We can only judge truth and reality when they become acrobats on a tightrope. So goes a line from Oscar Wilde’s The Picture of Dorian Gray. Because how are we supposed to judge an acrobat relaxing in a lounge chair? To tell how good he is we’ll have to see him pushing the boundaries of his skills in terms of balance, coordination and agility. The same applies to the relationship between a paradox and the truth. Luckily, the world abounds with paradoxical examples of mind-bending contradictions and peculiar logic.
At first glance, a paradoxical proposition might seem pointless or irreconcilably absurd. It requires careful investigation to figure out what’s true and false. That’s why paradoxes have long been a staple of philosophy. Many may be fictional, but in one form or another, we all have encountered them in real life. Here are seven paradoxical examples plus an encore.
1. Buridan’s Bridge: Don’t Cross Socrates
Buridan’s Bridge is a paradox around a self-referential conditional promise. It was invented by French philosopher Jean Buridan in the 14th century. The conundrum’s protagonists are the ancient Greek philosopher Plato and his teacher Socrates. Plato, so the premise, is guarding a narrow bridge. No one shall pass without his say-so. Socrates comes along, asking Plato for permission to cross. The following exchange ensues:
Plato: “Socrates, if in the first proposition which you utter, you speak the truth, I will permit you to cross. But surely, if you speak falsely, I shall throw you into the water.”
Socrates: “You will throw me into the water.”
The first of our paradoxical examples started as a witty exchange and turned into a contradictory promise. Socrates’ punchline begs the question of whether he did tell the truth and should be allowed to cross the bridge. If Socrates’ statement is true, he must not be thrown into the water. But not being thrown in the water would render his statement untrue, for which there is only one punishment: being thrown into the water. So was Socrates truthful and Plato made a false promise? What’s the bridge guardian going to do and what’s Socrates’ favourite colour?
Buridan’s Bridge forces us to take a very close look at the meaning of truth and its integrity over time. How a momentarily true proposition can sometimes change to falsehood within seconds. As Buridan himself implied, it can also be read as a commentary on the sincerity of carelessly made promises. Several attempts have been made to solve the paradox. The wittiest one is probably to advise Plato to let Socrates cross and then throw him from the bridge.
2. Sorites Paradox: The Essence of Borderline Cases
Imagine a pile of sand. 100,000 grains to be precise. Now imagine we’d remove a single grain. The question is whether 99,999 grains of sand still constitute a heap. If yes, the question then becomes how many grains we need to remove until the pile of sand will cease to be a heap.
Sorites comes from Ancient Greek and Latin meaning heap. This conundrum is another one of the paradoxical examples proposed in Ancient Greece. The problem can be narrowed down to the definition of the word ‘heap’. Surely a single grain is not a heap. However, would it also be wrong to call two grains of sand a heap? Does it matter if they’re stacked on top of each other or are scattered around? Pondering on piles of sand might seem irrelevant, but Sorites Paradox has a wider application as it can be applied to any number of attributes.
We can probably all agree that putting a baby monitor in your infant’s room is perfectly normal and responsible behaviour. We might also agree that doing the same thing to an 18-year-old is rather creepy. The real question is at what point in a child’s life does this responsible behaviour become Orwellian — and under what conditions? Where exactly is the cut-off point?
Considering these questions encourages high-resolution thinking and precision with our language. This probably sounds like a painful and frustrating process. We may be inclined to circumvent the difficult question, to cut corners by pointing to the obvious extreme instances. As Loki’s Wager demonstrates, it’s the borderline cases that are most challenging as they come down to grainy detail. The first step to good decision-making is to recognise that fixing things is hard. Unless you’re John Morton who tried to get around it all by creating his very own paradox.
3. Morton’s Fork: Justifying the Unjustifiable
Back in the 15th century, John Morton was the archbishop of Canterbury and Lord Chancellor to Henry VII, King of England. Knowing his way around marketing-lingo, he raised a benevolence tax for the monarch. His reasoning was rather extraordinary. If you lived well, Morton suggested, you could certainly afford to pay the tax. If you lived humbly, however, it meant you must have had savings and could pay the tax as well.
Essentially, the ancient spin doctor crafted two statements that led to the same conclusion despite being contradictory. It’s certainly not the way of truth. It’s a strategy of starting with the conclusion and bending your arguments and reality to match it. There are several variations of this linguistic trick from which there’s no escape. Morton’s Fork is reminiscent of paradoxical situations such as Catch-22 or a Kafka Trap; decision dilemmas designed to leave an individual no way out — as long as they’re willing to participate in the game.
4. Abilene Paradox: The Perils of Silent Disagreement
Imagine you’re with a group of friends and one of them suggests you should go for a hike in the mountains. That’s not really how you want to spend your Sunday but the group seems happy with it. So you go along. When you return, one of your friends casually mentions that hiking is really not for her. Suddenly, the truth comes to light. One by one, your friends admit they didn’t enjoy it either. Paradoxically, nobody wanted to go hiking but everyone thought this was what the group wanted.
How is that possible? The group was unable to manage let alone communicate their disagreement. No member questioned the decision. Maybe out of fear of exclusion from the group or simply not to cause any trouble. In general, the paradox occurs whenever a group unknowingly makes a decision that goes against everyone’s will or at least that of the majority.
Not all paradoxical examples originated in Ancient Greece or medieval France. The Abilene Paradox was coined by management expert Jerry B. Harvey. He described the phenomenon in his 1974 article The Abilene Paradox: The Management of Agreement. In case you were wondering, it has its name from a trip to the small town of Abilene, TX. A trip nobody ever wanted to make.
