Chapter 12
“I’M AFRAID YOU COULDN’T BE MORE WRONG!”: SHELDON AND BEING RIGHT ABOUT BEING WRONG
Leonard, Sheldon, and Raj are brilliant physicists, and Howard (“Mr. Wolowitz”) is a gifted engineer, but even the smartest guy, Sheldon Cooper, with his impressive list of degrees—B.S., M.S., M.A., Ph.D., Sc.D.—sometimes errs. For instance, he misidentifies “Toby” in “The Jiminy Conjecture” as a snowy field cricket. And in “The Bozeman Reaction,” his belief that he would be safer living in Montana is almost immediately disconfirmed. Sheldon’s errant beliefs are not simply about factual matters, though. Sometimes they’re about concepts, including what it means to be wrong. In this chapter, we’ll see how Sheldon is sometimes wrong about the nature of being wrong, and we’ll highlight some philosophical issues associated with that interesting error, all in the hope of shedding some light on the character of Sheldon Cooper.
Recall this exchange from “The Hofstadter Isotope” between Sheldon and comic book store owner Stuart:
Stuart: Ooh, Sheldon, I’m afraid you couldn’t be more wrong.
Sheldon: More wrong? Wrong is an absolute state and not subject to gradation.
Stuart: Of course it is. It’s a little wrong to say a tomato is a vegetable. It’s very wrong to say it’s a suspension bridge.
Here the debate is whether there are degrees of falsehood. Sheldon claims that there cannot be degrees of falsehood, but he does not give an argument in support of his claim. He does say that it is “an absolute state” but that merely rephrases his point without really supporting it. This is so typical of Sheldon. Recall in “The Cooper-Hofstadter Polarization,” when a perturbed Leonard asks, “So the entire scientific community is supposed to just take your word?” Sheldon replies, “They’re not supposed to, but they should.” Stuart, on the other hand, holds that there are indeed degrees of falsehood and even gives a description of a situation that seems intuitively powerful enough to refute Sheldon’s claim.
Stuart’s view suggests an analogy with scientific exploration. It certainly seems that science gets closer and closer to the truth. In Ancient Greece, the philosophers Leucippus (5th century BCE) and Democritus (c. 460–370 BCE) claimed that all physical matter is composed of tiny indivisible particles called atoms. Around the year 1800, John Dalton proposed a modern atomic model based on experimentation. Later, scientists discovered various subatomic particles. Gradually, scientific knowledge became more and more detailed. Now scientists dispute whether loop quantum gravity or string theory best explains the physical world, occasioning the “conversation” between Leslie and Leonard in “The Codpiece Topology” about which should be taught to their imaginary future children. Just as science confirmed the views of Leucippus and Democritus, it is widely believed that it will also resolve the debate between loop quantum gravity and string theory. Once it does, we will be closer to understanding the truth about the universe. There are truths about the universe yet to be learned, but with each scientific discovery, we get closer and closer to the truth. So, the idea of “closeness to truth” seems intelligible.
“In None of Them Am I Dancing”
Apart from the connection to scientific advancement, Stuart’s implicit position seems intuitive on its own merits. There certainly seems to be such a thing as closeness to truth. People often say, “There is some truth in that,” or, “That is fairly close to the truth.” So, if truth comes in degrees, why can’t falsity? After all, it would be absurd to claim that “A tomato is a suspension bridge” is no more wrong than to claim that “A tomato is a vegetable,” even if both are false. The second seems closer to the truth. The trick is articulating how and why.
Some philosophers rely on “possible worlds” to specify closeness to the truth. A possible world is a complete description of how things could have been, even if things are not actually that way. For any statement or state of affairs, either it or its denial (but not both) is included in a possible world’s description. For example, there are no possible worlds in which Sheldon both is and is not originally from Texas. In some possible worlds, though, Sheldon does not have a twin sister. A bit paradoxically, in some possible worlds, Sheldon Cooper is a physicist attempting to win a Nobel Prize, but in others—the actual world—he is a (fictional) television character played by Jim Parsons. In this way, the actual world—the real world—is one possible world among others, but it stands out exactly because it represents actuality and not fiction.
The Big Bang Theory conveys the idea of “possible worlds,” at least as it is sometimes employed by theoretical physicists. In “The Gothowitz Deviation,” Sheldon provides Penny, now Leonard’s girlfriend, with a glimpse of his understanding of possible worlds:
Penny: Morning, Sheldon. Come dance with me.
