Critical Legal Doubts About Language

Louis E. Wolcher^*

"Law is politics" is everywhere in danger of becoming merely a slogan. If what is in danger of happening actually does happen, critical legal studies will fade away like the Cheshire cat, leaving behind only the smile of its slogan.⁽¹⁾ As a law teacher who is also a critic of law, I am always searching for new ways to appropriate and communicate what I take to be the most basic truth expressed by "Law is politics." Truths, including basic truths, emerge as true only so long as we make them our own--only so long as we take steps to appropriate them, and to keep on appropriating them. Having myself struggled to appropriate the truth expressed by the previous sentence, I offer this article in the spirit of keeping alive--of reappropriating--the bottommost truth expressed by "Law is politics."

That truth is exceedingly hard to come by. Books and articles about the meaning of "Law is politics" will never secure the truth for us, for what they offer us is mere information in a predigested form. Our theme demands less information and more thought. Indeed, if we are to do justice to our theme, we ought not think about law at all. For if, after all, we fill up the hours of our days with busy thoughts "about law," we would be choosing to think about something that is set before us ready-made, like a hammer or a pot; and thus not to think about what is most important of all.⁽²⁾ (And if I were now to say "The most important thing of all is . . . ," neither you nor I would be thinking.) If we are to appropriate the bottommost truth expressed by "Law is politics," we would do better to think down to the place wherein our thinking "about law" (in the sense of acquiring mere information for using this way or that) is grounded. This is hard work. Accordingly, this article is hard work--for there is a sense in which it is not "about" anything at all (let alone law). Rather, it would be better to say that this article offers itself as a demonstration.

Legal language, and critiques of legal language, are kinds of language.

When it comes to talking about any kind of language, we are like a bug walking on a Möbius strip.⁽³⁾

The bug keeps walking on the same surface--what seems to the bug to be down will soon be up, and what seems to be up will soon be down. Like the bug, we think we have gotten on top of the matter of language, but the truth is we keep walking around and around on the same surface. Unlike the bug, however, we have the capacity to doubt. If we are to doubt all the way to the bottom of language, we must stop walking its surface and look down at what is just beneath our feet. Then what is pointed at in (1) will emerge and become clear to us:

Before we can stop walking we must first be walking at a slower pace. A paradox gives us a good direction in which to walk because a paradox, if we take it seriously, forces us to slow down. It is (past, beyond, contrary to) (opinion);⁽⁴⁾ it makes us traverse rough terrain, as it were, that comes upon us in the midst of our confidence in the power of reason to solve our problems. A paradox is a statement that appears to be contradictory but is not. If you have a set of assumptions and rules of inference which appear to be non-contradictory, and yet they go on to generate a sentence of the form " is and is not," then you have a paradox. Grelling's paradox,⁽⁵⁾ also called the heterological paradox, marks the path along which we will walk in this article. The article is not about the paradox in the sense of, say, being about the paradox's history or status in analytical philosophy or mathematical logic. Even less is the article written from a position that is located within one or the other of these disciplines.⁽⁶⁾ In this article we will occupy ourselves with the paradox--or rather, we will listen to what the paradox has to say to us about language. To begin doing this we will orient ourselves within a field of reference that is established by two texts concerning Grelling's paradox. We will not interpret these texts, in the sense of expressing some understanding of what the people who wrote them did or did not think, or even in the sense of expressing our opinion of what the texts mean. Instead we will use these texts for the sake of whatever light they may shed on our problem: namely, getting to the bottom of the matter of language so that what is pointed at in (1) will emerge and become clear to us.

The first text delivers the paradox to us in its traditional form, and was written by John van Heijenoort for The Encyclopedia of Philosophy:⁽⁷⁾

In 1908, Kurt Grelling presented a new paradox, that of "heterologicality" ("Bemerkungen zu den Paradoxien von Russell und Burali-Forti").^[(8)] A word is said to be "autological" if and only if it applies to itself--that is, if it satisfies the schema "`w' is w." Examples of autological words are "English," "short," "polysyllabic." If a word is not autological, it is "heterological." Examples of heterological words are "French," "useless," "monosyllabic." Now, is the word "heterological" heterological? If we assume that "heterological" is heterological, then, by the schema above, "heterological" is autological; on the other hand, if we assume that "heterological" is autological, then, by the definition of "autological," "heterological" is heterological.

To further illustrate the meaning of "heterological" and its opposite, consider the words "tortious" and "legal." Unless it appears in a libelous statement, the word "tortious" is not itself tortious (it is therefore heterological in most contexts); whereas the word "legal" can be legal (and therefore autological) if it appears in a legal document (e.g., a statute). If it is stipulated that, in any given use of it, a word can be autological or heterological, but not both, then it follows that an autological word is not heterological. Now consider the word "heterological" itself. If we let "not heterological" substitute for "autological," then using the apparently non-contradictory assumptions set forth in van Heijenoort's text we derive from the proposition "`heterological' is heterological" the proposition "`heterological' is not heterological," because the first proposition is of the form "`w' is w." On the other hand, we derive from the proposition "`heterological' is not heterological" the proposition "`heterological' is heterological," because if "heterological" applies to itself (i.e., is autological = not heterological), then it can be put into the form "`w' is w." The resulting

antinomies can be represented in the following form:

(2) "`Heterological' is heterological and `heterological' is not heterological."

The proposition expressed in (2) is a paradox and not a contradiction. But what is the status of the assumptions that lead to this paradoxical statement? One feels entitled to ask, after reading van Heijenoort's description of Grelling's paradox: How does a word "apply to itself"? And if the answer given to this is "see van Heijenoort's definition," one still feels entitled to ask: Then how is it that what is pointed at in (3),

satisfies the condition of being a kind of language (the kind that is called a "definition") at all? Surely what it says comes after, and not before, the fact that it is a saying in the first place. I mean, how is it we know that it says anything at all?

Our second text is taken from Elizabeth Anscombe's translation of a manuscript that Wittgenstein wrote sometime in 1944, and that was published after the latter's death in a book of his writings entitled Remarks on the Foundations of Mathematics:⁽⁹⁾

Why shouldn't it be said that such a contradiction as: `heterological' <sup>[(10)]</sup> heterological <sup>[(11)] [(12)]</sup> (`heterological' heterological), shews a logical property of the concept `heterological'?

"`Two-syllabled' is heterological", or "`Four-syllabled' is not heter-ological" are empirical propositions. It might be important in some contexts to find out whether adjectives possess the properties they stand for or not. The word "heterological" would in that case be used in a language-game.^[(13)] But now, is the proposition "`h' h" supposed to be an empirical proposition? It obviously is not one, nor should we admit it as a proposition in our language-game even if we had not discovered the contradiction.

`h' h (`h' h) might be called `a true contradiction'.--But this contradiction is not a significant proposition! Agreed, but the tautologies of logic aren't either.

"The contradiction is true" means: it is proved; derived from the rules for the word "h". Its employment is, to shew that "`h'" is one of those words which do not yield a proposition when inserted into `^[(14)] h'.

"The contradiction is true" means: This really is a contradiction, and so you cannot use the word "`h'" as an argument in ` h'.

This text invites us to solve the paradox first by reducing a word's meaning to its use in a language-game, and then by denying "`Heterological' is heterological" a use in any language-game. Still, one feels entitled to ask, after reading Wittgenstein's discussion of the paradox: How is the contradiction that is generated by the rules for the word "heterological" the kind of contradiction that is true? And if the answer given to this is "see what Wittgenstein says about `the word "`h'"' not being usable in a language-game," one still feels entitled to ask: Then how is it that "`h'" (or "`heterological'") satisfies the condition of being a word at all?⁽¹⁵⁾ I mean, how do we know that it is the kind of thing that is at least trying to say something to us--as opposed to, say, just lying there on the ground like a rock that we do not notice?

We intend to take Grelling's paradox very seriously. We will not dismiss it as being merely an arid word-problem of a kind that is fit only to attract the attention of sophists. This means that we will care about the fact that a human system of thought is capable of generating a statement that appears to be contradictory, but is not. However, it must be said that the reason we will care is not because we are linguistic purists who want to purge our language of all contradictions. Nor do we care because we seek to solve the paradox, in the sense of answering the question "Is `heterological' heterological?" in such a way that we feel entitled to forget the question and move on to the next philosophical problem.⁽¹⁶⁾ We will care about Grelling's paradox because if we adopt the attitude (and not just the pose) of caring, then we just might be able to slow down our pace on the Möbius strip of language long enough to see clearly what lies beneath our feet.

The importance of Grelling's paradox for our theme cannot be fully appreciated without paying close attention to what happens when objects begin to talk about themselves in sentences. (And here it must be said that to give a definition of "object" at this stage of the discussion would be premature--would, indeed, not be helpful at all, but rather in the nature of a hindering throw (jacere) in the way of (ob-) understanding⁽¹⁷⁾--would, in fact, be positively harmful.)

