On "On Denoting"

Bertrand Russell -- Notes on "On Denoting."
I wanted to extract and explore everything possible from this important piece. *'s denote descriptive remarks about certain sections, vaguely in the right order, which I hope show accurately my interpretation of the text. Paragraph breaks are digressions within remarks on the text, continued at length in the latter half. I found the critique of distinguishing 'denotation' from 'meaning' to be the most revealing portion in what is meant by 'meaning' and what is denoted by 'denotation.'
Remarks on specific aspects of text:
*names are of objects, and when they appear in sentences, the sentences are about the named objects.
*names are properties of objects, which can be predicated of them: they are part of the meaning of sentences about objects. They are not separate from meaning, but are subsumed by it, involved in it, mentioned by mention of meaning. Russell's restriction on names themselves from having inherent meaning cuts us off from the possibility of stating that there is meaning over and above the meaning of a sentence based on arbitrary label changes. I believe the priciple he's working off of is this: We can't add information simply by changing the shorthand associated with it.
*Different names refer to the same object by the following general formalism:
x = A and x = B <=> A = B = x. A and B stand for definite names, and x is an ambiguous anyname. This is the typical "transitivity" property of equivalence relations in action. If this identity is known, we know P(A) and P(B) have identical meaning. Linguistically,
The (a) author was Scott = There exists precisely (at least) one x such that x was the (a) author and x was Scott.
In this case, the former 'name' can work as a name or a property, but since actual names given to objects socially is part of their hypothetical list of properties, this is no difficulty for the theory. Knowing th identity 'The author is Scott' to be true, we could succeed this with a sentence about Scott which used either 'the author' or 'Scott' or 'him' to refer to him (if we know his gender!). We can alternate sentences using different names, and there need be no confusion for any reader who knows the identity to be established (otherwise it may only be surmisabe but uncertain). The idea is that we can make any identity with new names, so long as they are not taken, and use this in later sentences to yield identical meaning. Transitivity. However he only allows for one actual object to be named by a given name. The ability to phrase descriptions differently is supposed to account for the puzzle of unknown identity by showing that the meaning of A = B depends on the meaning of a sentence involving arbitrary phrasings of A and B, not their actual identity. (For in that case, the idea is that 'A=B' would mean essentially nothing, being only a restatement of a common logic axiom - this is given that, in the language of the theory, we know there's a x such that x=A and x=B)
*No details about how names are attached to obects, except that C(x) works regarldess of the specific form of the name 'x': We are forced to interpret x 'literally' as something a sentence can be about. This only addresses the apparent interchangibility of nouns, and is not adapted to differing verbs applying to the same noun.
*one has two types of identity: A = B for one denoted thing with two denotations (names), and logical identity P(A) = P(B). These are both denoted by the words "is" and "=". Russell avoids saying that the names A and B "are" the same thing, because he can only say they are anything at all by placing them in grammatical structure.
*The theory hinges on the belief that meaning and denotation are essentially functions from the realm of objects to language, and that the former is bijective (an object maps to the class of propositions, which have unique meaning for a given object) while the latter is not: One object maps to many formally symmetric (i.e. all are of the form f(x) for some name x) propositions featuring the different names of the object. The meaning of f(x) is the same for any name x of a given object.
*I introduce some new terms to make things clear. He objects to the idea that denotation and meaning can be disjoint, because the high-order operator '*' (which operates on language * by explicitly referring to words, phrases, or sentences) and the higher-order modifier M(*) (which assigns a meaning to language) can be used to show the two are not independent. His argument appears to be: Statements S('x') which mention a name as such should be about the denotation:
M(S_d('x')) is in the category of statements about the name 'x' regardless of the statement S_d and the particular name 'x'.
Thus, M(S_m(M('x')) is in the category of statements about M('x'), the meaning of what is denoted, which may or may not exist (existence is only allowed in the case that x is the name of a bit of language) but is specific to x, the actual named thing. In other words, M(S_m(M('x'))) is in the category of statements about x (since it is a meaning involving a specific object). But since S_m(M('x') includes the higher-order name variable 'x', M(S_m(M('x'))) must be in the category of things about names. So is the meaning M(S(M('x'))) about a thing or its name? By denying that a name can be "part of" a thing, Russell must concede that all this is basically nonsense.