Sheldon: No.
Penny: Why not?
Sheldon: Penny, while I subscribe to the many worlds theory, which posits the existence of an infinite number of Sheldons in an infinite number of universes, I assure you that in none of them am I dancing.
Penny: Are you fun in any of them?
Sheldon: The math would suggest that in a few I’m a clown made of candy. But I don’t dance.
It’s unclear from this exchange, though, whether Sheldon subscribes to the actual existence of these possible worlds, existing in various parallel dimensions or some such. (Imagine an infinite number of actual Sheldons—oy vey.) The vast majority of philosophers subscribe to a weaker notion of possible worlds by focusing on merely logically possible descriptions or, simply, the ability to consistently imagine the state of affairs in question. This interpretation of “possible worlds” is sufficient for our purposes of exploring the debate between Sheldon and Stuart.
Conveniently enough, Sheldon also expresses this weaker form of possible worlds. Recall the spat between Sheldon and Raj in “The Hot Troll Deviation”:
Raj: I’m telling you, if xenon emits ultraviolet light, then those dark matter discoveries must be wrong.
Sheldon: Yes, well, if we lived in a world where slow-moving xenon produced light, then you’d be correct. Also, pigs would fly, my derriere would produce cotton candy, and The Phantom Menace would be a timeless classic.
The interesting feature of this exchange is that Sheldon and Raj disagree about the actual properties of (slow-moving) xenon, namely, whether it emits light. Sheldon sarcastically retorts that Raj is correct about xenon in a different—or fictional—world. Xenon doesn’t actually emit light, at least according to Sheldon. Assume for the sake of argument that Sheldon is correct about xenon and Raj is mistaken. The larger point, at least implicitly, is that Sheldon suggests Raj’s claim is wildly false. Its being true doesn’t require only one thing about the actual world to be different, but a host of things, including flying pigs.
Accordingly, one strategy for determining whether a statement is more wrong than another is how far removed it is from the actual world. Take any two false theories. For example, take the theory that a tomato is a vegetable; for simplicity’s sake, let’s call it “vegetable theory.” Take a second theory that a tomato is a suspension bridge; let’s call it “suspension bridge theory.” Vegetable theory is wrong (or false), because, strictly speaking, a tomato is a fruit, rather than a vegetable. This is probably what Stuart had in mind. The actual world contains the following states of affairs regarding tomatoes: is a fruit, is edible, comes from a plant, isn’t a human-designed thing, isn’t a building. Vegetable theory is different from the actual state of affairs in one feature (isn’t a fruit) but similar in the other stipulated features. Thus, the truth of vegetable theory requires only one rather small alteration from the actual world. Suspension bridge theory is different in multiple facets regarding actual tomatoes. Hence, the vegetable theory is different from the actual world in only one aspect, and the suspension bridge theory is different from the actual world in at least six aspects. It seems that Stuart had in mind exactly this understanding of truth-likeness or false-likeness, when he said that it’s a little wrong to say a tomato is a vegetable, but it’s very wrong to say it’s a suspension bridge.
Even so, our discussion of possible worlds probably shouldn’t be interpreted as solving all aspects of the problem of truth-likeness. The vegetable example is fairly simple, and the measure of similarity by counting matching features to the actual world might not be the best measure. Perhaps one very large alteration (Sheldon is a robot) somehow outweighs one smaller change (Wolowitz has a Ph.D.). So, there is more work to do. Nevertheless, you can’t deny that Stuart’s example about tomatoes, vegetables, and suspension bridges makes a very good point about different things being wrong in different degrees.
Stuart’s move is clever on another level. If someone such as Sheldon says that being wrong isn’t subject to gradation, then, logically speaking, just one (true) example to the contrary suffices to refute him. This is exactly what Stuart gives Sheldon; the comic book store owner shows the theoretical physicist that he is wrong about being wrong. Sheldon may be the smarter guy, but Stuart, at least this time, has logic on his side. This would (or should) make any lifelong fan of Mr. Spock take notice.
“I Think You Mean I’m Improbable”
Perhaps Sheldon might resort to logic in a different way to defend himself about being wrong. Recall “The Pirate Solution,” where Sheldon (apologetically) admits that Raj is correct about a calculation but denies that this means he is wrong:
Sheldon: I looked over the board and it turns out you were right.