Sometimes it is the case that an object, besides being what it is, is also used and taken as the grammatical subject of a proposition about itself; that is, people use and take the object to symbolize itself, and only itself, in a sentence about itself. A very dirty automobile on whose dusty surface someone has traced ". . . needs washing" can be interpreted as a sentence which is comprised of the automobile standing for itself (and no other thing) in a sequence of signs completed by the words " . . . needs washing." Three other examples of what can be interpreted as sentences in which objects are used and taken to symbolize themselves, and only themselves, are shown in (4), (5), and (6):

(4) " is a picture of the sun."

this₄

(5) " is not a clock."⁽¹⁸⁾

this₅

(6) "

was not painted by

Parmigianino."⁽¹⁹⁾

this₆

The objects that this₄, this₅, and this₆ point at can be used and taken to stand for just themselves, and only themselves, in sentences which are completed by the words in (4)-(6). We will use the term "object sentence" to designate a sentence that is characterized by this kind of use of an object to represent itself, and only itself, in a statement about itself.⁽²⁰⁾

The first thing to notice about what the three "thises" point at in (4)-(6) is that they lack the characteristic of being easily portable as symbols in a written language. For example, one can imagine cutting out or peeling off just these objects from the pieces of paper where they appear, if that were physically possible, and then pasting the objects into other sentences about these objects--but surely that would be a very burdensome and time-consuming procedure, at best. Moreover, think of all the many bulky things there are in the world--the Empire State Building, Mt. Everest, a 10,000 pound lump of lead, etc.--as well as all the many fragile or ephemeral things--a faint veneer of print on rice paper, a wrinkle in a discarded garment, a cloud through which a slogan-pulling biplane can fly, etc. If someone wanted to incorporate a thing such as these into an object sentence, the thing's unwieldiness, fragility, or ephemerality would undoubtedly stand in the way of its being brought to a piece of paper containing printed words. Undoubtedly it would be the case that written words would have to be brought to the object if the intention of forming the desired expression is to be executed.⁽²¹⁾

The second thing to notice about what this₄, this₅, and this₆ are pointing at is that what, exactly, the three "thises" are pointing at can be made questionable. Imagine that I am at your side, and that I use my finger to stab vigorously at certain things on the paper as you are reading (4)-(6). Take (4) as an example. Is it the case that my gestures plus the written text must absolutely rule out--as a logical necessity for you--the possibility that I am really gesturing at just these things: the single short stroke protruding from the bottom of the circle in (4)?--or all of the strokes, but not the circle?--or the circle, but not the strokes surrounding it?--or an arc of the circle, but not the circle?--or merely the circle's diameter, and nothing else?--or the shallow indentions in the paper lying just underneath the sun-picture, but not the inked sun-picture sitting on top of the indentions?--or . . . etc., etc.?⁽²²⁾ These questions rightly bring into view the larger question of how, if ever, the gesture of pointing determines its object--how, in short, an object can be made to show just itself (i.e., itself and only itself) by virtue of the act of pointing.⁽²³⁾ What is more, on the answerability of this question hangs the answerability of still another question: How does the ostensive⁽²⁴⁾ definition of a word ever get itself established? How, for instance, can any word be made to stand for just what this gesture, , is pointing at? Indeed, while we're on the subject, where is our assurance that any word or sentence can determine what it is talking about? If the gesture of pointing has difficulty establishing its scope even when the intended object seems to be sitting right in front of us, how can a mere sentence that is unaccompanied by gestures have any better chance of establishing its scope, given that what it refers to is not necessarily even in the same room with it, let alone on the same page? It is almost as if one can hear the hue and cry from a certain kind of postmodernist at this point: "Let's stop fussing around with the tired old chestnut that words have meaning, and go right to the bottom line: We already know that words don't mean. People and words mean together. Isn't that what the hermeneutic circle⁽²⁵⁾ is all about?"⁽²⁶⁾

People who maintain a critical attitude towards law have a right, a duty even, to judge these questions as cogent. But despite their cogency, or perhaps because of it, it is precisely at this point in the discussion that our choice to care about Grelling's paradox becomes the hardest to maintain. For if we were to make a detour now into the domain of language's indeterminacy, we would dramatically quicken our pace, and this would be fatal to our project. If the gesture of pointing at an object is conceived as being a kind of language, or at least a part of language, then a discussion of the semantic content of the various parts of the language--what the words and gestures of the language do or do not mean--should come after, and not before, a discussion of the concept "language" (including the concept "pointing"). For otherwise we might lead ourselves into a fog of doubt about what we are doing (let alone referring to), if anything at all, when we discuss this: "language." For example, whatever it is that is pointed at in these marks on paper,

must first be taken to express, and not just be, something in order for the apparent sequence formed by the objects pointed at in (7) to tell us anything at all, including even the extremely minimal statement that these regular-looking splotches of ink happen to be printed on a piece of paper. Objects can and are sometimes interpreted as saying the equivalent of "I exist! Look at me!" (e.g., certain public sculptures), but they need not be interpreted as saying this, and they often are not interpreted as saying anything at all. Thus, for example, if we sometimes say that the earth's movements in relation to the sun are regular, we do not always say this. And when we do speak, any statement we make of or about that regularity is always spoken in a language. Even if someone were now to insist that the sequence of positions of the earth and sun speaks for itself--i.e., it expresses a regularity--would he not be telling us in a language that certain objects in the Universe speak in a language that he is able to hear?⁽²⁷⁾

We can summarize the preceding paragraph in a very few words: Language precedes all talk about language. (This is what might be called a "true tautology.") And this means, among other things, that language precedes all discussions about whether a legal expression (e.g., a rule) determines or does not determine what it is referring to, or what it requires us to do.

We will therefore choose to suspend any doubts we may have about whether an object is capable of representing itself, and only itself, in an object sentence. For if we choose at the outset to be reckless in the scope of our doubting--if our doubts ever and always extend that far down--we will not be able to hear what Grelling's paradox has to say to us.⁽²⁸⁾

Let it be the case that (8), (9) and (10) are object sentences:

(8) "Large is large, and large is not large."

(9) "small is small, and Small is not small."

(10) "Black is black, and Black is not black."

From what has been said already, it should be apparent that (8)-(10) are used and taken to express compound propositions with a sense, and not contradictions. What it means to say that (8)-(10) are used and taken to express propositions with a sense, and not contradictions, is this: most people would, without hesitation, know just what to point at if someone asked them to show what is large, and not large, in (8); small, and not small, in (9); black, and not black, in (10). They would not experience (8)-(10) as being contradictory statements. And it is precisely for this reason that what is paradoxical about (8)-(10)--the paradox of language that lies so very near the surface in Grelling's paradox--would be hidden from their view. Most people would take (8)-(10) as being odd, but true, sentences in a language, and thus they would fail to see how it is that (8)-(10) announce themselves as being language in the first place.

But now this question quite properly arises: What does it mean to say that a sentence is "experienced" as being contradictory or non-contradictory? Let us begin our engagement with this question by examining this sentence:

(11) "`Buzz' is heterological and `buzz' is not heterological."

Suppose that our inclination is to experience (11) as being a contradictory statement. This could mean that we immediately dismiss it as nonsense-talk which is unworthy of our further attention. But suppose that we let it sustain our attention for a while. Then our experiencing (11) as being contradictory could come in the form of our being puzzled by it--"What is this sentence saying?," we might ask ourselves. This kind of puzzlement is often characterized by the recognition that we have to work on an apparently contradictory statement like (11) if we are to have any chance of dissipating our puzzlement and making sense of it. If we now contrast the way in which (11) presents itself to us in this mode with the apparently non-contradictory presentations of (8)-(10), we can begin to see more clearly what it means to say that a sentence in a language is (or is not) experienced as being contradictory. We can also begin to see how an experience of contradiction-induced puzzlement can get dissipated by means of working through other sentences in a language.

The work required to dissipate the puzzlement induced by the apparent contradiction in (11) is best begun by stating the following proposition: The English word "buzz" is onomatopoetic, and this implies that (11) is not a contradiction. What this proposition means can be shown by an experiment. First look at what is pointed at in (12); then silently read the underlined part, and speak out loud the italicized part:

(12) `Buzz' does not buzz, and `buzz' buzzes.

Now do the same with what is pointed at in (13):

(13) `Buzz' is heterological and `buzz' is not heterological.

There is a proposition which can result from following the directions given for (13). It is expressed in a language (call it L) which permits sentences to be formed with both visible (written) signs that are read silently, and auditory (spoken) signs that are nowhere written down in the sentence. We will number this new proposition (14), but we will not, given our definition of L, be able to write it all down:

(14) "`Buzz' is heterological and ______ is not heterological."

