Fun with Negation

by Jon N. Hall    3/9/18

Not, nor, neither, never, no, un-, in-, a-, il-, dis-, non-, and other means of negation are things without which thought, as we know it, could not exist.

Please excuse that last “not,” but I just could not think of a way of not using it. Indeed, it’s difficult to imagine that there are any earthly languages that do not have at least one word or prefix that negates. Could we understand an alien race of extraterrestrials that didn’t use negation? Our minds, mind you, depend, in part, on the ability to handle negation. Or am I not seeing something? Yet, negation, as with so many other fundamental and essential features of Mind on this planet, is often misused and abused. Since so many Earthlings have not entirely mastered it, let’s look at some forms and aspects of negation, and have some fun.

In Zhouqin Burnikel’s May 8, 2017 crossword puzzle in The New York Times, “Not good” is the clue for 17-Across. As its answer is “bad,” the clue is a litotes; i.e. a figure of speech whereby “an affirmative is expressed by negating its opposite.” And with its ironic answer of “oh, fun,” we seem to also have litotes in the clue for 8-Down: “That sounds good … NOT.”

NOT, by the way, is the Big Daddy of negators. Without NOT, we couldn’t get computers to work, as they rely on the inverter circuit, or NOT gate. In logic, NOT is an essential connective and a Boolean operator. In English, “not” is an adverb. Whether in formal logic, or in a computer programming language, or in a “natural language” like English, the placement of a negator is paramount, to wit:

In a May 15, 2017 movie review at Vulture, Kevin Lincoln writes: “If anything’s been made clear by the preponderance of movies based on preexisting intellectual property, it’s that all IP is not good IP.” Ponder that last clause. The structure itself can be valid, e.g.: All IP is not physical property. But what Lincoln is literally saying is that there’s no such thing as “good IP.” (Tell that to President Xi and the Chicoms!) Where Mr. Lincoln errs is in his placement of “not.” What he should have written and surely intended is this: Not all IP is good IP.

I suppose we should ask: Just what is negation? Negation is contradiction, i.e. denial. Negation is when we say some specified thing is, uh, not. But negation doesn’t necessarily indicate what is. Just because something is “not good,” as with the litotes above, doesn’t mean that it must be bad, it could be average, mediocre. Mediocre is both not bad and not good, no? The only way that negation can really indicate what must be is with true binaries, like on and off. Not on is off, right? There’s the old joke about being “a little bit pregnant”; you’re either pregnant or you’re not. Not even yes and no are true binaries, as “maybe” might be the case.

One type of negation is “joint denial,” which one gets when one uses NOR. As this article strives to provide something for all tastes, masochists are advised to read up on the electronic circuit called the “NOR gate.” And here’s a free book on negation for your delectation: A Natural History of Negation by Laurence R. Horn, so don’t say I never gave you anything. (Whether or not Keats’ negative capability should be included in an article on negation I’ll leave to the reader.)

One place where folks get into trouble with negation is “double negatives,” that is, the negation of a negation. Schoolmarms have advised against the use of double negatives, as errant use of them can mark one as poorly educated. But sometimes we misuse double negatives deliberately, such as in “I can’t get no satisfaction” or “I ain’t got no money, honey” or “ain’t no sunshine when she’s gone.” One can find such solecisms amusing, endearing, or even soulful.

Double negatives per se are neither illogical nor uncommon, but when using them, do take care. Parmenides contended that: “Whatever is, is, and cannot not be.” There ain’t nothin’ wrong with that. Perhaps a corollary to Parmenides’ maxim might be: Whatever is not, is not, and cannot not not be (sic).

But now we’re having too much fun. My corollary contains a triple negative, which is what Groucho Marx used when he quipped “I cannot say that I do not disagree with you.” A better corollary might be: Whatever is not, is not, and cannot be. Old Parmenides could also have said: Whatever is, is, and must be. But negating a negative is too cool not to use; it has a certain je ne sais quoi, non?

The intelligences that we’re busy engineering, Artificial Intelligence, need to have an unambiguous grasp of negation, unlike their biological creators. And built into their silicon DNA should be the First Law of Robotics, which as it happens is negative: “A robot may not injure a human being or, through inaction, allow a human being to come to harm.”

