Long, long ago, during my first summer as a grad student (technically, I wasn’t even a student yet), in one of my first meetings with my graduate adviser, he suggested that I think about the problem of representing negation. The problem of representing negation? That seemed like an odd suggestion. I mean, I was looking for potential research projects, and negation, being so common in everyday speaking and thinking, seemed like an issue that would have been researched to death, so that there’s little I could have done with it. But as the grad student saying goes, ours’ is not to question why, at least not until we’ve officially registered for classes, so I asked for some references, and started reading up on negation. It turns out I was partially right — a ton of work has been done on negation. I was wrong, however, to think that there was nothing left for me to do. The more I read, the clearer it became that we really had no idea how negations are represented.

As you might expect given the ubiquity of negation in everyday speech, research on the topic was in full force at the very beginning of the cognitive revolution. Early researchers found that when asked to verify the truth of a sentence relative to a picture or their own background knowledge, sentences containing a negation took longer to verify than sentences that didn’t(1). This is true regardless of whether the negation is explicit (e.g., “Bob was not at the party”) or implicit (e.g., “Bob was absent from the party”)(2), and it’s true when you contrast the sentence with negation (e.g., “Three is not an even number”) with a positive sentence that it implies (e.g., “Three is an odd number”)(3). They also found that negated information is more difficult to remember than affirmed information(4). It seems that no matter how you look at it, negations are more difficult to process than affirmations. But why?

The problem appears to lie with how we have to represent negation, that is, how we represent an entity or condition as being absent. If you represent the situation without the negated entity or condition, e.g., if you represent the party without Bob, then you’re not representing “Bob wasn’t at the party,” but just the party. Or if you are representing Bob as absent from the party, you’re also representing everything else that wasn’t at the party as absent. You, for example, weren’t at the party (I know, ’cause I was there, and I didn’t see you). So when you represent one negation this way, you represent all possible negations. That’s not very effective. If, on the other hand, you represent Bob at the party, then, well, Bob’s at the party, and he’s therefore not not at the party, and we’ve made no more progress. So for negation, it seems that you need two representations: the affirmative one (Bob at the party) and the negative (the party without Bob, which was much better that way, trust me). As Bertrand Russel put it, “When I say truly ‘this is not blue’, there is, on the subjective side, consideration of ‘this is blue’, followed by a rejection” (5). But how would that work?

Or does it work that way? Others have suggested that you don’t need to represent an affirmative to represent a negation. For example, we could just represent Bob’s absence from the party by taking affirmative version (“Bob was at the party”) and then appending some marker than indicates that the affirmative version is false. This would mean that we represent negation generally, and never have to represent specific negations explicitly. In other words, we just need one general negative representation, the representation of “false,” and anytime we append that to an affirmative representation, we know that whatever it involves has been negated. How do we represent “false?” I have no idea, but if negation is so hard, only one is better than many, right?

I wish I could tell you that my reading all those years ago has led to me producing a breakthrough on negation myself, and proceed to blog about that, but alas, the negation literature got me interested in figuring out how we represent counterfactuals (something else we don’t know), and I’ve been obsessed with that ever since. But I check in on the negation literature now and then, and a recent paper by Hasson and Glucksberg(6), in a special issue on negation no less, takes us a pretty large step forward in our attempts to understand the problem. At the very least, it provides pretty strong evidence that allows us to distinguish between the two representations (the negation and the corresponding affirmation) and one (just the affirmation with the “false” marker) views, and it gives us some sense of the time course of representing negation.

The experiment Hasson and Glucksberg describe is pretty ingenious. They use a lexical decision task, which just involves presenting participants with a string of letters and asking them to indicate whether the string is a word. This is a common task that’s often used to measure priming. If you present people with a word or phrase or picture or whatever it is you’re using as a prime, and then give them a letter string that represents a word related to your prime, they’ll be able to verify that it’s a word faster. For their experiment, Hasson and Glucksberg used corresponding affirmative and negative statements. More specifically, they used corresponding metaphorical affirmative and negative statements? Why metaphorical? Well, because the meaning of a metaphorical statement isn’t necessarily directly related to the meanings of the words in the statement. This allows you to be sure that the priming is a result of the statement itself, and not just particular words within it.

So, for example, they gave participants the metaphor “This kindergarten is a zoo,” or its corresponding negation, “This kindergarten isn’t a zoo” on a computer screen. Participants indicated that they’d read the sentence by pressing the space bar, and after a short delay, they were presented with the target word and asked to indicate whether it was, in fact, a word. The targets were words that were consistent with either the affirmative or negative version of the metaphorical statement, or were irrelevant to it. Thus, after reading “The kindergarten is/isn’t a zoo,” they might have to determine whether “calm” or “noisy” are words (they’d only see one of those after reading the statement). “Calm” would be consistent with the negation (“The kindergarten isn’t a zoo”), while noisy would be consistent with the affirmation (“The kindergarten is a zoo”).

The key manipulation, for this experiment, was the length of the interval between the metaphorical statement and the presentation of the target word. They used three different delays: 150 ms, 500 ms, and 1000 ms. Why the different delays? Well, one way to tease out two different representations, as in the two-representation (affirmation and negation) version of negation, is to look at whether they become active at different times. Based on previous research, Hasson and Glucksberg hypothesized that when people read the negative metaphorical statements, they would initially represent the “counterfactual” scenario (that is, the affirmative version of the statement), and only later represent the “factual” scenario (the negated version).