What we can now do, however, is describe (14)'s syntax, in writing, in the language of symbolic logic. In form, (14) asserts the proposition that there is a visible sign⁽²⁹⁾ (B₁) and an audible sign⁽³⁰⁾ (B₂), such that B₁ has a certain property--heterologicality⁽³¹⁾ (h₁)--that does not hold for B₂. Thus, (14)'s syntax in L is the equivalent of

which is not a contradiction if B₁ differs from B₂ in semantic import. That we could use language to establish such a semantic distinction is easy to see: A sentence in a natural language--English, for instance--could be used and taken to mean, in some context, that a written sign that is not read out loud produces no sound whatsoever, whereas the same written sign, when read out loud, produces just the kind of sound that the sign itself signifies.⁽³²⁾

We are now ready to consolidate the gains of our experiment by returning our attention to (11) and re-reading it (silently) in the light of what (14) has shown us: namely, we are now ready to read (11) as saying the equivalent of what (14) says. How does this happen? Before our very eyes, one wants to say, the two signs "`Buzz'" and "`buzz'" in (11) differentiate themselves: we now read the first to signify all customary written symbolizations of the word "buzz," and the second to signify all customary spoken symbolizations of the word "buzz." What "customary written (or spoken) symbolizations" means is: "`Buzz'" and "`buzz'" are taken and used to signify, in turn, not a kind of sound--the kind that "buzz" signifies--but rather a kind of word-use--the kind that happens every time someone uses the word "buzz" in a written, or a spoken, sentence. In other words, we now read "`Buzz'" to mean, in (11): that of which every written use<sup>(33)</sup> of "buzz" is an instance; and we now read "`buzz'" to mean, in (11): that of which every spoken use⁽³⁴⁾ of "buzz" is an instance.⁽³⁵⁾

It could be said of the experience that we have just had upon re-reading (11)--in the light of (14)--that (11) seemed to reorganize itself (as it were) before our very eyes. It is this reorganization, we might say, which allowed (11) to cease expressing a contradiction to us. Although this kind of experience is not one in which we perceive (11) to be an object sentence like (8)-(10), we nonetheless are now able to see (11) as belonging to a class of expressions that (8)-(10) also belong to: namely, the class that contains what was earlier called "compound propositions with a sense." In other words, we find ourselves able to dissipate the experience of contradiction by giving (11) a significant use--which is exactly what Wittgenstein's text⁽³⁶⁾ tells us cannot be done for the words that express Grelling's paradox.

If we say that we experience (11) as seeming to reorganize itself so as to cease expressing a contradiction to us, the reorganization we speak of is, of course, not a physical one: there is an important sense in which (11) is the "same" sentence both before and after the reorganization. The experience of having our puzzlement over (11)'s apparent contradiction dissipate is thus very similar to the kind of experience we have when a picture we always saw as depicting this now presents itself to us for the first time as depicting something else.⁽³⁷⁾ One of the most famous examples of this phenomenon is evoked by Wittgenstein's drawing of the duck-rabbit:⁽³⁸⁾

Figure 2 can be seen as a picture either of a rabbit's head or a duck's. In Philosophical Investigations, Wittgenstein distinguishes between the "continuous seeing" of an aspect of the figure, and the "dawning" of a new aspect: he notes that someone who is shown the picture might begin by seeing nothing but a rabbit in it, until the moment when it dawns on her, for the very first time, that the picture is also that of a duck's head.⁽³⁹⁾

The analogy between the phenomenon of aspect-dawning described by Wittgenstein and the way that the experience of contradiction from our original reading of (11) got dissipated--just after we went through the experiment with (12)-(14)--would be perfect if we were able to read this sentence,

(16) "

is not

."

this_16a this_16b

as saying the equivalent of this sentence: "What this_16a is pointing at is a picture of a rabbit, and it is not the same as what this_16b is pointing at, which is a picture of a duck." The analogy would not be complete if we read (16) to assert the equivalent of "This particular thing is not that particular thing," for what this_16a and this_16b are pointing at might also be taken by us, at some other level, as being the same kind of thing: we might take them, for example, as being the same in one sense (e.g., we take them as being identical pictures of a rabbit), even though we take them as being different in another sense (e.g., we also recognize that they are two separate pictures, occupying different positions in space). The analogy would be incomplete, for example, if we took (16) in the same kind of way that we are prone to take this object sentence:

For the analogy between our experience with (16) and our experience with "`Buzz"' and "`buzz"' in (11) to be complete, we must take the objects pointed at in (16) as being different at a semantic level which may include, but must be higher than, the level of taking them as being just two spatially distinct objects in an object sentence. We must freeze, as it were, the referents of what this_16a and this_16b are pointing at into things that are situated at two different places in logical (and not merely physical) space. Let us now try to imagine that we have managed to do just that.

Language strives to preserve the gains that are achieved when apparently contradictory propositions like (11) and (16) are given sense. It does this in the form of more language: i.e., in the form of language talking about itself. It is almost as if, for language, it is not enough that the distinctions which allowed the contradictory sentences to be made sense of are understood by people; language seeks to inscribe, one might say, the distinctions that people have understood: it seeks to make a record of them.

But what if no distinctions are found in an apparently contradictory statement, and thus none understood? For example, suppose no one is able to perceive that the objects which this_16a and this_16b are pointing at in (16) are different at any level other than their being two distinct (but otherwise identical) objects in space, and thus everyone reads the last sentence of the previous section as a request to imagine the unimaginable. Or worse still, suppose that the concept of the object sentence makes no sense to any one, and hence no one is able to perceive the two things pointed at in (16) as being different in any sense at all. When such things happen language is prone to denigrate any further expression of the contradiction by calling it nonsense. And if it turns out that the contradiction is not a contradiction, but a paradox, language either solves the paradox, by giving each of its apparent antinomies a sense (thereby defanging the paradox, one might say), or else it tries to cast the paradox out of language altogether, by putting it in the category of that which should and must not be expressed.

How does this casting-out of insoluable paradoxes come about? The answer to this question is best shown by example. We will use, as our example of the tendency we have just described, Russell's response to his own paradox.⁽⁴⁰⁾ Russell's paradox (contemplation of which, by the way, led Grelling to formulate his)⁽⁴¹⁾ can be described well enough for our purposes as follows: Suppose there is a class, R, defined as the class of all classes which do not contain themselves as members. Now, does R contain itself? If R does contain itself (is a member of the class it names), then, by the definition of R, it does not contain itself. But if R does not contain itself, then, by the same definition, it is included as a member of the class it names, and thus R does contain itself after all. In other words, (R R) (R R).

Russell himself did not infer from the mere expression of these antinomies that R could not (and therefore does not) exist. Rather, he solved the paradox by putting forward the theory that language comes in types. His theory, in its most basic formulation,⁽⁴²⁾ asserts that a class is not an entity in the same sense that its members are entities: the two are of different "logical types."⁽⁴³⁾ For Russell,

[C]lasses are logical fictions, and a statement which appears to be about a class will only be significant if it is capable of translation into a form in which no mention is made of the class. This places a limitation upon the ways in which what are nominally, though not really, names for classes^[(44)] can occur significantly: a sentence or set of symbols in which such pseudo-names occur in wrong ways is not false, but strictly devoid of meaning.⁽⁴⁵⁾

If a class is of a different logical type than its members, then a class of classes differs in logical type from its members, and so on indefinitely. The payoff of Russell's theory of types is suggested by his assertion that "to construct symbolically any class whose members are not all of the same grade in the logical hierarchy is to use symbols in a way which makes them no longer symbolize anything."⁽⁴⁶⁾ If this premise is granted, then there can be, ontologically, no such entity as a class which does, or does not, include itself as a member, and thus the sentences "R R" and "R R" cannot be intelligibly formulated--i.e., they cannot be formulated so as to permit their affirmation or denial to make any sense.⁽⁴⁷⁾ Since the expression "(R R) (R R)" is senseless, Russell's theory of types asserts that this expression can and should be made to disappear from language by changing the rules for forming sentences, so that henceforth saying "(R R) (R R)" is forbidden.

Since the rules of logical syntax for forming sentences in the language with which Russell began did permit the expression "(R R) (R R)" to be formed, however, there is a sense in which the expression did not disappear from that system. It disappeared, one might say, only when the rules of the system were changed so as to forbid the utterance of the expression. When that happened, a new system, apparently shorn of the paradox, emerged from the ruins of the old. What used to be a problem apparently ceases to be one, because henceforth it is against the law, as it were, to say "(R R) (R R)."

Russell once asserted that the heterological paradox, like his own, made the establishment of a "hierarchy of languages . . . essential."⁽⁴⁸⁾ What this means is that there is a point of view from which paradoxes like his and Grelling's can be avoided only if language and metalanguage are kept separate, and metalanguage is confined to the task of talking about the language in which the paradoxes are expressed. The metalanguage is conceived as being outside the language, and, being outside, it cannot at the same time be inside what it is outside of. If it unhappily comes to pass that a paradoxical expression emerges in the metalanguage (as a consequence of its assumptions and rules of interference), then it follows from the Russellian premise of a hierarchy of languages that that paradox can be avoided only if a meta-metalanguage is created to talk about the metalanguage. Insoluable paradoxes are thus disposed of by stacking languages on top of one another like the layers of a wedding cake that is made to stand upside-down.

