Brain Games: 8 Philosophical Puzzles and Paradoxes
19. The only certainty is that nothing is ever certain. This realization almost made my head explode when I was 17.
20 Paradoxes That Are True
Some of the most important truths in life are contradictory on the surface. They seem like impossibilities, yet experience proves them to be obvious over and over again. It isn’t until you look a bit deeper, beneath the surface contradictions, that the real grains of wisdom emerge.
Below are 20 paradoxes I’ve come across which are, paradoxically, still true:
1. The more you hate a trait in someone else, the more likely you are avoiding it in yourself. Carl Jung believed that characteristics in others that bother us are reflections of the parts of ourselves that we deny. Freud referred to it as “projection.” Most people call it “being an asshole.” For example, the woman who is insecure about her weight will call everyone else fat. The man who’s insecure about his money will criticize others for theirs.
2. People who can’t trust, can’t be trusted. People who are chronically insecure in their relationships are more likely to sabotage them. Call it the Good Will Hunting syndrome, but one way people protect themselves from getting hurt is by hurting others first.
3. The more you try to impress people, the less impressed they’ll be. Nobody likes a try-hard.
4. The more you fail, the more likely you are to succeed. Insert inspirational famous person quote here. You’ve probably heard many of them. Edison tried over 10,000 prototypes before getting the lightbulb right. Michael Jordan got cut from his high school team. Success comes from improvement and improvement comes from failure. There’s no shortcut around it.
5. The more something scares you, the more you should probably do it. With the exception of genuinely life-threatening or physically harmful activities, our fight-or-flight response kicks in when we’re confronted with past traumas or actualizing the self we dream of being. For instance: speaking to an attractive person, cold-calling someone to get a new job, public speaking, starting a business, saying something controversial, being painfully honest with somebody, etc., etc. These are all things that make you scared, and they make you scared because they are things that should be done.
6. The more afraid you are of death, the less you’ll be able to enjoy life. Or as one of my favorite quotes puts it, “Life shrinks and expands in proportion to one’s courage.”
7. The more you learn, the more you realize how little you know. The old Socrates adage. Every time you gain a greater understanding, it creates even more questions than it answers.
8. The less you care about others, the less you care about yourself. I know this may go against every perception you’ve ever had of a self-serving asshole, but people treat people the way they treat themselves. It may not be apparent on the outside, but people who are cruel to the people around them are cruel to themselves.
9. The more connected we get, the more isolated we feel. Despite being in more constant communication than ever, research finds an increase in loneliness and depression in the developed world over the past few decades.
10. The more you’re afraid to fail, the more likely you are to fail. See: self-fulfilling prophecy.
11. The harder you push for something, the harder it will feel to achieve. When we expect something to be difficult, we often unconsciously make it more difficult. For instance, for years, I assumed starting a conversation with a stranger was something that was highly abnormal and therefore “difficult.” As a result, I spent a lot of time strategizing and studying ways to relate to people I didn’t know. Little did I realize all I had to do was say “Hi” and then ask a simple question; that would get me 90% of the way there. But because it felt hard, I proceeded to make it hard for myself.
12. The more available something is, the less you will want it. Humans have a strong scarcity bias. We unconsciously assume things that are scarce are valuable and things that are abundant are not. This is not the case.
13. The best way to meet someone else is to not need to be with someone else. The defining theme of my book on dating was non-neediness and how that plays out in our relationships. The fact remains that the best way to find a sexual relationship — committed or otherwise — is by not needing a sexual relationship to be happy and investing more in yourself.
14. The more honest you are about your faults, the more people will think you’re perfect. The amazing thing about vulnerability is the more comfortable you are about not being that great, the more people will think you are.
15. The more you try to keep someone close, the further away you’ll push them. This is the argument against jealousy in relationships: once actions or feelings become obligations, they lose all meaning. If your girlfriend feels obligated to spend her weekends with you, then the time you spend together has become meaningless.
