(Not) The Most Powerful Word

Estimated read time (minus contemplative pauses): 10 min.

Here I am, staring out the window, Satie on, mug of hot Rishi English Breakfast, daydreaming about which (English) word is the most powerful. ‘Can do the most,’ I think is what I mean.

Arranged from weakest to strongest, “I,” “you,” “love,” “hate,” and certain slurs can do a lot, can win hearts and cost livelihoods, the latter being accomplished with special ease, with a single utterance in the right context (a policy of saying only “porcupine” at work—where “Give us the report, Tom” is met with “Porcupine porcupine porcupine porcupine…”—would do it, but not because of that choice of word).

Undesirable words tend to be more potent than desirable ones. This conforms to the general asymmetry between creativity–destruction, pleasure–pain, etc., where the uglier of those phenomena are always accomplished most easily and with much greater depth. (My go-to example: Think how hard it would be to give someone a pleasure whose duration and intensity are equal to that attending the pain of simply setting them on fire; a similar asymmetry is observed in, say, music and food).

Many words (and phrases) have contextual power—as when an on-the-clock umpire yells “strike three!” or Captain Picard says “make it so.”

I’m reminded here of Christopher Hitchens reminiscing, in Hitch-22, about an early job “held for about six months before its editor said something to me that made it impossible to go on working for him,” and then, in a footnote: “‘You’re fired’ were the exact words as I remember them.”1)

The word “God” might bear a mention, but I think for most English speakers its common uses are barely noticed. Maybe “democracy,” too, has some power, but again is such a staple of every politician’s vocabulary that it hardly commands notice (compare this to the much stronger “Nazism”: ugly words overpower the rest).

The word I landed on is more elemental than all that, less context-dependent, more operation than word. From an imagined critic:

I’ve closely read your book. It’s nearly perfect. Just missing one word. After the last chapter’s last word, add a closing bracket: “]”. Before the first chapter’s first word, add an opening bracket preceded by a dash: “-[“. In front of that dash print the word “not.” Now it’s perfect.

Amazing what that little word can do. The example is pretty abstract, however. What, exactly, “not” does to the book isn’t immediately clear (though the critic’s point is unmissable). Logically speaking, if we’re being technical, the critic’s move reverses all qualifiers and adds “not” to all predicates.

Here’s an example in which the quantifier goes from “all” to “some” and the predicate goes from ‘are mammals’ to ‘are not mammals.’

All dogs are mammals.
Not-[All dogs are mammals.]
This can be stated as: It’s not the case that all dogs are mammals.
Or distribute the “not” to get: Some dogs are not mammals.

Here that is symbolically, to underscore its algorithmic clarity:

Let…

represent “all” and similar (e.g., “every”, “each”)
represent “some” and similar (e.g., “there exists”, “at least one”)
~ represent “not” (i.e., negation)
d represent “dog” or “dogs”
M(x) represent “x is a mammal” or “x are mammals”

All dogs are mammals: dM(d) (i.e., For every dd is a mammal.)
Not-[All dogs are mammals]: ~[∀dM(d)] (i.e., It is not the case that for every dd is a mammal.)
Some dogs are not mammals: (∃d)(~M(d)) (i.e., There exists some d, such that d is not a mammal.)

(Depending on how penetratingly we distribute the “not,” we may need to take care for things like De Morgan’s law, where not-[p AND q] becomes [not-p OR notq]. Read a symbolic logic textbook for such details.)

Seems reasonable. Or at least clear. If a bit arbitrary. It might not reflect the critic’s intention. Of course, it’s almost unthinkable that a human would mean that sarcastic note in any formal sense. But the (imaginary) critic does mean something by the word “not.” For sake of the present mind-wander, I’ll assume something formal, which is to say consistent, even if it’s unclearly so or produces absurdities.

For example, the critic could mean that no dogs are mammals. This would require a different placement of the “not” operator:

All dogs are not-[mammals].
(∀d)(~M(d))

Even less clear—more towards absurdity—would be the intention for the “not” to toggle every word in the book to its opposite. How? “Dog” doesn’t become “cat” or “God.” Nor does it become “not-dog,” as that term, strictly construed, includes everything in the universe that isn’t that dog, including the particles that compose that dog!