The disposition of paradoxes that this method offers can be seen, however, to be the same kind of treatment that we give to a dirty floor when we sweep the dirt under the rug. This is because the unsuppressible possibility that a paradoxical expression will crop up in each level of language as it talks about the language just beneath it implies an endless regress of languages. That this regress verges on a limit--language itself--was very clearly seen, albeit cryptically expressed, by Wittgenstein: "No proposition can make a statement about itself, because a propositional sign cannot be contained in itself (that is the whole of the `theory of types')."⁽⁴⁹⁾ What this proposition asserts, in essence, is that no matter how you slice it, the wedding cake of languages is one cake, after all.⁽⁵⁰⁾ The sense of this last remark can be put into a more precise technical form as follows: The regularities displayed by semantically empty signs, which logical syntax takes as the objects of its investigation, are always ordered in a language for which the distinction between syntax and semantics holds. This last remark very definitely does not mean that the answer to the question,

this₁₈

can only be expressed semantically; for the way in which what this₁₈ is pointing at is part of a syntactical unit--e.g., is (18) an object sentence or a non-object sentence?--can be expressed only by means of something which is taken to be a regular series of signs. If someone were to program a machine to express, in semantically empty language, the regularities displayed by every series of signs in the Universe,⁽⁵¹⁾ the machine would still have to know that (18) is a series of signs before it could express anything about it. The machine's practice of classifying something as a series of signs would be neither semantical nor syntactical in nature. Rather, the machine's practice of classification would presuppose that the distinction between syntax and semantics holds for the objects that it classifies: A left shoe would not be classified as a member of "a pair of shoes" if no one ever made a shoe for people to wear on their right feet.

Now, a language that does not use anything to make itself understood (sounds, marks on paper, gestures, etc.) is mute--it says nothing at all. But a language that sometimes uses objects as symbols of themselves, and only themselves, and sometimes does not, is capable of generating propositions like (4)-(6) and (8)-(10). Furthermore, it is only a very small step from (4)-(6) and (8)-(10) to propositions that look like this:

(19) "Nothing is something, and nothing is not something."

this₁₉

Although (19) seems to be of the form " is and is not," it may or may not be a contradiction. This is because it may or may not contain an object that represents itself, and only itself, in a sentence about itself. If what this₁₉ is pointing at represents itself in an object sentence, for example, then (19) could be interpreted as a compound empirical proposition asserting: first, that what this_l9 is pointing at does exist; and second, either that what "nothing" signifies does not exist,⁽⁵²⁾ or that it does not exist in the same way that the ink stain which this₁₉ is pointing at exists.⁽⁵³⁾

Our earlier discussions have already indicated how it is that language determines if propositions like (19) are contradictions. It does this by talking about itself. Like some of the notions that are expressed in Greek when the prefix µ- (from which "meta-" is derived) is added to a word,⁽⁵⁴⁾ when language talks about itself it must both change the nature of itself and act in common with itself. We will intentionally refrain from calling language in the mode of talking about itself a "metalanguage," however, because this way of putting things carries a connotation of separation between language and itself which we do not mean to convey. If there is a separation between language talking about language and what it is that language in this mode is talking about, it is the same kind of separation that exists between "I" and "I" in the sentence: "I hate what I have become."

Language that talks about itself must act in common with itself, in the sense of being about itself, and not about something else. But language in this mode must also change itself, in the sense of indexing itself by the use of signs which, unlike the signs used in (4)-(6) and (8)-(10), must never count as symbols of themselves. For suppose that language does, after all, sometimes use objects as symbols of themselves when it is talking about itself. Suppose, for example, that language, in talking about itself, gives "`' is " as a definition, and then later the proposition shown in the first line of (20) appears, without the subtextual reference:

(20) " is not "

this₂₀

Then it could be the case that (20) is not a contradiction, but rather an empirical proposition in which what this₂₀ is pointing at is used and taken to represent itself in an object sentence which denies that what this₂₀ is pointing at is the number . To generalize the point: If one supposes that language in the mode of talking about itself is allowed to contain object sentences, then what a sentence appears to be saying about "`x' in the language" might not be about something in the language at all, but just about one or more objects appearing in the sentence that the language uses to say whatever it is that it says. And here it must be said that the expression of a rule in the language saying when it is permissible to use object sentences, and when not, would help matters only if the rule's expression were somehow able to ensure that it itself is a rule for forming sentences, and not an object sentence!

It would seem, then, that language must bind itself, in whole or in part, not to use object sentences, if it is to perform the task of ferreting out contradictions in itself. But here there is a problem: Whether or not language uses objects as symbols of themselves--and hence whether or not language can determine whether the propositions it has generated are contradictions--cannot be determined just by an axiom, rule, or theorem that is expressed in the language: for the expression of any such axiom, rule, or theorem might, after all, use an object as a symbol

of itself.⁽⁵⁵⁾ For example, the axiom "In this language, objects are not allowed to represent themselves in any sentence!" could be asserting that the word "objects" means the italicized objects which appear between the word "are" and the right-hand quotation mark of the sentence. In order for language to determine whether its propositions are or are not contradictions, language must appeal to a rule outside of its own expression that absolutely, definitely, and for sure does not use an object as a symbol of itself in order to make itself understood. The rule must be understood--as distinguished from being written down, spoken, or gestured--if language is to determine which of its apparently contradictory propositions are really contradictions.⁽⁵⁶⁾ The rule must point without pointing, for even the gesture of pointing () does not contain a rule which establishes that it is not pointing at just itself.

If we now draw a distinction between the rule which we have just alluded to, on the one hand, and what causes us to follow it, on the other hand, then it would not be altogether meaningless to say: we are the rule that we follow.⁽⁵⁷⁾ And if someone were now to ask, "What causes us to follow the rule?," we would be inclined to put this question into a class which includes such questions as "What is a rule?," "What is a human being?," and "What is the world?" We would be so inclined because we take all of these questions, as well as any answers that we would be likely to give to them, as being written or spoken in a context in which the rule applies. Do not read this last statement as saying that language (or at least language which is understood to generalize beyond what this, , is pointing at) precedes the world; read it, rather, as saying that to the extent that the world does precede language, this fact can only be discussed in language.⁽⁵⁸⁾ (Prudence requires the observation that we are not saying anything profound here, but are merely reporting another "true tautology.")

That we usually take the rule we have alluded to for granted is an accident of history, one might say, and not a logical necessity. For there could be a group of people for whom the application of the rule is more obvious. Imagine a written language (call it H) that is very much like English, but with this difference: In H, every adjective is also used and taken to assert about its own expression (the adjectival sign) whether or not it itself possesses the property that it predicates of the subject of the sentence in which it appears. Adjectives in H do this by being underlined or not underlined: If an adjectival sign is not underlined, it asserts of itself the same thing that it predicates of the subject of the sentence; and if an adjectival sign is underlined, it asserts that it does not possess the property that it predicates of the subject of the sentence. Thus, for example, "The night is black" would always be read as a compound sentence asserting, first, that the night is black, and second, that the adjective appearing in the sentence which expresses this fact is also black. (And if this sentence happened to be printed in white-on-black outline--as in "The night is black"--everyone would read this sentence as asserting both that the night is black, and that the underlined sign used to predicate blackness of the night is, itself, not black.) To give this language a bit of context: Imagine that the people who use H are aesthetes in matters of typography, and that they always read their sentences at least twice over--once for the sense of the sentence taken as a non-object sentence, and then again for the sense of the adjectives in it taken as miniature object sentences which assert something in their own right.

Now it is clear that the people who use H would have no need to write sentences like "`English' is not heterological" and "`German' is heterological"; indeed, there would be no need for them to have the adjective "heterological" in their vocabulary at all.⁽⁵⁹⁾ Instead, anyone who wanted to convey, in H, the same sense as one of the English sentences just mentioned would simply write the non-compound H-sentence:

"English."

Or they would write:

"German."

Everyone reading these two sentences would know immediately what is being asserted: namely, that "English" is an English word, and that "German" is not a German word. Here are a few other examples of non-compound H-sentences of this sort: "Monosyllabic."; "Polysyllabic."; "White."; "White."; "Reversed."; "desreveR."

The rule which we alluded to earlier in this section would not be taken for granted by the people who use H to anywhere near the same extent that we take it for granted. And if Grelling's paradox were translated into H, the people who use H would find it much easier than we do to listen to what Grelling's paradox has to say to them about language, even though (or rather just because) their own vocabulary did not contain the word "heterological" until it got translated into H for them. One possible translation: "`Heterological' means what we H-people do with our words when we read and write sentences containing adjectives. The word is used by non-H people as an adjective, and gives rise to this paradox: `Heterological and heterological'."

Given what we showed in the previous section, at this stage of our thinking the temptation may be very great to solve Grelling's paradox by means of a strategy of categorization.⁽⁶⁰⁾ This section describes an example of such a strategy, so that we can exhibit how reason is prone to trick itself into thinking that it is getting on top of the matter of language by just continuing to walk around and around on the same surface.

The strategy begins by our choosing, very self-consciously, to bind ourselves to a (fervently embraced) "rule" barring any object sentences that we ourselves do not authorize in the reading of them. Then we proceed to express, in the form of what we take to be non-object sentences, a strong distinction between object sentences and non-object sentences. Finally, we give the question that originally led us to formulate the antinomies of Grelling's paradox--"Is `heterological' heterological?"--a good going over according to what will be called the criterion of "answerability."