Harvey also distinguished the paradox from groupthink. Whereas in groupthink, people tend to abandon thinking for themselves, the Abilene Paradox causes people to act consciously (and unnecessarily) against their own preferences. Either way, the Tenth Man Rule, a form of institutionalised devil’s advocacy, could’ve surfaced the truth and kept us from wasting our time in the mountains. Speaking of wasting our time.
5. Fredkin’s Paradox: Wasting Time
Should we get the delicious chocolate cake or the mouth-watering cheesecake? We can only have one so we must choose wisely. It’s a hard decision that can make or break a Sunday afternoon. It requires careful deliberation and is the place where Fredkin’s Paradox lurks. This paradoxical example of contradictory decision-making was proposed by physicist Edward Fredkin. It reads as follows:
The more equally attractive two alternatives seem, the harder it can be to choose between them — no matter that, to the same degree, the choice can only matter less.Edward Fredkin, The Society of Mind
Put differently, the least important decisions to make are often the ones we waste time on. As cognitive psychologist Gary Klein writes in Bounded Rationality, we could attempt to optimise decision-making by gauging the importance of a decision. Though, that wouldn’t necessarily speed up the process. It would open up another paradox instead. Is our cake decision really worth deliberating and optimising? Is it even worth thinking about if it’s worth thinking about? Now we have to factor in the time it takes us to optimise our decision-making process, which in turn has to be further optimised.
While we’re still overthinking the most delicious answer, our coffee gets cold. Calls like this are the reason why our mind tends to take mental shortcuts intuitively. Fredkin’s Paradox is also reminiscent of the Law of Triviality, the idea that groups tend to spend the most time discussing trivial issues rather than on the ones that have lots of money involved. At the end of the day, it seems to come down to knowing intuitively when we face an important decision. Such as the next one.
6. The Crocodile Paradox: Anticipating the Next Move
The crocodile of this story has some good news and bad news for us. The bad news is that it has stolen a child. The good news is that the crocodile is promising to return the kid if we correctly predict what it’s going to do next. Predicting the reptile will return the child puts us at ease — at least logically. Though, anticipating that the crocodile won’t return its victim puts the poor animal into a dilemma.
If the croc doesn’t return the kid, our prediction was correct and the child must be released. The only problem is that this would violate the crocodile’s own terms. Because if the child is returned, after all, our prediction would suddenly become incorrect. What would you do if you were a crocodile obsessed with adhering to its self-imposed logic?
While similar to our first paradoxical example, Buridan’s Bridge, there don’t seem to be any workarounds for the Crocodile Paradox. Perhaps unless we’re willing to meddle with the definition of the verb ‘to return’ in the spirit of Sorites.
7. Schrödinger’s Cat: Dead? Alive? Both?
The last of our paradoxical examples is the strangest contradiction of them all. At the same time, it’s also surprisingly factual. Schrödinger’s Cat is a thought experiment proposed by Austrian physicist Erwin Schrödinger. In 1935 he wrote:
One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid.
If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.Erwin Schrödinger
Simply put, Schrödinger’s Cat demonstrates how two contradictory situations can simultaneously be true. The cat can be considered both, dead and alive. Has the deadly mechanism already been triggered? Or are we waiting for Godot? We can’t know until we open the apparatus to check on the poor kitty.
The experiment also highlights how the mechanics of an invisible micro-cosmos can be made visible by observing the outcome of a macro experiment. In other words, it turns the abstract notion of a decaying atom into a vivid picture of a possibly deceased cat.
Mind you, this is a thought experiment of quantum mechanics. No cats were harmed. There are plenty of mind-bending interpretations that exceed my ability to explain. Though, Schrödinger’s Cat has been widely referenced in popular culture. Outside of physics, they often come down to a simplified life lesson: Until we’ve observed the outcome of a decision, it can be considered a good call, a poor one, or both.
Encore: Grandfather’s Axe Paradox
Suppose you inherited your grandfather’s axe. It’s a beautiful piece of workmanship with a wooden handle and an axe head. Unfortunately, the handle is soon rotting away, so you need to replace it. As the years go by, the elements also affect the axe head, which you’ll eventually replace as well. Here’s the question: Given that both, the head and handle are now replaced, is it still your grandfather’s axe?
Grandfather’s axe is a simpler variation of the famous Ship of Theseus paradox of identity. The mythical king’s ship consists of many planks that are replaced over time. Both paradoxical examples bring up the question that things are nothing more than a sum of all their parts. By extension, the paradoxes raise the same question about our own identity and its inevitable change over time. Given how different we are at the age of 40 compared to when we were born, who are we really?
Pondering paradoxes pushes our reasoning beyond its limits, sharpening our critical thinking, problem-solving and decision-making skills. Some of our paradoxical examples can be solved, others remain irreconcilably impossible. If we stick with Oscar Wilde’s acrobatic analogy, we might also ask what kind of acrobats we’re dealing with.
Buridan’s Bridge is the banter between two philosophers, designed to challenge each other’s thinking, much like Alan Watts’ conception of Zen school or the Trolley Problem Meme Complex. Paradoxical examples such as Abilene’s Paradox lead us to understand better and probe the truth. Others, such as Morton’s Fork, can be used to deceive and manipulate. Either way, it’s reason enough to invest in cultivating our critical thinking skills.