The rights enumerated in our Bill of Rights are negative. These negative rights forbid the government from taking away the unalienable rights endowed by the Creator. The dispute between conservatives and progressives largely concerns the debate over negative and positive rights.

In Goethe’s Faust, Mephistopheles claims, “I am the spirit that negates.” That serves as the title for an aria in Boito’s Mefistofele: “Son lo spirito che nega.” (Opera lovers can click here for commentary on the aria by Neil Kurtzman, and some terrific historical audios, especially the one of Ghiaurov.)

A regular killjoy, Mephistopheles says “no” to everything, (except of course to the damnation of Faust, about which he’s quite keen). Unlike Mephisto, one of the big problems of Modern Man, especially the American variety, is that we seem to have no ability whatsoever to say “no.” Folks give in to their every whim and impulse. This inability to say “no” accounts for much of today’s social pathology.

In David Lean’s Lawrence of Arabia, Colonel Brighton tells General Allenby as Damascus falls: “Look, sir, we can’t just do nothing.” Allenby replies: “Why not? It’s usually best.” (“Don’t just do something; stand there!”). Elsewhere in the flick, Prince Feisal tells Lawrence: “I think you are another of these desert-loving English: Doughty, Stanhope, Gordon of Khartoum. No Arab loves the desert. We love water and green trees, there is nothing in the desert. No man needs nothing.”

Oh, but we do need nothing, don’t we? By confronting Nothing we come to terms with ourselves and with life. We go into the desert to “find ourselves” by staring into the abyss at Nothing. And when we emerge from the desert, we are renewed and ready to forge ahead, all because we dealt with Nothing. I’ll be damned if we don’t need Nothing.

Surely “nothing” is the ultimate in negation. In Mad Max Beyond Thunderdome, the Waiting Ones call the desert wasteland created by nuclear war “the nothing.” To get to Bartertown, Max and a couple of kids must make the perilous trek across the nothing.

It’s been said, “Nothing is, but thinking makes it so.” Indeed, without thinking, where would nothing be? Perhaps we invented “nothing” when we thought of what would be the opposite of everything, i.e. when we negated everything. After that we were able to invent the number zero. And after that we conceived of negative numbers and nothing’s been the same since.

But does “nothing” really exist? I vaguely remember that some physicists have hypothesized that there is no “nothing,” not even in a vacuum. So unoccupied space may not exist; it may be only a concept, a product of negation. On the bright side: “When you ain’t got nothing, you got nothing to lose.” But, don’t you also have nothing to lose when you do have “a whole lot of nothing”?

If you have nothing better to do, you can read Less than Nothing by Slavoj Žižek. But by no means should you buy the book, as the author is a Marxist and therefore not in need any money. Instead, download this free PDF of the book. And don’t ever say I never gave you less than nothing.

The quintessence of nothing is surely Nothingness. In Fellini’s , the film critic tells the director: “If we can’t have everything, Nothingness is true perfection.” Given the alternatives, most normal folks would gladly do without perfection and settle for less than everything.

Heidegger asked: “Why is there something rather than nothing?” I’ve gotta think that’s a fairly big question, and above my pay grade. Some hold that the spark we think of as Mind is destined for annihilation, i.e. nothing, and that we ourselves will be utterly negated when we “kick the bucket.” If so, at that point we won’t be able to have any more fun, not even with negation. So until you suffer total negation, quit being so negative and have some fun.

Jon N. Hall of Ultracon Opinion is a programmer/analyst from Kansas City. • (137 views)

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16 Responses to Fun with Negation

  1. Timothy Lane says:

    Back during my college studies, which included a required course on computer design, the main logic gates were NAND gates, or so we were taught.

    Interestingly, the word commonly used for “not” in French (pas) actually means “pace” or “step” (e.g., the Pas de Calais). Long ago there were several words paired with ne (which does mean “not”) to say, for example, “no step” or “nobody” (ne personne) or “no more” (ne plus) or “never” (ne jamais), all of which have survived, as well as several others. And the “ne” is often dropped, which means the words can refer to both a concept and its opposite.

    An interesting situation, n’est-ce pas?