We might say, for instance, that this object sentence,

(21) "small is small,"

this₂₁

resides at a semantic level which is different than the semantic level of

this non-object sentence:

(22) "`English' is English."

this₂₂

We could support this assertion by the argument that the signified of the grammatical subject in (21) is this particular splotch of ink on paper--namely, what this₂₁ is pointing at--whereas the signified of the grammatical subject in (22) is not the ink stain that this₂₂ is pointing at, but rather what the word "`English'" stands for. We could say that what the word "`English'" stands for is that which is representable by an indefinitely large number of type faces, styles of handwriting, accents, and so forth--it is what is written, printed, said, signed, etc., whenever someone means to predicate of something that it is English. Recalling the lesson of our experiment with "`Buzz'", "`buzz'", and "buzz" in (11), we could say that what "`English'" means in (22) resides at a semantic level which is below the level of what the word "English" means in (22) (the latter covers all English things, and not just English words), but one or more levels above the semantic level of the object that this₂₂ is pointing at.⁽⁶¹⁾ In other words, we could conclude that (22)'s semantic scope is much, much broader than (21)'s: the latter's subject mentions itself, but refers to nothing beyond itself, we might say, whereas the former's subject mentions nothing, but still manages to refer outside of itself to all possible uses of the word "English."

From what we have learned from comparing the sense-levels of (21) and (22), we might now feel entitled to solve Grelling's paradox by interrogating the syntax of (23):

this_23a this_23b

We could then classify the results of our interrogation according to a Neo-Russellian criterion that we will call the criterion of answerability. That is, we could ask whether or not the syntactical units that we have identified reside at different semantic levels--and thus whether or not they exhibit the possibility of sense. How might our feeling of entitlement to do this manifest itself? Well, for one thing, our project would not require us to assign any particular semantic content to what this_23a and this_23b are pointing at, for we would be in a context in which we have already reassured ourselves that it is only the possibility of sense which concerns us.

Proceeding from the premise that a sign's semantic scope (its possibility of sense) is different from its semantic content (its particular meaning, in this or that use of it), suppose that we first try classifying (23) syntactically as an object sentence. Then it is relatively easy to show that we would be inclined to regard the question asked by (23) as being answerable. We would be able to conclude that (23) possesses the possibility of sense on any possible interpretation: i.e., whether either, or both, of the "thises" are pointing at an object which symbolizes itself, and only itself, in (23). Here would be our reasoning: First, if we assume that only this_23a is pointing at such an object, then (23) resides at the same (answerable) semantic level as "Does this object have the property that "heterological" symbolizes (whatever that property may be)?"⁽⁶²⁾ Second, if we take both "thises" as pointing at object-words, then (23) resides at the same (also answerable) semantic level as "Is this thing the same as that thing?"⁽⁶³⁾ And lastly, if we assume that only this_23b is pointing at such a word-object, then (23) resides at the same (still answerable) semantic level as "Is the word "`heterological'" the same as this thing?"⁽⁶⁴⁾

(At this point it is almost as if we can hear ourselves saying: "So much for Grelling's paradox, if we suppose that the question which led us to formulate its antinomies (too hastily, it seems) is an object-sentence." Solve paradoxes or banish them, so that we can move on to the next problem!--that's the credo that we are supposing for ourselves.)

But our work is not quite finished. Now we must classify (23) as a non-object sentence, and then re-interrogate its semantic scope in accordance with our criterion of answerability. If (23) is not an object sentence, then both "thises" must be pointing at a word which represents something which resides at a semantic level which is higher than the particular objects that this_23a and this23b are pointing at. In order to interrogate the semantic scope of (23) on this assumption we will let this question be our guide: Does what "`heterological'" refers to in (23) have the property that "heterological" refers to in (23)?⁽⁶⁵⁾ The possibilities that now present themselves to us are two.

First, if we assume that "`heterological'" refers to the same thing as the predicate "heterological" (e.g., the property of heterologicality), then we would be inclined to say that the question's sense is of the same order as the sense of the question: "Does the set of all sets that do not contain themselves as members contain itself?" And what this means is: we would be inclined to call the question "nonsense," because neither the affirmation nor the denial of the proposition "`heterological' is heterological" satisfies the Russellian criterion of translatability.⁽⁶⁶⁾ Another way to put this would be to say that, while an adjectival sign, or a particular use of it, can have this or that property, it makes no sense to say that the property the sign represents either has, or does not have, the property that it represents--e.g., neither the sentence "red is red" nor the sentence "red is not red" makes any sense; and the sentence "red is neither red, nor is it not red" might be used to draw attention to just this fact.⁽⁶⁷⁾

Second, if we assume that "`heterological'" and "heterological" refer to different things (i.e., the first to an object, and the second to a predicate), then we would be inclined to say that the question does possess the possibility of sense. What this means is: we would be inclined to say that the question is capable of being answered by a non-contradictory empirical proposition of the form "Yes, x has property P," or "No, x does not have property P." (That we might not immediately know which answer to give is beside the point for our present discussion, for what we are seeking to show here is the phenomenological structure of our sense that the question is answerable at all.)

To summarize: on the assumption that (23) is not an object sentence, the "same thing" interpretation leads to the question being dismissed as nonsense; the "different thing" interpretation leads to its being considered answerable. Either way, given our Neo-Russellian criterion of answerability, we would be inclined to say that Grelling's paradox has been disposed of.

At this point it becomes useful for our project to describe those ways of taking the question "Is `heterological' heterological?" that were exhibited in the previous section in terms of the concept of pointing.⁽⁶⁸⁾ We will not express a "definition" of that concept in the usual sense of the word, but will, instead, give its meaning ostensively--i.e., by example. First we will exhibit the concept of pointing by describing the essential structural differences between object and non-object sentences. And when that has been accomplished, we will exhibit the form of a paradox of language itself--a paradox whose comprehension as a paradox is founded on our comprehension of object and non-object sentences in terms of what we call their different "pointing-structures." Since it does not matter for our present purposes which particular word or word-object is taken to be doing the pointing, we will simply use various forms of the word "this" in the numbered sentences we exhibit throughout this section.

Consider first the pointing structure of the non-object sentence. To the extent that none of the words in (23) were taken in the previous section to mention or refer to anything inside of (23), it can be said that they were all taken as mentioning or referring to something outside of (23). This means: we took them to mention or refer either to something outside that is the same, or to something outside that is different, but in either event to something outside that is something else. If we conceive this mentioning or referring as a kind of pointing, we can now characterize, in the following manner, that interpretation of (23) in which we took it to be a non-object sentence of the kind that we called "nonsense":

And further, we can characterize as follows our other non-object sentence interpretation of (23) (the one in which we took (23) to express a question of the kind that we said was "capable of being answered by a non-contradictory empirical proposition"):⁽⁶⁹⁾

Let it be said at this point that we have not written (24) and (25) in this manner in order to support anything that we intend to offer as a "theory of meaning." Rather, we have written them this way to make progress towards another goal. The goal is to show how the structure of (23), when it is taken in its mode of being a non-object sentence, stands in relation to the structure that (23) exhibits when it is taken in its mode of being an object sentence. Continuing to employ the concept of "pointing" that we used to formulate (24) and (25), we are now ready to represent the forms of the three interpretations that we gave (23), in the previous section, when we acted on the assumption that it

was an object sentence:

(27) "Is this this?"

We are now ready to simplify the forms of (24)-(25) and (26)-(28) further still. We can readily dispose of the signs "Is" and "?" in these sentences, on the justification that carrying forward a multiplicity of signs would unnecessarily burden our comprehension of the relevant distinctions. Next, if we bear in mind that (27) is a double-object sentence (and is thus only a kind of object sentence) we need not carry forward the multiplicity of object-words that it displays in order to exhibit the form of the object sentence in general. Finally, since the italicized non-object words "this" in (26) and (28) point outside of themselves in the same way as the "thises" in (24) and (25) point outside of themselves, we can drop the "thises" from (26) and (28), on the justification that we are not, at the moment, trying to exhibit what is similar about object and non-object sentences, but rather what is different about them. What we are left with is the following representation of the essential pointing structure of an object sentence:

What (29) means is the equivalent of "I am me--I exist." Its message would be heard clearly by the typographical aesthetes whom we imagined earlier when we described language H. It is also like the messages that we sometimes see inscribed on the buildings of corporate America--"IBM," "General Motors," and so forth--and on the bodies of people who wear tatoos.⁽⁷¹⁾

In contrast to what we have just said about (29), the "thises" in (24) and (25) do not call attention to themselves at all. Whatever the words in non-object sentences mean--i.e., whether they are regarded as sense or nonsense--the words themselves are taken to point away from themselves. If we simplify (24) and (25) in accordance with a criterion which asks what they have in common with one another that they do not have in common with (29), we derive this representation of what is essential about the pointing structure of a non-object sentence:

What (30) means is the equivalent of "Look at this! It exists."

