complement'), and so do appear to specify the 'rules for naming' in western Indo-European languagings.


But by contrasting to both the Tao and to my commentings, the linguistic rendering of the "Laws of Thought" does not explicitly mention the 'topic' of the setting or 'context' of opposing nounings, and so by defaulting appears to define them on some "UNIVERSAL 'universe of discourse'" analogized to an "infinite" Euclidean 'plane'; nor does it explicitly mention 'words' vs. 'not-words', and so by defaulting appears to postulate their 'Identity'; nor does it explicitly mention the 'organism' who elaborates 'words', and so by defaulting appears to eliminate from considering any 'organism' who might elaborate 'words', and thus appears to posit what Korzybski (1951) calls "projections," namely, a disembodied 'Universe' (unspecified as to 'level') devoid of 'living systems' (an "isolated" 'domain' sui generis, the 'realm' of "the 'mind'").



And although the set-theory rendering of the "Laws of Thought" does perforce delimit the 'universe of discourse' and so takes into its accounting the setting or 'context' of the opposing nounings, it still neglects the other two distinguishings, and so appears to posit a similar, disembodied 'realm'.


But these failings seem precisely what I should expect from a rendering of the 'logic of opposites' built up out of the 'noun'-'verb' splitting, the "notion" of 'Identity', and the terming to be.


a) The logico-linguistic 'role' of 'noun' already tacitly contains the notioning of 'selfsame' or 'identical with itself', which notioning, as I showed above, effectively presumes tacit 'Identity', viz., that 'word' and 'not-word' qualify as 'absolutely the same in all respects'.


b) The explicit sensing of 'Identity' presumes a "comparing," a comparing of two nounings and/or of the 'linguistic isolate(s) designated by the(se) nouning(s). But as I showed above, hetero-referentially speaking, the relationing of 'Identity' serves solely and exclusively to "replace" some more interesting relationing which the 'organism' involved does not bother to specify precisely; and self-referentially speaking, serves solely and exclusively to affirm that the 'organism' involved subscribes to restricted and restrictive but traditional metaphysical assumings such as those underlying the western Indo-European languagings.


And since Western 'logicians', 'mathematicians', etc., have over the 'centuries' concurred in admitting the notioning of 'Identity', I conclude that this notioning, in both "affirming" and "replacing," successfully covers up for the logically imprecise expressings of its 'user'. And by thus "covering up," this notioning successfully insures that the "loyal" 'organism' involved will not discover that the explicit notioning of 'Identity' which he accepted from his progenitors, and now uses, posits 'conditions' impossible to attain: that no 'amount' of evidencing, no feasible "comparings" or "measurings," would suffice to establish even one 'instance' of "Identity'.


c) The linguistic 'means' for asserting explicit 'Identity' -- the terming to be -- in its 'is of identity' using (and also in its 'is of predication' using) serves by its linguistic structuring alone to presume the (tacit) 'Identity' of 'words' and 'not-words' (or of 'verbal levels', 'object-level', and 'event-level'), and so serves to eliminate from the 'user's' considering how his own functioning enters into his own experiencing. The discursive and/or formalized 'sentences' resulting from this eliminating contain no explicit mentioning of the 'organism', and so qualify as what Korzybski (1951) calls "projections."




As I promised, I have:


(a) Named the traditional assumings I criticize;


(b) Specified their mutual inter-relationings;


(c) Scrutinized them to show how they qualify as untenable;


(d) Showed how they figure in the traditional 'World-View' specified by the

logico-linguistic structuring of western Indo-European languagings;


(e) Thus provided 'criteria' for judging whether or not any given expressing, discursive or formalized, presumes-and-expresses these traditional assumings.


But in doing this much, I have already done more than I promised: I have demonstrated, by exampling and beyond reasonable doubting, that we CAN operate without these traditional but untenable assumings:



(f) I have provided a reasonably intelligible discursive languaging which


i) Does not utilize the terming to be (Bourland, 1965/66, pp. 111-114), and which


ii) Attempts to avoid tacitly assuming 'Identity' via the 'noun'-'verb' splitting, either by replacing traditional nounings by other already-available constructings; or else, by orthographically flagging nounings with single quotings, reminds us to beware.


Furthermore, to cap off this "insult to" (disconfirming of) the traditional explicit and tacit assumings, elsewhere (as I make plain in the beginning sections of this paper) I have already elaborated a new relational languaging which starts ab initio from the non-aristotelian premisings of Korzybski, and so specifically forbids any tacit and/or explicit postulating of 'Identity'.