  2. Brad Nelson Brad Nelson says:

    Noun. Verb. Adjective. Negation. These seem like inherently logical aspects of things and how to describe things.

    Heidegger asked: “Why is there something rather than nothing?” I’ve gotta think that’s a fairly big question, and above my pay grade. Some hold that the spark we think of as Mind is destined for annihilation, i.e. nothing, and that we ourselves will be utterly negated when we “kick the bucket.”

    God has been negated only to be replaced by a “quantum foam.” Where this “quantum foam” gets its ability and agency to crank out not only endless substances but substance itself is taken as a given. “Taken as a given” is much like the saner and more honest people relate to the idea of a Creator (no matter how unknown and obscure that Creator may be in our day-to-day experience).

    In David Lean’s Lawrence of Arabia, Colonel Brighton tells General Allenby as Damascus falls: “Look, sir, we can’t just do nothing.” Allenby replies: “Why not? It’s usually best.”

    That’s one of my favorite lines from one of my favorite movies. That sounds completely British and definitely conservative.

    As for the more esoteric aspects of “nothingness” (and negation, self-extinction, etc.), we might note that reality itself is thoroughly a progressive undertaking. It would seem to have as its guiding force “You can’t make an omelet without breaking a few eggs.” Nature does indeed abhor a vacuum. In reality, when people don’t know what to do, the impulse is to “Do something.”

    Life moves onward. It is always about more or different. We might from time to time wish to take a breather and “negate”-out a bit of this onrushing cacophony, but few can make it a lifestyle. It’s not natural. It’s not life-affirming. Thus for most who do, it is only an affection. Life itself is about being rather than non-being, doing rather than non-doing.

    Our life is about change, moving forward, and all those catchy phrases the Left has turned from metaphysical acknowledgments to political dogma which have, at their heart, the negation of the human being as a moral and free force for his own life.

    As usual, Frank Sinatra had his finger on the pulse of this situation when he sang All or Nothing at All. Nothing just ain’t cool and definitely doesn’t get the chicks.

    • Patrick Tarzwell says:

      Micheal Medved wrote about “Do something disease” an affliction of legislators and elected officials of all stripes or political party. I wish that more of them would take Allenby’s advise.

      • Timothy Lane says:

        Calvin Coolidge had a similar notion. He argued that if you ignored a problem you could see in the distance, it would probably disappear before you really needed to deal with it. The problem is that doing something, anything, is an occupational hazard for politicians. Just like spending other people’s money.

        • Pst4gop says:

          So true Timothy. Coolidge is one of my favorite Presidents, maybe #1. All politicians think they are elected to do something, and I agree they are, but the something that I think they should do is defend our God given rights and reduce the size of the government back to where it would fit within the confines of the Constitution.

  3. Jon N. Hall says:

    Readers, I sent the URL of this (hopefully) fun piece to philosophy professor Adam Sennet. Elsewhere, I’d linked to his article on Ambiguity at Stanford:

    Here’s what he wrote back to me; it’s heavy stuff:::::::

    That is a fun piece, I like it! I especially like the Zizek paragraph, though in my experience Marxists are frequently in need of money. Especially Marx himself.

    One or two small notes (if I may):

    A technical note you probably already know: a first order language for propositional logic can technically get by without a one place negation operator — Scheffer proved that he could define a two place operator (the sheffer stroke!) that is capable of defining all negated sentences in the language without loss of truth conditions (basically not-P is translated as P|P, where if you assigned ‘true’ to P, P|P assigns F to it and vice versa for false). It’s obviously not very helpful from the point of view of computer science, efficient in proof theory etc but it can be done. I realize that this technical point is very much fun, and won’t help anyone’s mastery of negation but I’d feel remiss not giving due to Scheffer. Larry Horn’s book has a quick discussion of it and another equivalent two place operator. Negation is interesting in being the only standard one place propositional operator which makes it so useful and efficient.