Now that’s interesting. Pick one of the dog’s brain cells at random. That cell is not that dog. So we need to interpret “not-dog” as ‘no particles that contribute to that dog’s composition’ or ‘anything not in the region of space precisely occupied by that dog.’

Those seem to be statements about synchronic (i.e., at-an-instant) identity. Maybe it should be stricter, should be diachronically (i.e., over-time) oriented, thus excluding any particles that ever contribute to that dog’s composition. And so the usual mereological problems arise (e.g., what is a particle and which ones of them compose the dog?). (There may be other things to exclude as well. Moving on…)

The point is that ‘everything in the universe that isn’t that dog’ is not the necessarily the opposite of ‘this dog’—which, by the way, in many instances would mean some particular dog, rather than referring to, say, the general “dog” concept or the word “dog” in itself or ‘the concatenated letters d, o, and g.’ The opposite of ‘this particular dog’ could be some other particular dog, or perhaps some human: one’s ‘worst enemy’—which could still mean or denote the same dog, because “worst” here is the opposite of “best,” so it literally means ‘the one worst at being one’s enemy,’ which I suppose would be one’s best friend.

So we must reverse not just the general meaning of the word, but the word in context, the word as it’s intended. Better yet, that of the sentence. Or book. But then we’re back at the original problem of interpreting the critic’s comment. (Not to mention, say: What’s the opposite of you? Of “you”? The negation of these?) (What is the opposite of a hungry kangaroo? It’s not a cooked one, though the former eats, the latter is eaten.)

The logical, algorithmic interpretation of mere negation seems the most promising. In which case, it might be worth stating the obvious point that there is a difference between negations and opposites. It’s a common fallacy to assume that, if a claim is false, then it’s opposite is true, though this may sometimes be the only option.

The negation of the end of the world isn’t its beginning, but its opposite might be.

To negate ‘it is snowing’ is to imply that it’s not snowing (i.e., its opposite, at least arguably), but the negation of ‘it is not snowing’ is not that it is snowing (it could be raining).

The negation of ‘Margaret Mead did not believe me to be kind’ is not its most readily assumed opposite (i.e., that she did believe me to be kind). The negation could simply intend that Mead had no beliefs at all about me (which, she didn’t).

But this is a (amateur) logician’s interpretation, in which “not,” or negation more generally, is held to a stricter use than it is in its ordinary or—what’s the word I saw in a book the other day?—demotic sense. Such questions as I’m asking here do come up in everyday life, or so it frequently seems to me. As in the common sentiment: “Every word in that book is a lie.” Point made, I guess, but literally impossible.

The slightly sinister shape of the pretty sounding demotic (“demote,” “demonic,” with “people” at its root) brings to mind a specific instance. It involves an often overbearing and annoying fixture of my pre-adult years, yelling at me in the kitchen about the Bible: “If you can prove one word of this book a lie, I’ll throw it out the window.”

Or did he say “false”? A statement can be false without being a lie. “False” is more easily dealt with given the “not” question. It’s harder to figure out what someone’s statement means, what goals and intentions motivate it, when said as a lie than when the statement is merely false. On top of this, if something is a lie, it can be accidentally true, or it can be intentionally or accidentally false (i.e., you could get lucky—get Gettiered, as epistemologists put it—about something’s falseness). A sincerely said falsehood, on the other hand, just means the statement is incorrect.

[I wonder which is scarier to the believer, a Bible that’s a lie, particularly if still believed to have been written or inspired by God, or one that’s merely false.]

Whatever the case, it’s a good thing he—who I don’t think was trying to save my soul by then (he also accused me of faking my atheism, in other words of trucking towards eternal mega-torture on fucking purpose) so much as the integrity of his own beliefs—wasn’t holding the Wicked Bible. From Wikipedia (accessed 1/28/20):

The Wicked Bible, sometimes called Adulterous Bible or Sinners’ Bible, is an edition of the Bible published in 1631 by Robert Barker and Martin Lucas, the royal printers in London, meant to be a reprint of the King James Bible. The name is derived from a mistake made by the compositors: in the Ten Commandments (Exodus 20:14), the word “not” in the sentence “Thou shalt not commit adultery” was omitted, thus changing the sentence into “Thou shalt commit adultery.”