Now, it is absolutely essential that we avoid thinking that the concept which we have exhibited of an object "pointing at" itself inside an object sentence, and of a word "pointing outside" itself in a non-object sentence, signifies an action that is performed by the object or word. Objects and words have neither the will nor the fingers to gesture with, and we should never fall into the trap of thinking or imagining that ink-stains like , , and are gesturing with their body parts. We choose to adopt the concept of pointing to help us elucidate the various relations that hold between what is called a "symbol" and its manner of expression. When an object "expresses" (as it were) a symbol, the object expressing the symbol is not taken to be the same as the symbol; as Walter Benjamin put it, "The word must communicate something (other than itself)."⁽⁷²⁾ One might say that the way it feels from within language (at least most of the time) is that words are about something other than themselves.⁽⁷³⁾ And if the objects expressing symbols were taken to be the same as the symbols they express, then they would not be language. This shows what it means to say that the object in (29) "points at" itself and the "this" in (30) "points outside" itself: Both sentences are kinds of language.

What does this last statement mean? Objects in object sentences both are themselves and mean themselves. They speak their own presence in the sentences in which they appear. This remarkable characteristic furnishes us with a perspective from which to interrogate (29) and (30) for what it means to say that an object--any object--can be "represented by a symbol."

If we ask our simplified object sentence, (29), to show us what would be the case if what is doing the symbolizing in that sentence were absent, we would see what is being pointed at in (31):

You should not see anything being pointed at in (31). This implies: if what is symbolic about the object in (29) were absent, then that object would be like a random water stain on the page of a book which, whether or not it is noticed, is not taken to be part of language.

And if we ask our simplified non-object sentence, (30), to show us what would be the case if what is doing the symbolizing in that sentence were absent, we would see what is being pointed at in (32):

You should not see anything being pointed at in (32). This implies: if what is object-like about the symbol in (30) were absent, then there would be nothing in (30) to announce itself as being that symbol which refers to . The symbol would be like the hole in the page of a book after an important word has been cut out. There would be nothing there to uncover as being what it is.

One might summarize and generalize the sense of the previous discussion in the following proposition: In language, symbols can stand for objects, but objects cannot stand for symbols. What this proposition means can be represented as follows:

(33) "This is language if and only if this is not language."

. . . . . . . . . . . . . . . . . .

If we were now to give the definitions "`This' = a<sub>1</sub>" and "a<sub>2</sub> = what `this' is pointing at," and then were to say "a₁ is language a₂ is not language," this would not mean the same as (33), for the supposition that a₁ a₂ would differentiate a symbol from what does the symbolizing, and this is absolutely contrary to the sense of (33). Nor could we capture (33)'s sense by giving the name "a" to both "This" and what "this" is pointing at (i.e., by restoring "this"'s unity with itself), and then by tensing it: e.g., by saying "La at Time₁ (La at Time₂)."⁽⁷⁴⁾ This sentence would still not succeed in saying the same as (33), because (33) is a synchronic proposition. In other words, (33) asserts that what is being pointed at there is language if and only if it is not language at the same time that it is language.

The proposition expressed in (33) is what might be called the extension of Grelling's paradox: It holds equally for object and non-object sentences. It is a true contradiction, whose sole employment is to show that when it comes to talking about any kind of language we are like a bug walking on a Möbius strip.

Symbols uncover things; they let things be pointed at. We let things symbolize; we let them point. And if we were now to say, "The pointer is us," wouldn't this be a terribly misleading way to identify the source of the paradox in (33)? Can we truthfully say that we experience a "we" pointing this way and that as we read and listen to language? Would it not be more accurate to say that we drink in language, letting it show us . . . just exactly what it shows us?⁽⁷⁵⁾ And do not now rush to say, "The reason he or she reads the text this way rather than that way is because of his or her social situation," for this move comes after the paradox expressed in (33) has worked its way with all of us.

If you were required to answer the question "How does language work?" in a single sentence, you could do a lot worse than this object sentence:

(34) "Watch what happens when you read THE SUBJECT IS THE OBJECT, AND THE OBJECT IS THE SUBJECT , and then you will see how language works."

Any theory of language--whether mainstream or critical--that cannot show how (34)'s status as language gets itself established would have a very hard time showing how anything's status as language gets itself established.

If you were required to answer the question "How does the meaning of a legal text get established?" in a single sentence, you could do a lot worse than this sentence:

(35) "Watch what happens when you read LAW , and then you will see how the meaning of a legal text gets established."

Any theory of law--whether mainstream or critical--that cannot show how (35)'s meaning gets itself established would have a very hard time showing how the meaning of any legal text gets itself established.

The bottommost truth expressed by "Law is politics" is suggested by this: what is pointed at in (1) can, but need not be, language. And further, by this: If what is pointed at in (1) can, but need not be, language, then what is pointed at inside of any legal text can, but need not be language.

This, in the end, is what Grelling's paradox has to say to us about language, if we have ears to hear it: Language that we dismiss as meaningless, as nonsense, as . . . anything at all,⁽⁷⁶⁾ must still be language enough to mean that it is meaningless, is nonsense, is . . . anything at all.⁽⁷⁷⁾ It must say to us, as it were, "I am language. Now, do with me what you will." And anyone who chooses to seek verification of this truth, and of its significance for the concept "Law is politics," will find that verification and significance written in the experiences of those human beings, and other occupants of the world, whose voices are regularly heard either as the kind of noise that is not called language, or else not at all.

The significance of this truth for legal studies is this: More stupid things are said, and more bad things are done, when people draw the conclusion that what we have just said is false than when they draw the conclusion that it is true. But since this last assertion is not a conclusion that we have drawn from solving the paradox expressed by (33), its significance cannot be established from a place inside of language. Its significance can only be established by using language in the world. When law is politics, legal language is used this way, and not that way, but the significance of this distinction is not to be found in language. "The Rule of Law" is not false; it is language. And the Rule of Law is not true; it is what happens when legal language is used.

* Professor of Law, University of Washington School of Law. A version of this article was presented at the Critical Legal Conference's 1994 Annual Meeting at the University of Warwick. Special thanks are due to my colleague Mike Townsend for his consistently excellent and valuable advice on this project. I hasten to add that any errors in this article are mine alone.

1. Lewis Carroll, Alice's Adventures in Wonderland 87-88 (Heritage Press 1941) (1865).

2. This sentence is grounded in Heidegger's distinction between logos as "authentic discourse" (an event of unconcealment of entities in the world), and logos as a mere statement about something that is set before the statement ready-made, and in such a way that the statement must correspond to the thing-that-is-already-there in order to be called "true." See Martin Heidegger, An Introduction to Metaphysics 186 (Ralph Manheim trans., Yale Univ. Press 1959) (1953) [hereinafter An Introduction to Metaphysics].

3. Augustus Ferdinand Möbius (1790-1868). Morris Kline, Mathematical Thought from Ancient to Modern Times 852 (1972). According to Courant & Robbins:Moebius made the surprising discovery that there are surfaces with only one side. The simplest such surface is the so-called Moebius strip, formed by taking a long rectangular strip of paper and pasting its two ends together after giving one a half-twist . . . . A bug crawling along this surface, keeping always to the middle of the strip, will return to its original position upside down . . . .

Richard Courant & Herbert Robbins, Topology, in 1 The World of Mathematics 581, 595 (James R. Newman ed., 1956). Figure 1 is reproduced from a drawing in Courant & Robbins, supra, that is subtitled "figure 18--Reversal of up and down on traversing a Moebius strip." Id. at 596.

4. 2 Oxford English Dictionary 2072 (compact ed. 1971).

5. Kurt Grelling (1886-1942, in Auschwitz). A.R. Lacey, A Dictionary of Philosophy 92 (2d ed. 1986).

6. The CD-ROM version of The Philosopher's Index, for example, shows that 39 articles in English on or about Grelling's paradox have been written in philosophy journals since 1945 alone. This article is not "on" or "about" the paradox in the same sense that these papers are.

7. John van Heijenoort, Logical Paradoxes, in 5 The Encyclopedia of Philosophy 45, 47 (P. Edwards ed., 1967).

8. Kurt Grelling & Leonard Nelson, Bemerkungen zu den Paradoxien von Russell und Burali-Forti, in N.S. 2 Abhandlungen der Fries'schen Schule 301-04 (1908).

9. Ludwig Wittgenstein, Remarks on the Foundations of Mathematics 395-96 (G.E.M. Anscombe trans., G.H. von Wright et al. eds., rev. ed., The MIT Press 1978) (1956) [hereinafter Foundations of Mathematics].

10. Translate "" as "is a member of the class of."

11. Translate "" as "if and only if."

12. Translate "" as "it is not the case that."

13. Translate "a language-game" as a "whole process of using words," "consisting of language and the actions into which it is woven." Cf. Ludwig Wittgenstein, Philosophical Investigations 5e (G.E.M. Anscombe trans., 3d ed. 1958) [hereinafter Philosophical Investigations].

14. Translate "" as "a variable ranging over all those things of which it can be asserted that h holds, or h does not hold."

15. Lest this be misinterpreted, let it be stressed that the question draws a distinction between the words "h" and "heterological" and what is pointed at here: "`h'" and "`heterological'" . When Wittgenstein says (in essence) that the word "heterological" has a use, but the word "`heterological'" in the sentence "`heterological' is heterological" does not, he draws a distinction between words, and thus presupposes that both are words.

