Back in May, the Cracked website produced a page called “20 Paradoxes Most Human Minds Can’t Wrap Themselves Around“. As a subscriber of the Cracked YouTube channel, I am well aware of Cracked’s penchant for misleading clickbaity titles. (Interestingly, the URL contains the string “insane-thought-experiments-thatll-blow-your-mind”, which is an entirely different concept.). I knew going into the article that at least some of the examples they presented would not be true paradoxes, nor would they be particularly difficult to comprehend. I was correct in my suspicion. This week I thought I’d take a break from the depressingly never-ending slideshow of racist, sexist, privilege-soaked memes to examine a group of memes that stretch the meaning of the word paradox to its very breaking point.
Consider the Twin Paradox. In the Twin Paradox, one half of a pair of twins sets off from Earth in a spaceship traveling very close to the speed of light. Einstein’s Theory of Special Relativity says that if you travel very close to the speed of light, a stationary observer will see your clock running more slowly than his own clock. Hence, the Earthbound twin, who is stationary for all intents and purposes, witnesses his twin aging slower than he is. When the traveling twin returns, he ought to be younger than the twin he left behind.
But Relativity also tells us that there is no preferred inertial reference frame; i.e. the traveling twin may reasonably view himself as being stationary while Earth speeds away and then returns to him. From the traveling twin’s reference frame, the Earthbound twin’s clock is running more slowly, so the traveling twin might expect to return to find that his Earthbound brother has aged less than he has. If both inertial reference frames are equal, then both twins ought to be correct – a contradictory answer.
Many paradoxes can be resolved with a deeper understanding. The resolution of the Twin Paradox comes from within Special Relativity. Since the traveling twin’s reference frame changes between the outward and homeward legs of his trip, it is he that ages less than his twin. The traveling twin returns to find that his brother (and everybody else on Earth) has experienced more time during his absence than he did.
A paradox need not be unsolveable, or even unsolved, to be called a paradox. But it must lead simultaneously to two contradictory outcomes, even if the contradiction disappears with further study. Without further ado, then, let’s see how Cracked’s list of paradox-bearing memes measures up.
(To be fair, some of the memes do depict actual paradoxes, and when they do, I’ll say so.)
Is this a paradox? In my opinion, yes. There are four answer choices. If they were all different, and if one of the answers were correct, then the probability of randomly choosing the correct answer would be 25%.
In this case, two of the answers are 25%, which means that you are twice as likely to choose 25%; ergo, your probability of picking that answer rises to 50%. But if the correct answer is now 50%, and 50% only appears once as an answer choice, then your probability of choosing the correct answer drops back down to 25%.
Is there a resolution? Not that I can see. In reality, this question has no unambiguously correct answer, which means your probability of picking the correct answer is 0%. If Raymond Johnson had been truly evil, he would have made choice C zero percent.
Is this a paradox? No. Unlike the previous meme, it doesn’t present contradictory outcomes. If you answer yes, there is no logical train that leads to a negative position, or vice versa. This is a thought experiment.
Molyneux’s Problem has been answered, by the way, and the answer is no. People whose congenital blindness is later corrected by surgery do not automatically learn to connect their senses of touch and sight. That takes time.
Is this a paradox? Not really. This falls into a sub-category of mind twisters that I’ll call pseudoparadoxes. It has the feel of a paradox – that is, it tends to draw you into a back-and-forth internal argument that has no resolution – but it lacks a certain concreteness that true paradoxes have.
For one, your interpretation of this alleged “paradox” will vary depending on the philosophy of mind to which you subscribe. If you are a materialist who believes that your mind – your sense of consciousness – is merely the result of a functioning brain, then the answer is obvious: this type of teleporter kills the original you and creates a duplicate who only thinks himself or herself to be you.
On the other hand, perhaps you believe that the physical brain is only a vessel for your immaterial mind. In that case, maybe your displaced soul automatically transfers itself into your new vessel on Mars, and your sense of self continues uninterrupted. If a teleporter malfunction failed to destroy the original body, perhaps your consciousness would somehow be “split” to exist simultaneously among the two identical yous.
Regardless of your stance on the relationship between mind and body, quantum mechanics indicates that particle-for-particle teleportation is impossible, or at least incredibly unreliable, rendering the issue essentially moot.
It seems that the milkman needs glasses as well.
Is this a paradox? No. This is an epistemological problem (epistemology being the theory of knowledge: how it is constructed, what it is, and how it compares to opinions and beliefs). The philosopher Plato defined knowledge as justified true belief, or JTB. In order to say that you know P – where P is a proposition – three criteria must be met:
- P must be true.