16. The more you try to argue with someone, the less likely you are to convince them of your perspective. The reason for this is that most arguments are emotional in nature. They come from someone’s values or self-perceptions being violated. Logic is only used to validate those pre-existing beliefs and values. It’s rarely about the objective or logical truth as much as it is repairing people’s worldviews. For any real debate to truly exist, both parties must be making an honest concession to put their egos aside and only deal with the data. This is rare, as anyone who’s spent any time on an internet forum could tell you.
17. The more choices you have, the less satisfied you are with each one. The old “paradox of choice.” Research shows that when we’re presented with more options, we become less satisfied with any particular one we go with. The theory is that when we have so many options, we have greater opportunity costs to selecting each particular one; therefore, we’re less happy with our decision.
18. The more convinced someone is that they’re right, the less they probably know. There’s a direct correlation between how open a person is to differing perspectives and how much that person actually knows about any given subject. Or as the philosopher Bertrand Russell once said: “The trouble with the world is that the stupid are cocksure and the intelligent are full of doubt.”
19. The only certainty is that nothing is ever certain. This realization almost made my head explode when I was 17.
20. The only constant is change. One of those little banal statements that feels really profound but doesn’t actually mean anything. But it’s still true!
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About the Author
Mark is the three-time #1 New York Times bestselling author of The Subtle Art of Not Giving a F*ck as well as other titles. His books have sold around 20 million copies, been translated into more than 65 languages, and reached number one in more than a dozen countries. In 2023, a feature film about his life and ideas was released worldwide by Universal Pictures.
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Mark is the three-time #1 New York Times bestselling author of The Subtle Art of Not Giving a F*ck, as well as other titles. His books have sold around 20 million copies, been translated into more than 65 languages, and reached number one in more than a dozen countries. In 2023, a feature film about his life and ideas was released worldwide by Universal Pictures.
Brain Games: 8 Philosophical Puzzles and Paradoxes
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Brian Duignan is a senior editor at Encyclopædia Britannica. His subject areas include philosophy, law, social science, politics, political theory, and religion.
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Plato and Aristotle both held that philosophy begins in wonder, by which they meant puzzlement or perplexity, and many philosophers after them have agreed. Ludwig Wittgenstein considered the aim of philosophy to be “to show the fly the way out of the fly bottle”—to liberate ourselves from the puzzles and paradoxes created by our own misunderstanding of language. His teacher, Bertrand Russell, remarked in a joking mood that “The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it.”
Whether paradox is the beginning or the end of philosophy, it has certainly stimulated a great deal of philosophical thinking, and many paradoxes have served to encapsulate important philosophical problems (many others have been exposed as fallacies).
The following list presents eight influential philosophical puzzles and paradoxes dating from ancient times to the present. Take a look and be perplexed.
The liar
Suppose someone tells you “I am lying.” If what she tells you is true, then she is lying, in which case what she tells you is false. On the other hand, if what she tells you is false, then she is not lying, in which case what she tells you is true. In short: if “I am lying” is true then it is false, and if it is false then it is true. The paradox arises for any sentence that says or implies of itself that it is false (the simplest example being “This sentence is false”). It is attributed to the ancient Greek seer Epimenides (fl. c. 6th century BCE), an inhabitant of Crete, who famously declared that “All Cretans are liars” (consider what follows if the declaration is true). The liar paradox is important in part because it creates severe difficulties for logically rigorous theories of truth; it was not adequately addressed (which is not to say solved) until the 20th century.