Raj: So you were wrong.
Sheldon: I didn’t say that.
Raj: That’s the only logical inference.
Sheldon: Nevertheless, I didn’t say it.
Given that Sheldon and Raj argued about the very same thing, and given that Raj is indeed right, is Sheldon’s wrongness the only logical inference? The answer is both yes and no. More particularly, it depends on the logic one adheres to in this situation.
Raj’s position that Sheldon’s being wrong “is the only logical inference” assumes what philosophers call classical logic. One of the fundamental principles of this logic is the law of excluded middle: every (meaningful) statement has to be either true or false. There’s no other possibility. It’s called the law of excluded middle because it excludes the possibility of any middle ground between true and false. This sheds light on another law of classical logic—the law of noncontradiction, which holds that a statement can’t be both true and false. In other words, a statement can’t contradict itself. Hence, if Raj is right and Sheldon contradicts him, then Sheldon must be wrong.
People often like to say, though, that the world isn’t only black and white; there are shades of gray. Many-valued logics have been developed exactly for this reason. For example, if one wants to capture three states of affairs—true, false, and indeterminate—one can use for that a corresponding three-valued logic. In many-valued logics, one can have as many truth-values as one wants to. There’s only one basic principle for calculating truth-values (where 1 means completely true, 0 means completely false, and all of the other possible truth-values are between 0 and 1): the degree of false = 1 – the degree of truth; and the degree of truth = 1 – the degree of false. For example, if the truth-value of “A” is 0.8, then the truth-value of “not A” is 0.2, or if “B” is true to the degree of 0.4, then “not B” is true to the degree of 0.6.
Therefore, given many-valued, nonclassical logic, there’s a way for Raj to be right and for Sheldon not to be wrong. We can say, for example, that Raj is right but not completely, and, because of that, Sheldon isn’t completely wrong but rather very slightly, yet still somewhat, right. So the only way for Sheldon not to be wrong and for Raj to be right is if there are degrees of truth and falsity. Yet this comes with a price. Recall the debate between Sheldon and Stuart in “The Hofstadter Isotope.” There, Sheldon was emphatic that being wrong was not subject to gradation. So, his new implicit position with Raj, if correct, seemingly makes him wrong about his previous position with Stuart! (And no, Sheldon, that’s not sarcasm, just logic.)
The Big Bang Theory is replete with examples of Sheldon professing his incredibly large and accurate knowledge base (thanks in part to his eidetic memory, no doubt). He goes so far as to smugly tell Penny in “The Prestidigitation Approximation” that “Oh, oh, please, if I don’t know, you don’t know. That’s axiomatic.” In “The Bat Jar Conjecture,” she humorously reveals his hubris by asking him questions such as “Which Ridgemont High alumnus was married to Madonna?” and “Who replaced David Lee Roth as the lead singer of Van Halen?” He is ignorant of both answers. She possesses knowledge he lacks, thus falsifying his claim.
In “The Jiminy Conjecture,” Sheldon puts forward a similar claim to Wolowitz: “Howard, you know me to be a very smart man. Don’t you think if I were wrong, I’d know it?” There is more than a sliver of arrogance here, too, but note that it differs from the claim made to Penny in the following way. There may be topics about which Sheldon is ignorant, but he would not assert something as true that wasn’t. He would never (knowingly) make that sort of error. As we’ll see, this position harbors some interesting implications about truth and knowledge.
Given Sheldon’s implicit position expressed to Howard, it seems to follow that if Sheldon correctly asserts something, then he knows what he’s right about, so he knows what’s true. It also seems to follow that if Sheldon incorrectly asserts something, then he knows what he’s wrong about, so he knows that the contrary thing is true. For any assertion Sheldon makes, it is either correct or incorrect, but either way he knows what is true. Hence, if Sheldon’s statement to Howard is true, then Sheldon never holds a false belief! If someone would object and reply that Sheldon might know when he’s wrong, but this doesn’t mean that he knows when he’s right, then consider this. If Sheldon knows he’s wrong every time he’s wrong, then the only time he wouldn’t know he’s wrong would be the time when he’s right.
True, this argument contains a false premise because it’s not the case that Sheldon (always) knows when he is asserting something false. His mistaken attribution of Toby as a snowy field cricket is an obvious example, but so is (it seems) the claim he makes to Stuart about truth and falsity not admitting of degrees. Yet even ignoring those examples, interesting philosophical insights follow. Seemingly, it can be proved that when Sheldon is wrong, he can’t know that he’s wrong at all.