Essentially, this: 'C' is a denotation of C, so statements involving the meaning of 'C' should be about that denotation. But 'the meaning of 'C'' is about C, not any particular denotation 'C'. Meaning can only be said when speaking of 'C', yet using simply C yields meaningful sentence about the thing denoted by 'C' without mentioning the use of '*' explicitly, hence using C in a sentence is not simply denotation.

By predicating of one another, he shows that meaning and denotation are tangled together: "inseparable." But they are not identical, nor is one illusory. In fact, they only indistinguishable in higher-order language - 'within' language that doesn't reference one of the concepts (meaning resp. denotation), it can't be said that any sentence should be about the other (denotation resp. meaning); those meanings aren't presumed to exist. Russell's solution amounts to disallowing 'meaning' to be predicated of explicitly referenced names. But we could equally take the dual route; the topology of the logic here is symmetric, since we aren't explicitly referencing the actual differences between meaning and denotation!! (in this type of solution). So we still haven't accounted for why it seems like nouns in themselves have meaning. My name appears to be imbued with meaning historically, culturally, socially, personally. If it has no type of meaning on its own, why is my mind sparked by its sound? Its meaning may be diffuse, but its meaning is quite real. From a 3rd person point of view, an animal responds to a name without any grammatical structure given the lived structure of its life; social animals benefit by getting each others attention in specific oral ways. This is similar to the particular characters of bird calls; the meaning of the sign is understood, however diffusely, without any other spoken/shown grammatical struture.
His argument hinges on the idea that meanings of propositions go with the things they are about directly, regardless of how the object is named. We could just as well try it the other way around, however, taking the meaning of denoting phrases as given, asserting that grammatical structure has no denotation on its own, but rather acquires the ability to "point" by virtue of the specific meanings of the denotary phrases in it. This feels at least as natural, since in all discourse the meaning of sentence types changes based on the particular names in it. "I'm in your house" is different than "I'm in your wife." Since the same "category" of linguistic construct (names) can refer to different "categories" of objects, this contingency is perfectly natural. We might re-arrange a sentence from his essay as follows:
meaning is essentially part of a denotation, without which sentences make no sense. Observe how easy it is to argue: Boo is gaa unless faa Me fa soo long. u and v are w unless p q x y z. What might this sentence mean? There is no meaning to empty, skeletal structure, which waits for the flesh of reference to fill it with logos.
The validity of would-be theorems/syllogism majors "If u and v are w, then p q x y z" cannot be judged on its structure alone. It only acquires logos by putting in explicit properties, whose meanings are known to those familiar with them.
What I'm saying is that we could flip meaning and denotation in a large part of the essay (aside from the critique of Frege) and there'd be not difference. The idea is that instead of meaning created through structure of phrases, it is created from denoting particular entities.
Instead of saying things like " 'There is no bald King of France' means 'It is never true that P(f(x)) = 1,' hence it is true ", we'd be saying things like " 'King of France' denotes no entity; hence 'There is no bald King of France' is true."
I won't flesh this out in the same detail as Russell, but if you're skeptical I'd encourage you to prove me wrong.
I don't think either reductive approach is useful in this arena. We must allow the full wealth of experience to guide our thinking about the interface between grammar and knowledge. Word is given and its meaning felt; its truth is debated later. The lack of freedom in immediate perception of names should be reconciled with the relative freedom of reflection upon sentences in which they occur, at which time we find ourselves imagining would-bes, and judge the possibility or impossibility of their replacement by another name, and the logical results; these two aspects of names and their meanings are commensurate, not at odds.
*Names denote by have no meaning. Contrary to Frege, who says meanings of propositions are built from th meanings of their parts.
e.g. For Frege, f(x,y,z) has a meaning dependent on the meanings of x, y, and z, and the structure of f, but for Russell it is f which imbues x y and z with meaning, which are meaningless on their own - there are either objects such that f(x,y,z) = 1, or no objects such that f(x,y,z) = 1: in the latter case, the quantified assignment  'f(v) = 0 for all v' is made. Of course, building negation into the fundamental semantics means  that if we find contradiction, we know that 'lack of existence' of an object has been negated by explicit reference in a grammatical structure (as existing). Identifying the cases in which f is untrue and which f(v) is not satisfied by any object-vector v, we identify contradiction with the class { "truth simultaneous with non-existence", "truth simultaneous with falsity")
This is a lack of distinction between adjectives that are binary, and those that are not. For instance, suppose I tell you I am 6'5". I am actually a bit of change under that height, but it will suffice for many purposes that I tell you the approximate number. There are two different ways you can contradict me, and they have to do with order of difference. If I were 4", the height would be a lie to anyone; they would all say I have uttered something false: They will positively tell you that I am of a height, and that "6 foot 5" is a height they recognize, but that these two heights do not positively coincide: Their coincidence, from a human viewpoint (i.e. on an organismic scale), is perhaps 0.