Zeno’s paradoxes
In the 5th century BCE, Zeno of Elea devised a number of paradoxes designed to show that reality is single (there is only one thing) and motionless, as his friend Parmenides had claimed. The paradoxes take the form of arguments in which the assumption of plurality (the existence of more than one thing) or motion are shown to lead to contradictions or absurdity. Here are two of the arguments: Against plurality: (A) Suppose that reality is plural. Then the number of things there are is only as many as the number of things there are (the number of things there are is neither more nor less than the number of things there are). If the number of things there are is only as many as the number of things there are, then the number of things there are is finite. (B) Suppose that reality is plural. Then there are at least two distinct things. Two things can be distinct only if there is a third thing between them (even if it is only air). It follows that there is a third thing that is distinct from the other two. But if the third thing is distinct, then there must be a fourth thing between it and the second (or first) thing. And so on to infinity. (C) Therefore, if reality is plural, it is finite and not finite, infinite and not infinite, a contradiction. Against motion: Suppose that there is motion. Suppose in particular that Achilles and a tortoise are moving around a track in a foot race, in which the tortoise has been given a modest lead. Naturally, Achilles is running faster than the tortoise. If Achilles is at point A and the tortoise at point B, then in order to catch the tortoise Achilles will have to traverse the interval AB. But in the time it takes Achilles to arrive at point B, the tortoise will have moved on (however slowly) to point C. Then in order to catch the tortoise, Achilles will have to traverse the interval BC. But in the time it takes him to arrive at point C, the tortoise will have moved on to point D, and so on for an infinite number of intervals. It follows that Achilles can never catch the tortoise, which is absurd. Zeno’s paradoxes have posed a serious challenge to theories of space, time, and infinity for more than 2,400 years, and for many of them there is still no general agreement about how they should be solved.
Sorites
Also called “the heap,” this paradox arises for any predicate (e.g., “… is a heap”, “… is bald”) whose application is, for whatever reason, not precisely defined. Consider a single grain of rice, which is not a heap. Adding one grain of rice to it will not create a heap. Likewise adding one grain of rice to two grains or three grains or four grains. In general, for any number N, if N grains does not constitute a heap, then N+1 grains also does not constitute a heap. (Similarly, if N grains does constitute a heap, then N-1 grains also constitutes a heap.) It follows that one can never create a heap of rice from something that is not a heap of rice by adding one grain at a time. But that is absurd. Among modern perspectives on the sorites paradox, one holds that we simply haven’t gotten around to deciding exactly what a heap is (the “lazy solution”); another asserts that such predicates are inherently vague, so any attempt to define them precisely is wrongheaded.
Buridan’s ass
Although it bears his name, the medieval philosopher Jean Buridan did not invent this paradox, which probably originated as a parody of his theory of free will, according to which human freedom consists in the ability to defer for further consideration a choice between two apparently equally good alternatives (the will is otherwise compelled to choose what appears to be the best). Imagine a hungry donkey who is placed between two equidistant and identical bales of hay. Assume that the surrounding environments on both sides are also identical. The donkey cannot choose between the two bales and so dies of hunger, which is absurd. The paradox was later thought to constitute a counterexample to Leibniz’s principle of sufficient reason, one version of which states that there is an explanation (in the sense of a reason or cause) for every contingent event. Whether the donkey chooses one bale or the other is a contingent event, but there is apparently no reason or cause to determine the donkey’s choice. Yet the donkey will not starve. Leibniz, for what it is worth, vehemently rejected the paradox, claiming that it was unrealistic.
The surprise test
A teacher announces to her class that there will be a surprise test sometime during the following week. The students begin to speculate about when it might occur, until one of them announces that there is no reason to worry, because a surprise test is impossible. The test cannot be given on Friday, she says, because by the end of the day on Thursday we would know that the test must be given the next day. Nor can the test be given on Thursday, she continues, because, given that we know that the test cannot be given on Friday, by the end of the day on Wednesday we would know that the test must be given the next day. And likewise for Wednesday, Tuesday, and Monday. The students spend a restful weekend not studying for the test, and they are all surprised when it is given on Wednesday. How could this happen? (There are various versions of the paradox; one of them, called the Hangman, concerns a condemned prisoner who is clever but ultimately overconfident.) The implications of the paradox are as yet unclear, and there is virtually no agreement about how it should be solved.