Let’s assume for the sake of the argument that Sheldon knew that he asserted something false, say, Toby’s being a snowy field cricket. For this to happen, two things have to be true. First, it has to be true that Sheldon knows that Toby is actually a common field cricket. In other words, in order to know that you’re wrong, you have to know what’s right. Second, it has to be true that Sheldon knows that he doesn’t know that Toby is a common field cricket. In other words, in order to know that you’re wrong, you have to know what you’re wrong about.
Now, if you know something, then this thing you know has to be true. Truth is a necessary condition of knowledge. You may believe that The Big Bang Theory moved from Tuesday to Thursday nights on CBS, but you cannot know this. This is grounded in the intuition that knowledge is opposed to ignorance. Your belief about the change in the CBS schedule demonstrates your ignorance of the facts, not the knowledge of them. Hence, if Sheldon knows that he doesn’t know that Toby is a common field cricket, then it’s also true that Sheldon doesn’t know that Toby is a common field cricket. Yet this contradicts our beginning assumption, namely, that Sheldon knows that Toby is a common field cricket. If we made a supposition and inferred a contradiction from it, then our supposition has to be false. (Philosophers sometimes call this an indirect proof.) We made a supposition that Sheldon knows that he’s wrong and derived a contradiction. Therefore, this supposition is wrong: Sheldon can’t know that he’s wrong!
Where’s the paradox? A paradox is something that has contradictory qualities. On one hand, Sheldon claims that if he were wrong, he’d know it. On the other hand, we just saw that Sheldon can’t possibly know that he’s wrong about something. The paradox may be further strengthened: that he’s wrong about his claim to Wolowitz is the only (relevant) thing Sheldon can know for sure.
“Of Course I’m Right—What Are the Odds I’d Be Wrong Twice in One Week?”
Even though, conceptually speaking, Sheldon can’t know that he’s wrong, there’s a sense in which Sheldon can be wrong and know about it, thanks to inductive inference.
Inductive inferences note similarities or regularities among a group of data and then make generalized conclusions about them. These conclusions are often predictive. Given what we have observed in the past, conclusions about future events are made. For example, suppose that for the last fifty consecutive Saturdays, you observed that Sheldon awakens at 6:15, pours a bowl of cereal, adds a quarter cup of milk, sits on his end of the couch, turns on BBC America, and watches Doctor Who. Given these prior experiences and knowing what a creature of habit Sheldon tends to be, someone such as Leonard can confidently predict Sheldon’s behavior next Saturday morning at 6:15 A.M.
The connection to Toby the field cricket is fairly obvious. Yes, Sheldon mistakenly identifies him as a snowy field cricket, but the chances that he will utter another falsehood in the next seven days are incredibly low. This belief is strengthened by all of Sheldon’s past experiences, especially noting how rare it is that he utters a falsehood. So, in a way, his being proved wrong about Toby has interesting ramifications for his other beliefs (all things being equal). Yet there’s a hitch. The worry has to do with Sheldon’s affirmation that “Of course, he’s right” about his other knowledge claims in light of misidentifying Toby. If he means that he must be right about all of his other beliefs in the current seven-day window, he again runs the risk of being wrong about being right.
The potential error is rather straightforward: any generalization based on past experiences could, no matter how unlikely, turn out to be false. Recall “The Dumpling Paradox,” in which Sheldon finds Penny sleeping on his couch one Saturday morning; as he ponders the situation, his cereal quickly loses all of its molecular integrity, and he misses the beginning of Doctor Who. Or consider Leonard’s season 1 lamentation that girls like Penny never end up with guys who own time machines. In his experience—perhaps in anyone’s experience—girls like Penny simply don’t become involved with guys who are preoccupied (obsessed?) with classic science fiction and fantasy memorabilia. Yet no matter how many unfortunate time machines owners you may have observed, this doesn’t guarantee that the next time machine owner can’t have a girlfriend like Penny. The Scottish philosopher David Hume (1711–1776) is often credited for his succinct formulation of the relevant worry: “That the sun will not rise to-morrow is no less intelligible a proposition, and implies no more contradiction, than the affirmation, that it will rise.”1 Thus, Sheldon cannot know, at least not with any certainty, that his false belief about Toby guarantees that his other recent knowledge claims are true.2
Although we can’t ever be sure that our inductive inferences are true, at least we can sometimes be sure when our inductive inferences are false. The statement “Girls like Penny never end up with guys who own time machines” isn’t guaranteed simply because we can’t possibly observe each and every future time machine owner’s private life. If, however, we observe at least one time machine owner who has a pretty girlfriend like Penny, for example, Leonard during the third season, then we’re more than definitely justified to believe that the generalization “Girls like Penny never end up with guys who own time machines” is false. This result may finally comfort Sheldon. He can’t ever be sure that his inductive generalizations are true, but, at least, he can sometimes know when his generalizations are false. He may, at last and in some sense, be wrong and know about it.