- You must believe P is true.
- You must be justified in believing P is true.
The first two criteria are fairly non-controversial, but philosophers have long struggled to develop a theory of justification. How do you determine whether a person is justified in knowing something? In 1963, Edmund Gettier, a professor of philosophy at the University of Massachusetts Amherst, published a short paper called Is Justified True Belief Knowledge? (Spoiler alert: Gettier doesn’t think so.) Gettier’s paper provides two counterexamples to the JTB model of knowledge; however, the cow problem is not one of them. I do not know if Gettier actually devised this problem himself, as the meme suggests, or if it is a Gettier-style problem created by somebody else.
One can imagine many Gettier-style problems that might challenge the JTB model of knowledge. Here’s another example: Suppose I am speaking to a room full of college students. One of them is named John. At some point in the past I have seen John’s driver’s license, and the license indicates that John is from Charlotte, North Carolina. Based on that, I know the following proposition: one of the students in the room is from Charlotte. Unknown to me, however, John’s ID is fake: he isn’t really from Charlotte. Also unknown to me, another student, Lucy, is from Charlotte.
Do I really know, then, that one of my students is from Charlotte? According to Gettier, the JTB model of knowledge implies that I do; after all:
- The proposition is true: one of my students is from Charlotte.
- I believe it is true.
- I have justification – maybe – for believing it is true.
But of course my knowledge is flawed, as it is based on a false premise. It isn’t a genuine case of knowledge. If it were revealed to me that John’s ID is fake, I would no longer have justification for knowing the proposition, even though the proposition would still be true.
Gettier’s paper launched a flurry of responses from philosophers, some looking to defend the JTB model by claiming that Gettier’s definition of justification was too broad, others looking to amend the JTB model to specifically exclude false pretenses. Consider the cow problem: Gettier’s detractors might argue that the milkman didn’t really have justification for believing he had seen the cow; after all, he clearly did not get close enough – or his eyesight is insufficient – to distinguish between a set of black and white sheets and a large grazing mammal. To the student problem, Gettier’s critics might respond that I lacked justification for believing one of my students to be from Charlotte, since I did not closely investigate John’s license to ensure that it was real. In other words, I was trying to build knowledge from not-knowledge.
This isn’t a paradox, in any case. Gettier problems don’t lead to contradictory outcomes; they merely ask you to question what it means to know something. If you accept Gettier’s claim that knowledge requires more than justified true belief, you won’t then be forced into a contradictory position where JTB is sufficient for building knowledge. If you think Gettier is all wet, you will not logically be drawn into accepting his claims.
Is this a paradox? Yes, but it is stated poorly in this meme. For maximum effectiveness, the second sentence should read “He will be released if and only if his father guesses what the crocodile will do.” As written, the problem is too vague; it leaves some wiggle room because we are not guaranteed that anything tragic will happen if the father guesses incorrectly.
Also, I don’t think the word correctly should appear in the penultimate sentence. As we are about to see, the father’s answer cannot be judged correct or incorrect. That’s what makes this a paradox.
Let’s start by examining what would happen if the father says “You will release the boy.” The crocodile can then refuse to release the boy. In doing so, he makes the father’s guess incorrect, so in a circular sort of way, the croc does exactly what he promised to do.
But of course the clever father does’t say that. He gives the best possible answer, because now the crocodile is trapped in a paradox. If the crocodile refuses to let the boy go, then the father’s prediction was correct, in which case the boy should be released. But if the reptile releases the child, then the father’s prediction wasn’t correct, in which case the child should still be a captive. One line of logic leads to the other, and back again, over and over ad infinitum.
Is there a resolution? In the simple premise put forth by this paradox, no. The father (with the crocodile’s unwitting assistance) has created a never-ending logical loop. Perhaps the crocodile, stymied by his inability to decide what course of action to take, will spend the next several hours tossing the situation back and forth in his mind, during which time the boy and his father will have the good sense to walk away. Or perhaps the crocodile is a deceitful liar who never really intended to release the boy, in which case the boy will be gobbled. There will probably be a meeting at the Crocodile Council, during which they will resolutely ban crocodiles from promising to return their victims if the victim’s next of kin can stump them with a logical paradox.
That’s enough for one day. We’ve considered five memes, only two of which contain paradoxes. There are still 15 paradoxes, pseudoparadoxes, and non-paradoxes to explore, so stay tuned the rest of this week for more logical lunacy.