The lottery
You buy a lottery ticket, for no good reason. Indeed, you know that the chance that your ticket will win is at least 10 million to one, since at least 10 million tickets have been sold, as you learn later on the evening news, before the drawing (assume that the lottery is fair and that a winning ticket exists). So you are rationally justified in believing that your ticket will lose—in fact, you’d be crazy to believe that your ticket will win. Likewise, you are justified in believing that your friend Jane’s ticket will lose, that your uncle Harvey’s ticket will lose, that your dog Ralph’s ticket will lose, that the ticket bought by the guy ahead of you in line at the convenience store will lose, and so on for each ticket bought by anyone you know or don’t know. In general, for each ticket sold in the lottery, you are justified in believing: “That ticket will lose.” It follows that you are justified in believing that all tickets will lose, or (equivalently) that no ticket will win. But, of course, you know that one ticket will win. So you’re justified in believing what you know to be false (that no ticket will win). How can that be? The lottery constitutes an apparent counterexample to one version of a principle known as the deductive closure of justification: If one is justified in believing P and justified in believing Q, then one is justified in believing any proposition that follows deductively (necessarily) from P and Q. For example, if I am justified in believing that my lottery ticket is in the envelope (because I put it there), and if I am justified in believing that the envelope is in the paper shredder (because I put it there), then I am justified in believing that my lottery ticket is in the paper shredder. Since its introduction in the early 1960s, the lottery paradox has provoked much discussion of possible alternatives to the closure principle, as well as new theories of knowledge and belief that would retain the principle while avoiding its paradoxical consequences.
Meno’s problem
This ancient paradox is named for a character in Plato’s eponymous dialogue. Socrates and Meno are engaged in a conversation about the nature of virtue. Meno offers a series of suggestions, each of which Socrates shows to be inadequate. Socrates himself professes not to know what virtue is. How then, asks Meno, would you recognize it, if you ever encounter it? How would you see that a certain answer to the the question “What is virtue?” is correct, unless you already knew the correct answer? It seems to follow that no one ever learns anything by asking questions, which is implausible, if not absurd. Socrates’ solution is to suggest that basic elements of knowledge, enough to recognize a correct answer, can be “recollected” from a previous life, given the right kind of encouragement. As proof he shows how a slave boy can be prompted to solve geometrical problems, though he has never had instruction in geometry. Although the recollection theory is no longer a live option (almost no philosophers believe in reincarnation), Socrates’ assertion that knowledge is latent in each individual is now widely (though not universally) accepted, at least for some kinds of knowledge. It constitutes an answer to the modern form of Meno’s problem, which is: how do people successfully acquire certain rich systems of knowledge on the basis of little or no evidence or instruction? The paradigm case of such “learning” (there is debate about whether “learning” is the correct term) is first-language acquisition, in which very young (normal) children manage to acquire complex grammatical systems effortlessly, despite evidence that is completely inadequate and often downright misleading (the ungrammatical speech and erroneous instruction of adults). In this case, the answer, originally proposed by Noam Chomsky in the 1950s, is that the basic elements of the grammars of all human languages are innate, ultimately a genetic endowment reflecting the cognitive evolution of the human species.
Moore’s puzzle
Suppose you are sitting in a windowless room. It begins to rain outside. You have not heard a weather report, so you don’t know that it’s raining. So you don’t believe that it’s raining. Thus your friend McGillicuddy, who knows your situation, can say truly of you, “It’s raining, but MacIntosh doesn’t believe it is.” But if you, MacIntosh, were to say exactly the same thing to McGillicuddy—“It’s raining, but I don’t believe it is”—your friend would rightly think you’d lost your mind. Why, then, is the second sentence absurd? As G.E. Moore put it, “Why is it absurd for me to say something true about myself?” The problem Moore identified turned out to be profound. It helped to stimulate Wittgenstein’s later work on the nature of knowledge and certainty, and it even helped to give birth (in the 1950s) to a new field of philosophically inspired language study, pragmatics. I’ll leave you to ponder a solution.
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