So they predicted that if a participant read a negation (“The kindergarten isn’t a zoo”), then after only a 150 ms delay he or she would only have represented the counterfactual (i.e., affirmative) version of the scenario, and thus would be faster at verifying target words implied by that version (e.g., “noisy”) relative to the baseline for that word, but not words implied by the factual (i.e., negative) version (e.g., “calm”). As time passed, however, the participant would represent the factual version of the scenario, which would serve as a prime for words associated with that version (“calm”). Because the factual version would eventually replace the counterfactual version (once you have the negation nicely represented, you don’t need the affirmative version anymore), after longer delays, the negative metaphorical statements would no longer prime the words associated with the affirmation (“noisy”).

To make this more explicit, let’s look at the results for the affirmation condition. When participants read metaphorical statements like “The kindergarten is a zoo,” they were faster at verifying affirmative target words (e.g., “noisy”) relative to the baseline for those words (the same words used with unrelated metaphorical statements) regardless of the delay. Thus, the affirmative metaphorical statements primed affirmative target words. In this condition, however, participants were actually slower to verify the negative words relative to the baseline for those words, regardless of the delay. Thus, representing the affirmative version of the statement actually hurt the processing of the negative target words.

The picture was different for the negation condition, though. When participants read statements like “The kindergarten isn’t a zoo,” the results looked like this (from their Figure 2, p. 1022):

The y-axis in this graph represents “facilitation,” which means the difference between the baseline condition and the negation condition. A positive score on this axis means that the verification time for target words were faster by that amount at the delay represented on the x-axis. So the figure shows that at delays of 150 and 500 ms, the affirmative target words were facilitated (by about 20 ms, relative to their baseline), while verification of the negative target words was actually slower, relative to their baseline. This is the same pattern they found in the affirmation condition at all three delays. This implies that at least up to 500 ms, the representation of “The kindergarten isn’t a zoo” is the same as the representation of “The kindergarten is a zoo.” In other words, only the affirmative version was represented up to that point. At 1000 ms, however, the verification times for the affirmative words dropped to the baseline (0 on the y-axis), and verification times for the negative targets was facilitated (i.e., faster than the baseline). At 1000 ms, then, the participants were representing the negative version and not the counterfactual affirmative version.

In the course of analyzing the data, Hasson and Glucksberg apparently realized that some of the metaphors they used might be taken as being meant ironically in their affirmative versions. So they had a separate set of participants rate how ironic the different metaphors were, and then using only the low-irony metaphors, they again looked at the facilitation pattern for negative metaphorical statements. As in the previous analysis, only the affirmative target words were facilitated at 150 and 500 ms, while the verification times for the negative targets were actually slower than the baseline. At 1000 ms, however, the facilitation for the negative targets was 40 ms (twice what it is in the above graph).

What do these results mean? Two things: First, they suggest that people really are representing negations using both the affirmative (“Bob was at the party”) and negative (“Bob wasn’t at the party”), contrary to the single-version theory (i.e., “Bob was at the party” = False). Second, at some point between 500 and 1000 ms, the affirmative version passes the baton to the negative version, and ceases to be active itself. At that point, then, the negation is represented only with the negative version of the scenario.

Though they don’t discuss it, Hasson and Glucksberg’s results actually suggest a reason for the difficulty in processing negation observed in the sentence verification tasks mentioned at the beginning of this post. Way back in the early 70s, Wason (yes, that Wason), noted that when people hear negations in everyday speech, they usually hear them in a context that includes discussion of the corresponding affirmative scenario(7). He thus argued that the reason people have trouble processing negation in sentence verification tasks is because the negations are presented to them without that context. Hasson and Glucksberg’s results support this argument. If, in order to represent a negation, we first have to represent its corresponding affirmation, and only after doing so (much later, in processing terms) can we represent its negation, then if the context in which the negation is presented doesn’t supply the affirmation, we have to work from the negation (which can suggest several exclusive affirmative versions, sans context) to sort out the appropriate affirmation to represent. Naturally, this would make things much more difficult.

¹E.g., Wason, P. C. (1961). Response to affirmative and negative binary statements. British Journal of Psychology, 52, 133-142; Clark, H. H., & Chase, W. G. (1972). On the process of comparing sentences against pictures. Cognitive Psychology, 3, 472-517.
²Just, M. A., & Carpenter, P. A. (1971). Comprehension of negation with quantification. Journal of Verbal Learning and Verbal Behavior, 10, 244-253. Cited in Kaup, B., Zwaan, R. A., & Lüdtke, J. (In Press). The experiential view of language comprehension: How is negated text information represented? To appear in F. Schmalhofer & C.A. Perfetti (Eds.), Higher Level Language Processes In the Brain: Inference and Comprehension Processes. Mahwah, NJ: Erlbaum.
³Wason (1961).
⁴Cornish, E.R., & Wason, P.C. (1970). The recall of affirmative and negative sentences in an incidental learning task. The Quarterly Journal of Experimental Psychology, 22, 109-114.
⁵As quoted in Hasson, U., & Glucksberg, S. (2006). Does negation entail affirmation? The case of negated metaphors. Journal of Pragmatics, 38, 1015-1032.
⁶Ibid.
⁷Wason, P.C., (1965), The contexts of plausible denial. Journal of Verbal Learning and Verbal Behavior, 4, 7-11.