“Throw All the French around You Want, It Doesn’t Make You Right.”
Sheldon shows us how nonrational factors often impinge on one’s rationality. He has grown so accustomed to being right that it is difficult for him to accept that he is wrong or even doesn’t know something. The final question of the Physics Bowl competition in “The Bat Jar Conjecture” is excellent evidence of this. Sheldon would rather lose to Leslie and the guys than allow another member of his team to answer correctly. He would rather lose the competition than not answer all of the questions himself.
This sort of psychological idiosyncrasy also sometimes leads Sheldon to argue irrationally. Recall another part of Sheldon’s discussion with Stuart in “The Hofstadter Isotope” about who is the logical successor to the Bat Cowl if Batman’s death proves permanent:
Sheldon: Removing Joe Chill as the killer of Batman’s parents effectively deprived him of his raison d’être [reason for existence].
Stuart: You can throw all the French around you want, it doesn’t make you right.
Sheldon: Au contraire [on the contrary].
The implication is that by simply infusing his argument with words from the French language, Sheldon’s position is somehow established. Yet this is a faulty inference, and Stuart is wise to call him on it.
As their argument wears on into the wee hours of the morning, and after Penny falls asleep—which reminds us of why we’re inclined to say guys like Leonard don’t wind up with girls like Penny—Stuart finally relents.
Stuart: Okay. Look, Sheldon, it’s late. I’ve gotta get some sleep.
Sheldon: So I win.
Stuart: No, I’m tired.
Sheldon: So I win.
Stuart: Fine, you win.
Sheldon: Darn tooting, I win.
Here again, Sheldon appeals to something other than the subject matter of the argument. Now Sheldon plays on Stuart’s tiredness in order to “prove” his point. Stuart won’t be allowed to leave until he accepts that Sheldon is right. The implication is that if Stuart gives up and goes home, Sheldon’s conclusion is thereby established. Yet again, this is faulty reasoning. Stuart knows this, but he simply needs a break from Sheldon. Again, Stuart has logic on his side.
Philosophers have a name for the type of “argument” Sheldon is employing here: logical fallacy. Logical fallacies, of which there are many kinds, are faulty pieces of reasoning because they do not and cannot establish a rational link between premises and a conclusion of an argument. Nevertheless, they are often rhetorically persuasive. Instead of logically proving something, they psychologically or emotionally persuade the listener to accept a position.3
That Sheldon sometimes resorts to logical fallacies to persuade his dialogue partner is telling. Very much unlike his favorite Star Trek character, he is so overcome with the emotional need to be right that he is willing to sacrifice logic. Perhaps, in the end, this as much as anything else explains why Sheldon cannot accept that Stuart is correct about truth admitting of degrees; why, if Raj’s competing calculation was correct, his was not mistaken; and why he takes his ill-advised “axiomatic” position about Penny’s knowledge base. And so, we see a pattern develop. Rather than admit he was wrong or simply doesn’t know, he invariably resorts to nonrational behavior, including rhetorical ploys. In this, perhaps Sheldon is again wrong about being wrong—at least, that’s what Spock might say.
NOTES
1. David Hume, An Enquiry Concerning Human Understanding (New York: Oxford University Press, 2007), p. 18.
2. Actually, Hume is invariably credited with formulating an even deeper problem about induction. He famously argued that the very process of induction as a way to extend our knowledge is flawed. Inductive inferences, especially those that make predictions from past observations, ultimately assume what they are trying to prove: that some natural occurrence (the sunrise) will continue to happen as it has repeatedly in the past.
3. Of course, employing logical fallacies may have pragmatic or perhaps even evolutionary benefits.