    ” But negation doesn’t necessarily indicate what is.” I’ve pondered this idea many times. I think there is a bit of a slide between not indicating what is and not indicated precisely what is. So, for example, if I say that it is not cold, I don’t say that it is warm. But I do say something that entails that it is some temperature that is above cold. If I say the sentence ‘The temperature is above the minimum temperature for being cold’ I do tell you what is, I just don’t tell you very precisely what there is. (Same as I fi say that my dog is 9 or 10 years old, there’s a sense in which I indicate what is since its true, though I don’t tell you very precisely). But I know what you mean when you say that you don’t indicate what is. I think this is often expressed by saying that two sentences can be contraries but not contradictories since both can be false but not both can be true. (i.e. ‘it’s not cold’ and ‘its not hot’ can both be false, but they can’t both be true.) I think this is related to why it has been difficult to give clear criteria for the distinction between negative and positive rights, since if you know the option space, a negation can be rephrased as a positive statement about the remaining option space.

    One interesting point — I”m not sure that the Groucho Marx quip is actually triple negation. Multiple negation isn’t just the total number of negations in a sentence in the intended sense — it requires that they all have each other in their direct scope. SO for example, If I say:

    (a) I believe that you are not not smart.

    You get the cancellation effect. But:

    (b) I don’t believe that you are not smart.

    Doesn’t mean the same things as or entail:

    (c) I believe that you are smart.

    If I don’t know anything about how smart you are, I won’t believe that you are smart and I won’t believe that you are not smart. In that case, (b) is true since I don’t believe anything about your smartness but (c) isn’t true so they can’t mean the same. Marx’s quote is:

    (d) I cannot say that I do not disagree with you.

    Is of the form of (b) with an extra negation in the scope of ‘say that’ cause. It doesn’t mean quite the same as:

    I disagree with you.

    Since after all, if Marx didn’t know what you said and thereby wasn’t able to say whether he agreed or didn’t, it would be true that he couldn’t say that he doesn’t disagree with you but not true that he could say that he agrees.

    One last more fun point — also discussed in Horn’s book extensively — is metalinguistic negation. If you say to a child who just used the word ‘shit’ ‘The dog didn’t shit on the floor, he pooped’, its pretty clear that you don’t mean that the dog didn’t shit — especially if you put intonation on the word ‘shit’ and ‘pooped’. Linguists hypothesized that in this case negation is in effect a rejection of word choice rather than a negative predication (in effect you are saying ‘the dog didn’t do something you should called ;shitting’, the dog did something you should call ‘pooping’). Mixing this up with regular negation has been at the root of some surprising errors in the history of linguistic analysis.

    Anyhow, thanks for sending me the article. I enjoyed it and the free pdf links contained with in.

    • Timothy Lane says:

      Well, an awful lot of that was hard to follow. I guess that’s how philosophy professors “communicate”. The parts I could understand (I think) are interesting and do make a good point: that negating a negative isn’t necessarily the same thing as affirming a positive.

      • adam sennet says:

        In my defence, it was a personal email to Jon. It could certainly use some editing. I’m glad some of it was comprehensible 🙂

    • Brad Nelson Brad Nelson says:

      Probably this is like getting on your hands and knees to look at a pebble of sand through a microscope while a charging rhino is bearing down on you. Dishonest use of language (and various problems of doublethink, groupthink, etc.) is the rhino. And it’s stampeding all over. But I know of no politician who is bamboozling us with too-clever-by-half uses of negation.

      However, a case can be made where this kind of navel-gazing and irrelevancies are infecting academia. If you can’t stop the charging rhino, these small grains are meaningless, even a hindrance to obtaining the truth and engaging in critical thinking.

      But as a pure puzzle, well, okay, fine. I like puzzles.

      • Adam Sennet says:

        Pebbles are way too big to stop a rhino! It’s looking at the REALLY small constituents of pebbles that yielded sources and methods of harnessing destructive power that could stop way more than a rhino (perhaps even a bear). No doubt there were plenty of people saying that looking at atoms under appropriate apparatus was meaningless navel gazing irrelevance too. Wonder how they are doing these days.

        Maybe it’s a blessing and a curse that we study a variety of things that may initially seem useless rather than prejudging which ways most effectively stop charging rhinos and diagnosing from afar what’s ‘infecting’ academia. Sometimes you realize that you solve more than just a ‘pure’ puzzle or perhaps create a much larger impure monster. Sometimes you get a small piece of the puzzle that contributes to a larger one. Sometimes you hit a dead end and it really is irrelevant. But it is hard to know until you actually look.