16. Ryle, for example, got rid of the question by means of a theory of category mistakes. From the major premise that logicians' category-words are not among the words listed under those category-words, and the minor premise that "heterological" and "homological" ("homological" = "autological") are logicians' category words, Ryle concluded that "it is an improper question even to ask whether `heterological' is heterological or homological." Gilbert Ryle, Heterologicality, in Philosophy and Analysis 45, 45 (Margaret MacDonald ed., 1954). For Ryle, as for Wittgenstein, the heterological paradox only seems to be a paradox, in the sense that its apparent antinomies arise solely from the way that philosophers are prone to misuse language. Id. at 51-53. He thus overlooks the possibility that the paradox says something paradoxical about language itself.

17. The word "object" derives from the Latin ob- (in the way) and jacere (to throw). Webster's New Collegiate Dictionary 784 (1981).

18. Compare this reproduction of a reproduction of René Magritte's painting The Wind and the Song, taken from William S. Rubin, Dada, Surrealism, and Their Heritage 96 (1968):

19. Girolamo Francesco Maria Mazzola (called "Parmigianino") (1503-1540). 9 The New Encyclopædia Britannica 164 (15th ed. 1994). Parmigianino painted Self-Portrait in a Convex Mirror in 1524. Id. The original, a tempera done on a 9 " oval panel, is in Vienna's Kunsthistorisches Museum. See John Walker, Portraits: 5,000 Years 96 (1983). What "this₆" points at in (6) comes from a reproduction of the painting contained in Walker's book. Id. For a poet's perspective on the painting, see John Ashbery, Self-Portrait in a Convex Mirror, in John Ashbery, Selected Poems 188-204 (1985).

20. This definition of "object sentence" should not be confused with Carnap's definition of "object language" as that language which is the object of a semantical investigation in a metalanguage. Rudolf Carnap, Introduction to Semantics 4 (1942). However, an object sentence, as we have defined it, could be characterized as a kind of object language in another sense: the sense in which "object language" is defined as "language used to talk about things, rather than about other languages." Boruch A. Brody, Glossary of Logical Terms, in 5 The Encyclopedia of Philosophy 57, 70 (P. Edwards ed., 1967).

21. For example, a paper note with the words "exists and would exist even if there were no humans in the Universe" typed on it could have been attached to the moon by the Apollo astronauts; but it would be much harder for an earth-bound human to do the attaching the other way around.

22. This series of questions begins to get to the truth expressed in Stevens's lines: It is a world of words to the end of it,

In which nothing solid is its solid self.

Wallace Stevens, Description Without Place, in The Collected Poems of Wallace Stevens 339, 345 (1990).

23. Consider, for example, Wittgenstein's observations on this point (which point?):[B]ecause we cannot specify any one bodily action which we call pointing to the shape (as opposed, for example, to the colour), we say that a spiritual [mental, intellectual] activity corresponds to these words.

Where our language suggests a body and there is none: there, we should like to say, is a spirit.

Philosophical Investigations, supra note 13, § 36, at 18e (second alteration in original).

24. From the Latin ostendere: "to show." Cassel's Latin & English Dictionary 157 (Macmillan 1987) (1963).

25. Here I can only say: If you have not done so already, please take about six months off to read Being and Time, line by line, and very slowly. Martin Heidegger, Being and Time (John Macquarrie & Edward Robinson trans., Harper & Row 1962) (1927) [hereinafter Being and Time]. Then read Truth and Method, at a brisker pace. Hans-Georg Gadamer, Truth and Method (Joel Weinsheimer & Donald G. Marshall trans., 2d ed., Crossroad 1990) (1960) [hereinafter Truth and Method]. For a collection of recent essays in which various concepts of the hermeneutic circle are applied to legal studies, see Legal Hermeneutics: History, Theory, and Practice (Gregory Leyh ed., 1992).

26. It isn't. The reason it isn't is because if we just say (without more) that meaning gets established, not by words alone, but by people standing in a certain kind of relation to words, then we risk putting our situation with respect to the word "meaning" in a privileged place that is outside the hermeneutic circle; whereas the whole point of this concept is that we are already and always "permanently set in motion and caught in the hermeneutic circle," even when we are talking about words like "meaning" and "hermeneutic circle." Martin Heidegger & Eugen Fink, Heraclitus Seminar 17 (Charles H. Seibert trans., Northwestern Univ. Press 1993) (1970).

27. The language of God, perhaps? Or would it be the language of Newton? Compare Being and Time, supra note 25, at 269, where Heidegger says this by way of clarifying his remark that "[b]efore Newton's laws were discovered, they were not `true'; [but from this] it does not follow that they were false":To say that before Newton his laws were neither true nor false, cannot signify that before him there were no such entities as have been uncovered and pointed out by those laws. Through Newton the laws became true; and with them, entities became accessible in themselves to Dasein [the Being of humans]. Once entities have been uncovered, they show themselves precisely as entities which beforehand already were. Such uncovering is the kind of Being which belongs to `truth'.

Id.

28. Compare Heidegger's remark that "[t]o undergo an experience with language . . . means to let ourselves be properly concerned by the claim of language by entering into and submitting to it." Martin Heidegger, On the Way to Language 57 (Peter D. Hertz trans., Harper & Row 1982) (1959) [hereinafter On the Way to Language]. See also Gadamer's assertion that "a hermeneutically trained consciousness must be, from the start, sensitive to the text's alterity." Truth and Method, supra note 25, at 269.

29. The visible sign "`Buzz'" as it appears in (14).

30. The audible sign that is spoken after "and" is read silently, and before "is" is read silently, in (14).

31. For the moment we will define the property of heterologicality as the property of a word's not applying to itself.

32. That this is so is suggested by the concept of `onomatopoeia' in poetry, which is usually understood as describing the use of a written word whose sounds, when imitated in speech, suggest the word's meaning. See, e.g., Elisabeth W. Schneider, Poems and Poetry 502 (1964); Wayne Shumaker, An Approach to Poetry 99-101 (1965).

33. I.e., whether the word appears in printed or handwritten form; in black type or red; in large font or small; etc., etc.

34. I.e., whether the word is spoken loudly or softly; in an American or an English accent; etc., etc.

35. This description of the distinctions that can be drawn to differentiate, semantically, the words "`Buzz'", "`buzz'", and "buzz" owes its formulation to the way Lawrence distinguishes among various levels of meaning of the word "word." Nathaniel Lawrence, Heterology and Hierarchy, in Philosophy and Analysis, supra note 16, at 37, 40-42.

36. Foundations of Mathematics, supra note 9, at 395-96.

37. The work of Wittgenstein and Heidegger on the phenomenon of seeing aspects is ably discussed in Stephen Mulhall, On Being in the World: Wittgenstein and Heidegger on Seeing Aspects (1990).

38. Figure 2 is taken from the reproduction of the duck-rabbit drawing that appears in Philosophical Investigations, supra note 13, at 194e.

39. Id. at 194e-96e.

40. Russell's paradox has been characterized as being of "profound importance for logic and the foundations of mathematics." Samuel Gorovitz, et al., Philosophical Analysis: An Introduction to its Language and Techniques 55 (3d ed. 1963).

41. See Grelling & Nelson, supra note 8; see also Abraham Fraenkel et al., Foundations of Set Theory 9 (2d ed. 1973) (Grelling & Nelson regarded their paradox as "only a variant of Russell's"). Hofstadter calls Grelling's paradox a "startling variant" of Russell's paradox. Douglas R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid 20 (1979).

42. We leave aside, as irrelevant to our theme, a discussion of the many elaborations that have been made by logicians, including Russell himself, of type-theoretical language systems--e.g., ramified type theories, liberalized type theories, and so forth. See Yehoshua Bar-Hillel, Theory of Types, in 8 The Encyclopedia of Philosophy 168, 168-72 (P. Edwards ed., 1967).

43. See Paul Edwards et al., Bertrand Arthur William Russell, in 7 The Encyclopedia of Philosophy 235, 245 (P. Edwards ed., 1967).

44. Here Russell's Platonism shows through quite clearly, in his supposition that it makes sense to distinguish "nominal" names from "real" names. One detects here the view that the material manifestations of language partake of "real" language the way the material world partakes of Plato's ideas--namely, as a mere copy of what really is. See An Introduction to Metaphysics, supra note 2, at 184.

45. Bertrand Russell, Introduction To Mathematical Philosophy 137 (Dover 1993) (1919).

46. Id.

47. E.g., by the criterion of translatablity, the "class of all classes" would have to be translated as the equivalent of "the world"; and it would be senseless to say that the world does, or does not, contain itself.

48. Bertrand Russell, An Inquiry into Meaning & Truth 96-97 (1940).

49. Ludwig Wittgenstein, Tractatus Logico-Philosophicus 16 (D.F. Pears & B.F. McGuinness trans., rev. ed., Humanities Press 1974) (1921).

50. Compare two of Wittgenstein's later remarks on Gödel's proof: "Gödel's proposition, which asserts something about itself, does not mention itself," and "My task is, not to talk about (e.g.) Gödel's proof, but to by-pass it." Foundations of Mathematics, supra note 9, at 383, 386.