But many people would accept my answer as "essentially" true: My perceived/felt height and my stated height coincide positively, if not perfectly.
To define height explicitly, we can use the notions of gravity, tangent surface (to the planet), perpindicular, and the 'supremum' of real analysis. If I say that a measuring stick of precisely (to whatever degree we have achieved in a particular standard-embodying system) 6'5" is the smallest that will fit over my head, I have told you something wrong, because a slightly shorter one will still bound the gravitational height of (the average highest point) of my body with respect to any linear approximation of the Earth's surface. "It is not true from every perspective."
However, using the fuzzily defined perspective of "planet Earth," we might say there is not enough difference between 4' and 6'5" to change any planetary calculations. This layering of perspectives usually means that discourse is made efficient in general by referencing a single understood context at a time, implicitly.
This is different from a situation in which we do not measure height by ordered marking on sticks, but still find need to classify the sizes of things (at least "that which I can carry/hold" will be). Picture people speaking about the difficulty of transporting insects; say they want to remove two moths from a lighted enclosure. In 'solving' the 'problem,' one inevitably uses the fact that a moth can be contained in a hand, or in some artifact which may be manipulated by hand. That something is coarsely "smaller" or "larger" doesn't change as we step back, it just becomes less certain. If it is more finely "about the same" can change as we step back, in addition to becoming less certain.
All this highlights the complications that follow when we seek to lock down meaning by making its context clear.

Back to the interpretation.

*all propositions are assumed to be decidable.
*meaning is assigned
*meaning is not assigned to individual phrases, but to structured ensembles of phrases
*phrases can be written symbolically to stand for "any phrase" (in a given domain - though of course, the necessity of stating his was not recognized)
e.g. x y. Russell places no lower bound on the phrase-length that defines a 'form', though I assume he'd agree that that 2 is natural. The 'empty phase,' he'd say, clearly means nothing because it is not said; it is no form, no assignment. As for 1.... ("x")
*phrases must be coupled to mean anything. by meaning, he means valid communication, but it's hard t make sense of exactly what criteria meaning must fulfill. It is clear that he thinks propositions that are invalid forms of denoting can be refuted on those grounds alone, and I have a feeling he felt that valid forms were somehow safeguarded from this type of dismissal. I don't think we can view this theory apart from the social ramifications of refutation in the tradition of philosophy. One can't help but supect some inherent defensiveness in the approach.
*Phrase variables are used to assess the validity of a statement, supposing implicitly a common domain X over which variables are quantified by all speakers/observers. The class of quantification determine which phrases
*In the formalism, all true propositions look like "P(x) = 1".
*No mention is made of cases in which the class X is not precisely knowable -- inherently uncertain. It would be 20 years before quantum mechanics was put on a firm mathematical basis; can't help but wonder how this theory would have changed if Bertie was born 20 years later.
*Hence, *any* P can only take values 0 and 1. It would be 60 years before the conception of generalized "fuzzy" logic.
*So we have that if any statement is true, it can be written as a proposition P(x), and there is an x (in) X such that P(x)=1. The assignment is assumed to be carried out under arbitrary conditions, out of necessity, absolutely. There is no mention of any deliberative process; there is no moment in which the value of P(x) uncertain; it is not constructed in this theory, but it appears. The assignment happens "behind" or "above" the theory.
*Because of the actual fuzziness of the class X (which, at the time of writing, existed in Russell's mind and memory. We use X to stand for our our own domains of interest, which exist in our worlds and minds), statements like "(exists) x (in) X: P(x) =1" convey relatively little, because we are only saying that at least one member of the class fits into the proposition; the only distinction is between one and all, since Russell didn't take the notion of plurality as essential, but did wish to include universality.
e.g. I can say: "I met a man, I met a man, and I met a man."
Which men do I mean, exactly? It doesn't matter, so long as there are entities that satisfy this. For this statement to satisfy P(x,y,z) = 1, it is only important that there are three, not which order I refer to them in, since I have no distinguished between them. In fact this ambiguity is completely unresolved in the theory: There is no distinction between the cases in which x =/= y and x=y, for example. Russell can only hope to decompose the statement into three separate statements:
P_1: "I met a man."