The omission of three letters cost them the equivalent of £49,067 in 2018 GBP (or about $62,266 2018 USD), plus cancellation as printers. The article goes on to cite a recommendation to use the term “innocent” rather than “not guilty,” due to the ease with which the most crucial word in the latter may be inadvertently left out.

“Not” is powerful even in its absence!

If you put “not-[ ]” around the Wicked Bible, at least you’d get the sixth commandment right. Provided, that is, you follow something like the clear and simple rules I introduce above, in which “not” simply negates.

Interestingly, the negation (and opposite) of “not”—perhaps “yes” or “true”—does practically nothing. Consider: True-[All dogs are mammals]. There’s no operator for “true,” except for two “~” in a row. “Not” alone, then, is powerful enough to negate itself: Not-(Not-[All dogs are mammals]) just says that all dogs are mammals.

So “not” can do a lot. It can negate a library.

Though come to think of it, there’s at least one library it can’t negate, assuming you don’t go in for one of the more absurd negation rules (such as where the opposite of “dog” and “cat” and “the” and “and” and so on are all the same—say, “nothing”; but this isn’t negation so much as destruction; you might as well burn the place down and call that negation).

In Jorge Luis Borges’s2 mind-bending 1941 short story “The Library of Babel,” he describes a library that contains every possible book. You cannot negate the Library of Babel, for to “not-bracket” the Library, also known as the “universe,” does not change its contents. Any intelligible sentence will have its negation somewhere else in the Library. Negating those two sentences only changes their locations in the library. Most of the books in the Library contain gibberish, however, which is also fine: the negation of gibberish is more gibberish.

(It occurs to me that you could get the same effect with a library of two books, each the negation of the other. But you can’t do it with three books of distinct content. You need an even number of books. Does this imply that the Library of Babel must have an even number of books as it must be true that any book in the Library has, somewhere in the Library, its exact negation?)

Maybe trying to come up with a stipulation that does not diminish the Library’s content is a test of a negation rule’s validity. This could be simplified to: You must be able to get back from where you started—namely, with two “not”‘s. (So maybe the negation of ‘this dog’ is tantamount to an opposite of the form ‘everything but that dog,’ as the opposite of ‘everything but that dog,’ is ‘nothing but that dog,’ unless, however, we toggle every word, in which case we get ‘nothing and everything but this dog’; but again this is absurd. So I stand by my original suggestion. What was that again? Moving on…).

The impossibility of negating the Library perhaps points to the deepest source of frustration and anguish for the Library’s most fanatical acolytes: the Library of Babel is useless. It’s not a source of information, but a collection of all the permutations (constrained by a small set of rules you can read the story to learn about) of a small set of shapes and a blank space, printed into objects consisting of bound paper (they are only books in the sense that such an object is a book even when the pages are blank). That a microscopic proportion of the resulting strings of shapes happen to appear meaningful (to some observer) is of no more consequence than when a cloud appears to shape itself into a toaster.

In the unlikely event that you come across some words you can actually read, you can’t learn anything from them. And yet, understandably, the Library’s inhabitants are easily driven to maddening frenzies by the understanding that, somewhere among the mindless permutations, is the right answer to everything.

Try it for yourself: https://libraryofbabel.info

Alright, that’s enough daydreaming.


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Further Reading

Footnotes:

  1. Hitch-22 pages 136 and 424; 2010. Grand Central Publishing. Kindle Edition.
  2. It occurs to me that my favorite moment in Hitchens’s memoir is perhaps when he meets his “literary hero,” Borges, in Borges’s apartment in Buenos Aires, 1977. “The courteous old genius,” nearly totally blind by then, asks Hitchens to read to him, which of course the “extremely shy” Hitchens does. The story has more impact if you’ve read the whole section on Argentina in which it appears (in the chapter “From Portugal to Poland”), or better yet the whole book up to that point.

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