        • Brad Nelson Brad Nelson says:

          No doubt there were plenty of people saying that looking at atoms under appropriate apparatus was meaningless navel gazing irrelevance too. Wonder how they are doing these days.

          You make a fair point, Adam. And, again, I like puzzles. And I like the fine points of language use. I still love reading the old “The Writer’s Art” articles by James Kilpatrick in which he delves into grammar and word usage. I just wonder if all this couldn’t be condensed down into a more Kilpatrick-succinct form and thereby make it more useful. Smashing atoms has its uses but in language it’s a smash to be succinct, relevant, and helpful.

          I would give my eye teeth (not sure which one those are) if Jon, or anyone else, would take up where Kilpatrick left off. But edit, edit, edit. That would require discipline and a fine ear for what will help the reader to understand and thereby become a better writer. And certainly Kilpatrick was a breeze to read.

          That’s a high standard, of course. But I’m not against learning proper word usage and the fine points of grammar. But when teaching others something about the use of language, it would help to make things a bit more succinct and readable.

          • Timothy Lane says:

            I think the eyeteeth are the wisdom teeth. Mine never came in, perhaps because I tended to avoid milk (though I ate lots of cheese). Indeed, I had 4 primary teeth left into early adulthood when 3 of them, over a period of many years, rotted out without replacements. I still have one left, though it’s badly chipped.

            In terms of writing style, I rely heavily on how it sounds to me. Occasionally I even reject grammatically correct usage that sounds pedantic or flows badly.

            • Brad Nelson Brad Nelson says:

              In terms of writing style, I rely heavily on how it sounds to me.

              Clarity. Brevity. And flows well (sounds good in the head). One thing enormously difficult to do is to read one’s own writing as would a third party. Too often “sounds good in the head” wallpapers over a number of issues. Often we fill in a lot of missing things “inside our head” which the third-party reader is not privy to. Reading our own writing with whatever objectivity we can fashion is a must.

              This is not to say that we should sweat over ever detail. We’re not being paid for this, right? But reading Kilpatrick, I can’t help but think he had a good approach. He was not trying to impress anyone with how smart he was (although clearly he was quite intelligent). He was trying to help the reader become a better writer. That focus made him a humble writer. He was there to serve, not to say in five paragraphs what he could have made clear in one.

              • Kung Fu Zu Kung Fu Zu says:

                One thing enormously difficult to do is to read one’s own writing as would a third party.

                I have found that if I am serious about a piece that I am writing, which is admittedly not often, I will read it out loud. This helps me find mistakes and smooth out jerky writing.

              • Timothy Lane says:

                This is actually closely related to the art of debugging a computer program. This is easier for programs you didn’t write because you don’t assume how it should work. My best debugging was done by trying to put my mind in pure computer mode, but that’s not easy to do. Much the same thing is needed in proofreading one’s writing — especially for content as opposed to grammar and spelling.

        • Brad Nelson Brad Nelson says:

          I was just reading a bit of James Kilpatrick, and here’s a good example of grammar instruction:

          10. We ought not to use words that have double meanings.

          Let me revert to an analogy I was using earlier. A writer is a kind of forest ranger, leading his readers like a troop of tenderfoots along an unfamiliar trail. If the guide does a good job, his charges will not stumble over strange words or awkward clauses; they will not lose their way in an underbrush of ambiguity; as readers, they will not suffer those almost imperceptible flickers of uncertain understanding that diminish their pleasure.

          One way to ease the hike is to avoid words that have double meanings—words that compel a reader to make an instantaneous choice of one meaning or another.

          By way of example: since. I know that all the dictionaries authorize its use in the sense of because, But in my experience, nine times out of ten because is a better choice than since. The problem arises because since telegraphs an instant connotation of time passing. The ear receives a sentence beginning, Since he entered the priesthood, and the ear tunes itself for a principal clause that will relate some happenings over a period of years. The ear is thus affronted when the sentence concludes, he could not marry. The reader has stumbled; he may not have stumbled seriously, but small stumbles are still stumbles

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