51. Compare Henri Poincaré's famous concept of the geometry machine: "[A]ssumptions were put in at one end, while the theorems came out at the other," thereby supposedly showing that "to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means." Ernest Nagel & James R. Newman, Goedel's Proof, in 3 The World of Mathematics 1668, 1668 (James R. Newman ed., 1956).

52. Cf. A.J. Ayer, The Genesis of Metaphysics, in Philosophy and Analysis, supra note 16, at 23, 24 (asserting that what sustains the "rubbish" of Heidegger's statements about "nothing" is "the single false assumption that the sentences `there is snow on the ground' and `there is nothing on the ground' express propositions of the same logical form").

53. Cf. An Introduction to Metaphysics, supra note 2, at 27 ("[T]here is something very interesting about nothing.").

54. 1 Oxford English Dictionary 1779 (compact ed. 1971).

55. Compare this remark by Wittgenstein:Where it is enough for me to get a proof that a contradiction or a trisection of an angle cannot be constructed in this way, the recursive proof achieves what is required of it. But if I had to fear that something somehow might at some time be interpreted as the construction of a contradiction, then no proof can take this indefinite fear from me.

The fence that I put around contradiction is not a super-fence.

Foundations of Mathematics, supra note 9, at 219.

56. Consider, for example, this assertion of a supposed rule in the English language forbidding the use of object sentences: "[T]he rules of English grammar require that no English sentence shall contain the objects to which it refers, but only their names." Nagel & Newman, supra note 51, at 1676. If this expression of the rule is to "work" the way Nagel and Newman undoubtedly want it to work, the expression must be understood to say (but cannot by itself say) that the italicized objects in it are words which stand for something other than themselves. For if, after all, they do stand only for themselves in the sentence in which they appear, that sentence would express no general rule against object sentences, but only a particular rule against the appearance of the first italicized object and in favor of the appearance of the second in all English sentences.

57. Compare what Wittgenstein is reported to have said about why no amount of measuring of the ratios of radius to circumference in the many circles that exist in the world could tell us the value of , or could get us to correct so as to make it correspond to what our measurements show:No measurement can tell us the value of or between what values it is to be found, the number is rather the standard by which we judge the quality of a measurement. . . . Thus when we say, has such and such a value, e.g. = 3.14159265. . . , this cannot mean that we want to say anything about the actual measurements, but only that we are stipulating when a measurement procedure is to be counted as correct and when not. Thus the axioms of geometry have the character of stipulations concerning the language in which we want to describe spatial objects. They are rules of syntax. The rules of syntax are not about anything; they are laid down by us.

We can stipulate only something that we ourselves do.

Wittgenstein and the Vienna Circle: Conversations Recorded by Friedrich Waismann 62 (Joachim Schulte & Brian McGuinness trans., Brian McGuinness ed., Basil Blackwell 1979) (1967) (footnote omitted) (second omission in original).

58. Heidegger's famous and poorly understood remark, "Language [is] . . . the house of Being," see On The Way to Language, supra note 28, at 5, does not say the same as "Language is Being"; and if it did say this, it would be stupid. When people ask and answer questions like "What is a human being?" with no awareness that their questions and their answers are language, then their context is one which can justly be called "doing metaphysics."

59. Here it seems fitting to report Kneale & Kneale's statement that "Grelling's paradox has to do with a newly invented word[,]" namely "heterological." William Kneale & Martha Kneale, The Development of Logic 656 (1962). The Oxford English Dictionary contains no listing for "heterological," but does show "heterologous"--which is said to denote "Having a different relation, or consisting of different elements; not corresponding; opp. to HOMOLOGOUS"--as having had a use in medical terminology as early as 1822. 1 Oxford English Dictionary 1298 (compact ed. 1971).

60. Here it would be useful to distinguish between categorizing to solve a paradox and categorizing to understand that a contradiction really is a paradox. This article's categorizing is of the latter type. Reflection on the kind of categorizing that can be done to solve the heterological paradox caused Wittgenstein to ask: "But why should we lie to ourselves like this?" Foundations of Mathematics, supra note 9, at 207.

61. For an example of this kind of argument, see Lawrence, supra note 35, at 40-43.

62. One possibility that might occur to us is that "heterological" in (23), as thus construed, refers to the property of an object not representing itself in an object sentence, in which case we might be inclined to say that the appropriate answer to (23), thus construed, is "No." Of course, if we behaved in this recklessly semantical way we would then have to go back and index "heterological" in the second half of (11)--". . . `buzz' is not heterological"--so as to indicate its different semantic content in the interpretation we gave it there. But then, lawyers have a lot of practice doing that sort of thing anyway. (We call it "distinguishing cases.")

63. On this supposition, we'd probably be inclined to say that the answer to (23) is "Obviously Not." But just here it would be useful (and humbling) to recall our experiment in interpreting the sense of (16)--the sentence that we were asked to imagine as asserting the non-identity of a duck-picture and a rabbit-picture.

64. On this supposition, those of us who are card-carrying nominalists/legal realists would probably be inclined to say that the only proper answer to (23) is "No--whatever it is that the word "`heterological'" symbolizes in (23), a name can never be the same as what it names." But just here it would be useful (and humbling) to ask ourselves this question: How is what this_23b is pointing at different from what it names in the sentence in which it appears?

65. We might say that if both "`heterological'" and "heterological" are taken to refer to objects (as distinguished from predicates of objects) other than themselves, then (23) is the uninteresting semantic equivalent of either "Is x the same as itself?" or "Is x the same as another thing, y?"; we might further say that the answer to the first question would be "yes," according to the Law of Identity, Brody, supra note 20, at 67 ("if anything is P, then it is P"); and the answer to the second question would be "no," according to the Law of Contradiction (id. ("nothing can be both P and not P")).

66. See supra text accompanying notes 42-47. Wittgenstein calls this kind of proposition "useless"--which for him is the same as "nonsense." See Philosophical Investigations, supra note 13, § 216, at 84e.

67. Compare Wittgenstein's remark about the standard meter-bar: "There is one thing of which one can say neither that it is one metre long, nor that it is not one metre long, and that is the standard metre in Paris." Philosophical Investigations, supra note 13, § 50, at 25e.

68. For Heidegger's conception of language as a kind of showing or pointing, see On the Way to Language, supra note 28, at 123.

69. corresponds, roughly, to the notion of `object', and corresponds, roughly, to the notion of `predicate of an object'; on the clear understanding, however, that these concepts are limited to the category of referents (objects or predicates) which are taken to be "outside" any sentence.

70. There is a joke hidden in this expression. Compare supra note 63 with supra notes 44 and 62.

71. Imagine that everyone had this tattooed on their forehead: "I am language, therefore I am." Cf. René Descartes, Discourse on Method 17 (Donald A. Cress trans., Hackett 1980) (1637) ("I think, therefore I am."). Now imagine the tattoos slowly fading away to nothing, leaving only the people. Can we not now hear the silent language of their presence saying to us what Samuel said to the Lord--"Here am I"? 1 Samuel 3:4 (King James).

72. Walter Benjamin, On Language as Such and on the Language of Man, in Reflections: Essays, Aphorisms, Autobiographical Writings 314, 327 (Peter Demetz ed., Edmund Jephcott trans., 1978).

73. This statement very definitely does not mean that language must be about something to be language. "Language is representational" is only one way to represent language: One could, for example, represent it as a "happening" of what- language-uncovers (see An Introduction to Metaphysics, supra note 2, at 186), or perhaps as a "language-game" that "is not based on grounds," but rather "is there--like our life." Ludwig Wittgenstein, On Certainty § 559, at 73e (Denis Paul & G.E.M. Anscombe trans., 1969). For the thesis that it is both nonsensical and necessary to represent, in language, that there is a perspective from which language can be seen, and spoken about, as being non-representational, see Louis Wolcher, What We Do Not Doubt: A Critical Legal Perspective, 46 Hastings L.J. (forthcoming 1995).

74. After first giving the definitions "L = the predicate of a being language in (33)," and "Time₁ Time₂."

75. Compare David Gallop's very timid translation of what Parmenides says in Fragment 8, lines 34-36 of his philosophical poem, dating from the sixth century B.C.--The same thing is for thinking and [is] that there is thought;

For not without what-is, on which [it] depends, having been declared,

Will you find thinking . . . .--

Parmenides of Elea: Fragments 71 (David Gallop trans., 1984) (alterations in original), with Ralph Manheim's English translation of Heidegger's very aggressive German translation of the same lines: There is an inherent bond between apprehension and that for

the sake of which apprehension occurs. For not without the

essent in which it (being) is already spoken, will you find

(attain) apprehension.

An Introduction to Metaphysics, supra note 2, at 173.

76. E.g., wrong, illogical, irrational, hysterical, etc.

77. Compare G.E. Moore, Wittgenstein's Lectures in 1930-33, in Ludwig Wittgenstein, Philosophical Occasions 1912-1951, at 46, 66-67 (James Klagge & Alfred Nordmann eds., 1993), which quotes Wittgenstein as saying: "[W]hen we call a sentence `nonsense', it is `because of some similarity to sentences which have sense.'"