P_2: "I met a man."
P_3: "I met a man."
The commas and "and" work together to make the statement coherent as a logical "AND" of the P_i. In fact, since P_1 = P_2 = P_3, all we need is one x such that any P_i(x) = 1, and we know that P_1(x) = P_2(x) = P_3(x) = 1. When we have z =/= x =/=y =/= z, the P_i actually must be resolved in different ways, even if they still turn out to be 1: They refer to actual differences in the world, though the form doesn't show it. Again, the resolution of propositions to discrete truth or falseness happens "above" the theory.
We also have that ambiguously denoted things ("a human") satisfy P(x) = 0 or 1 regardless of whether the statement is true for exactly one human, or for some general group of humans.
*Description classes are logically determined; any x such that "x is a man" necessarily satisfies "x is mortal." There is no mention of how this logic is achieved: Particularly there is no distinction between sequential and parallel processes.
e.g. Any "biological entity" and any "human" are described by "things which are mortal." "human" is a description of a specific biological entity. According to the theory we have,
If "x is a biological entity" =1 then "x is mortal" = 1
If "x is human" =  1, then "x is a biological entity" =  1.
If "x is human" = 1, then  "x is mortal" = 1,
The sequence would no doubt appeal to Aristotle, but it is important to realize that they could just as truly be stated in another order: The theory does not judge their order. In truth, these phrases are not independent of one another. We know life perishes, and that we are alive, so we know we are mortal. There is nothing special about humans that make them mortal, but the logical assignments of "1" cannot indicate this. "Because" is impossible.
*Math is preserved as always possibly true under his secondary interpretation, with arbitrary shorthand denoting the relations between actual things if they exist (or lack thereof), or lack of actual things to which hypotheses apply. (This is linguistically handy if you don't know whether a proposition is true or untrue, probably a large part of the motivation for modern day platonists) If we finally proclaim that there's no entity possible to which an f(x) applies, we state that as our truth: 'f(x)' is never true. To say f(A) for any definite A is thus to speak falsehood: this is speaking in the primary sense. We can speak primary and truly only about actual things. So you never have to admit you were speaking nonsense if you use the right grammar. The rule is that we were only describing things if indeed there were things like that.
*There is no strict need for acquantaince (which seems to mean a sort of directness of experience) in forming descriptions. This allows basically for us to describe any entity imaginable (describable), and we are never incohernt, simply wrong, false, if it turns out we can't directly experience anything that satisfies the description. If we do experience a thing, we now have the possibility of speaking truly about actual things, not only the domain of descriptions (pure structure, essentially, which can be true logically regardless of their truth when applied to any particular noun, or if there is actually such an object.
*Primary grammar states names as literal interpreations, and can be wrong as that insofar as they suppose a literal interpretation. Secondary grammar states names as properties of things. It's easy to get confused because there's no distinction between 1st and 3rd person; there's a social 2nd person at work in the background. Properties of things appear to people, observers. Second order statements necessarily reference the people making them, so his examples can be flushed out more fully to reveal more of the higher order picture:
There are both acquainted with a book written by a human. We have both read who the author is. We have heard of a king who knows the book, but not it's author, though he suspects an acquaintance.
Actually, I've never heard of the book in the essay, nor about the king, so the statement's false. Replacing the literal us with the literal Bertie and his intended audience makes it true; it's true when they say it to each other. But such statements can never be made false by more literally interpreting them, only by highlighting the difference in experiences between possible subjects, which would form a higher-order class in the theory, too vague for us to quantify over because we can only know one person's knowledge.  However we can always speak literally of particular subjects in the 1st and 2nd person, which is why the essay works. Indeed any shared reality can be spoken of truly, because we only reference our shared memory of these experiences. I'm not Bertie's intended audience, so I can't interpret his sentences literally; I simply don't know about the king and the book. When I say the above statement to you, whoever you are, I lie. It is the relative point of view that appears to change the proposition's truth based on who says it to who. This fact can't be formalized away; it is inherent in any meaning of communication.
It is the stipulation that names be interpreted literally in order to qualify for 'truth' that dominates the development of the theory. The theory simply re-interprets all phrases as their second order 'projection,' and determines whether the speech corresponds to anything in its knowledge bank. If not, the speaker is mistaken. If so, they will be right if their observations and inferences are valid, and wrong otherwise. This last point is pure Aristotle.
*Brief mention that 'relations' between nouns can be quantified as well as nouns. The logic is the same: Relations are entities proper, so there can either be an X such that 'a X b' is true, or no such R. This is for particular a and b. If we vary them as well, we see a three dimensional description, whose structure is completly indeterminate - we'd assume there exist x,y, and z such that 'x y z' because we have said true things (about actual things) with three phrases before.
*Final remark on the text: Russell's ending note is well heeded. Extending the theory has proved far more interesting than a simple denial; indeed, though I object to the character of the theory, I have no wish to proclaim it as "essentially" wrong. He 'chose' what the theory should do, and it does it. It also should do a lot of other things he'd find strange, but none that I interpret is inherent contradiction. It is a valid theory *if* it's stated that it preserves only literally intended statements. Otherwise, it is false.
Explorations and general impressions of the text:
I have tried to show briefly in above digressions that substantial fundamental changes can be made to the theory without changing a defining quality of it. I believe can say this thus: There is a class (in the supposed universe of all language) of statements whose truth does not change under the transformations of the theory : specifically, the class of statements intended to be taken literally. Modern parlance gives the term 'invariance' for the essential meanings of language of this class. Likewise, this feature of the theory can be seen to be invariant
We can probably choose a theory that preserves any clearly enough understood textual intention. e.g., we could make a theory that would preserve the eroticism of erotic writing, the comedy of comic writing, etc. It simply appears easier to make a theory that preserves statements we believe to be objectively true, rather than subjectvely apprehended. (I say this is appearance because I'm not sure we've fully understood wholly what is meant by 'literal interpretations,' regardless of my frequent use of that phrase; perhaps it is "actually" the case that eros and laughter are easier aspects of ourselves to understand.)
The importance of tihs point can't be over-emphasized - there is no way to tell simply by looking at a sentence whether the author means it literally or not. Since I am unfamiliar with what Russell takes as fact, I cannot distinguish between his fact and his fiction. If I may go one step further, I'd venture that the situation for Bertie was essentially the same -- unless he was personally acquainted with the king and the writer, then he takes this as fact from someone else, who communicated it to him. It is in this way that all of Bertie's 'true' statements fail to be true when interpreted literally - which is certainly not what he intended. To be literally true, his statements must include the fact that he heard the information secondhand, and trusts it to be fact, and furthermore. The correct statement for me is that I read an essay which bore the name "Bertrand Russell", who related a story about a King and a writer which he mentions as if it were fact, and I believe that he thought it was fact; I do not know if he story was fact. This is not merely more explicit, but actually literally true, whereas his account is lacking in this quality - by the theory, I am forced to conclude that Russell is either psychic or speaking falsehood. (Making a statement more explicit doesn't change its logic under the theory of literal propositions - 'I read' is just as true as 'I read it on July 28th', which is just as true as 'I read it on a web browser application on an electron/semi-conductor based computer on July 28th . I do not remember exactly how long it took to read it. I reread many sections many times over.' --- the logical algebra of such phrases is identical, because they are literally true.)
Note: The theories transformations actually change what I think of as their 'meaning.' We don't merely re-write the sentence with synonyms, but we alter its effective grammar. Without any artifically adhered-to theory, sentences are interpreted by each differently; we can say their effective grammar is the structure of the statement as apprehended by the listener/reader. Adhering to the theory would mean we re-interpret every statement we see, changing its grammar appropriately as prescribed by the theory.
I can't help but feel he'd find this unsatisfying. It means that, so long as we use this literal social interpretation, different "objects" can have the same name (hence "non-identity," A =/= A), such that indeed, this can be that and not be that. Despite Bertie's repeated claim that this leads to contradiction, the extension of his theory deals with it surprisingly easy: "There are two non-identical things x and y, such that I call x 'this' and y 'that', and you call x 'that' and y 'this." It is our belief in the non-identity of x and y which makes the contradiction appear  when we speak in our 'own languages' to one another, not bothering to translate. If we translate, we both know that "this -> that" and "that -> this" is the translation mapping that preserves the literal logos, though a third party without knowledge of the correct translations will perceive contradictions (and if he's a logician, likely become quite flustered).
Of course Russell didn't want his theory to be about beliefs about things, he wanted them to be about things themselves. The assumption there should be glaring by now: 'things have one reality arbitrary of how they are perceived, defined, described, and no account of observation is necessary to speak truly of objects themselves.'
This is where I essentially can never agree with him. A century and 10 can do wonders for metaphysical insight.
Grammar can't reveal a distinction between fiction and non-fiction, if there is enough truth in the fiction. Consider any story from your memory. Now suppose you told it with the names re-arranged (going to the 'wrong' people). Have you told a lie? Russell says yes. But I say you've said far more which is true than what is false (if the story is long or detailed), though how much differs on context.  There are fascinating practical instances of this difference; the modern archetype is a false accusation in court. These are cases in which there is no doubt of victimhood, but the transgressor is unknown. A false accusation story will truly state particular details . This is extremely
The other end is "true story" television series about crimes -  names are changed and faces obscured to 'protect the innocent'. Though Bert's theory says the whole thing references no-thing, by insisting that the language of the program must be of the form "There exist x, y, ... z such that ... [logical conjunction of many true propsitions about actual people], AND that x's names are {list of false names used in program}, AND that y's names are ... ", he would almost certainly agree with me that the story is essentially true.
In both the above cases, there's a problem if we simply say that there is such thing as an 'almost-truth' which can be transformed by a class of basic substitution-transformations into actual-truths. This: unless one assumes that one will someday discover all the true identities of the people in the program, one is forced to admit that it may not necessarily be possible to ever transform (via name substitutions) the statement into a true one.
You get the idea. In fact there is no topological differences between these two falsities, and yet the consequences are judged to be very different in polite society - one good, one bad: persecution of the innocent is wrong, we say. That is not a grammatical difference between the propositions, but should certainly weight in on how worried we are that the exact-truth was stated. In the former case, we see that Bert's mock-algorithm arrives at the 'right' conclusion - the person is lying about something very important, the identity of someone who will suffer consequences for a law they haven't broken. (Again, note my implicit acknowledgement of priors' factuality: How can you tell whether a sentence is intended to be first-order or second-order? A major problem for such theories. We both understand that these are hypothetical scenarios, but we are both fairly certain that they've actually been played out; they are true fiction, hypothetical reality.
We both know what courts are, about law. The nature of common shorthand must be acknowledged, though in common situations, we will simply take it as a given, which can lead to awkward conversations. It is like stating "Scott wrote Waverley" and then proceeding to use 'Scott' and 'the author' interchangably in a piece about the book. Statements we trust as true will often be false in their 'primary' sense;
We can see in the case of the false accusation why the theory can be thought to "work"... It rightly judges an important falsehood as importantly a falsehood.
But as a generalized theory of meaning, it is useless, simply judging all that which was not known prior to sentence to be either false or true only under higher-order interpretation. In the TV program case, it judges an unimportant falsehood as importantly a falsehood (according to my judgment! Switching names doesn't change the meaning of a story about people you don't know).
It is clear that the theory fails grossly in many forms of writing because an insistence that one name stand for only one object. Multi-layered meanings of names is one of the fundamental principles of poetry (in my opinion), so all poems are simply "false," in the theory; it says nothing about their true figurative meaning.
Haikus are an interesting case. The tradition is to make these essentially non-fictional, little portraits. Yet while the theory can simply say that perhaps a haiku is true, it conveys absolutely nothing about the more profound aspects of its subject that even little windows can show. Any literary interpretation is gramatically transformed into falsity unless it is filled to the brim with second-order caveats, ruining the essence of the interpretation: It means to say something true speculatively, not with any certainty. Art is often made without perfect clarity of intent; if some subtle connection is found by a viewer, the artist may even judge this 'correct' regardless of any feeling of explicit intention.
There are certainly ways for literary critiques to be truer and falser, but it is not due to the fact that they refer to fictional characters and events as if they were literal beings.
I just used a poetic bit of speech, in fact, and for a reason. I mean to speak vaguely because my meaning is vague; if you don't understand, I advise you to read a good collection of haiku. The theory has no transformations to make "profound aspects that little windows show" into a definite, literally embodiable phrase. Haikus are *like* windows in a way that I can't describe fully, because it involves my mind and the author's; it does no good to simply say that "Haikus are windows" is false. DUH!
It is in this way, by emphasizing that literal statements are the 'ultimately true,' which tends to grow a theory which keeps their meaning invariant under its allowed grammatical transformations.

Happy logic-ing.