As a kid I was fascinated by paradoxes and would daydream about them until my mind brought me back to skateboarding. In fact, I used to think solving a paradox was the primary job of a philosopher. Now that I’m older and I have kids, I sometimes like to tease them with variations of classical paradoxes that maybe I don’t get quite right.
For example, my 5 year old son loves chocolate milk. He told us that he can drink all the chocolate milk in the world–a serious boast of beverage omnipotence. He would use it as a meal substitute if he had it his way. Playing off his all-powerful claims, during dinner I asked the kids if Stuart could pour a glass of chocolate milk so big that even he couldn’t drink entirely. Quickly they all started developing wild scenarios of filling up the bathtub and giving him a straw or his open mouth at the bottom of a waterslide that has been converted to a chocolate milk delivery system.
The dilemma here is a boy who can drink any quantity of chocolate milk given to him coupled with an ever-bigger glass of chocolate milk. If both are true, then it is a paradox of infinite regress. The truth, however, is that my son is a bit of a lightweight when it comes to competitive milk drinking. After about 8 ounces he taps out and is off to play.
What Good Is A Paradox?
There are different types of paradoxes (you can read more about them on Wikipedia) but the way I’ve been explaining the definition to my kids is: a predicament or statement that is apperantly true but seems impossible because of opposing facts or contradictions. So what is the point of talking about a paradox? Paradoxes are especially great for kids because they can be interesting, silly and thought-provoking all at the same time. More importantly, picking them apart can help them discover unstated assumptions or flaws in what we think we know.
Here are a few activities that will introduce your kids to paradoxes.
Funny Sayings
The following are sayings that include a paradox within them. Read them to your kids and ask two questions for each: 1) what is the contradiction, and 2) What are they really trying to say? I added some hints to the first two. Have your kids give their own interpretations. Can you think of any other similar sayings like these?
| Saying | Contradiction | Whadya Mean? |
|---|---|---|
| “Nobody goes to that restaurant because it’s too crowded.” | How can it be too crowded if nobody goes? | Nobody who wants to wait for their food goes to that restaurant. |
| “Hey! You shut your mouth when you’re talking to me!” | How can you talk with a “shut” mouth? | Well, maybe this means “don’t talk like that to me.” |
| “Don’t go near the water until you learn how to swim.” | ||
| “I can’t believe she wrote such a terrible article. She doesn’t know how to write.” |
Circular Impossibilities
There is also a class of paradoxes that make a statement then provide a case which seems to fit but is logically impossible. See how your kids explain what is going on with each of the following. My kids especially like the Pinocchio paradox.
| Paradox | Logical Problem |
|---|---|
| A bullet which can shoot through any barrier hits armor which nothing can penetrate. Is there any way out of this? | Both the bullet and the armor make an absolute claim that seems to contradict the other’s claim. So one of the claims must be false or the scenario is logically impossible. |
| Can God create a rock so heavy that even he cannot lift?1 | This gets at God being all-powerful where he can create all things and also lift all things. So is God lacking in the all-powerful or the lifting abilities? Or is this just another logical impossibility? |
| Pinocchio says, “My nose grows now.”2 | If his nose starts growing then what he says is true. But his nose only grows when he lies. So this can’t be. But if his nose doesn’t start growing, then he has lied. And if he has lied, his nose would have grown. Is there any way out of this paradox? |
| In a village, the barber shaves everyone who does not shave themself, but no one else. Who shaves the barber?3 |
2. The Pinocchio paradox was proposed in February 2001 by 11-year-old Veronique Eldridge-Smith.
3. The Barber’s Paradox is attributed to Bertrand Russell in 1901 and is also known as Russell’s paradox.
The Ship Of Theseus
My favorite paradox is found in the story of the Ship of Theseus. The questions this story raises have to do with the philosophy of identity or sameness. Read with your kids the description of Theseus’ ship as told by the philosopher Plutarch.
The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.
After reading this, ask your kids to summarize the question. Hint: After the old planks were replaced, is this the same ship that Theseus and the youth of Athens sailed to fight great battles?
Let’s expand on the details a little more for this exercise. Assume that the mast, sails and hull have all been replaced over time but all match the original specifications. Is this the same ship?
Here’s the activity:
- Have your kids draw a picture of a ship–complete with mast, sail, oars or whatever else seems fitting to them. Give the ship a name.
- On the back or on another piece of paper, have them list all the materials that would go into constructing their ship. Have them include at least 5 things but they don’t need to go crazy with listing the details (e.g. sail, mast, hull, planks, nails, canons, anchor, rudder, rope).
- Go through each item listed. Consider the importance of the item to the identity of the ship as a whole. Now classify each item by writing next to it either ‘low’, ‘medium’ or ‘high’.
- Starting with the lows, imagine that these items are all replaced with a newer and updated version. Does the ship remain the same? Move up to the mediums and then the highs. The goal is to determine at what point the ship is no longer the same ship. Is it when the lows and mediums are replaced? Do you make it up to some of the highs? Or is it still the same ship when everything is replaced?
- If your kids believe that it remains the same ship even when everything is replaced, what is it beyond the parts that gives it identity? Is it the name it was given? Is it its history–battles or journeys it’s been a part of?
- Imagine that all the old pieces that had been replaced on your ship were saved in a warehouse and then re-assembled. Now there are two ships. Which ship is yours? Are they both your ship?
If your kids are like mine, they will be quick to agree that the ship is not the same as the old reassembled ship. But let them consider themselves as a comparison. They are very different from their 5 year old self. Most of the cells in their body have long since been replaced by new ones. And it’s almost assured that their personalities have changed. Are they the same person as their 5 year old self?
The point of all this is to explore what it means to be the same–specifically the same over time. To explore a little more on identity and sameness, see 5 Things Kids Should Consider About Who They Are.
Hopefully these activities help your kids see value in pushing ideas to their edges to see where they fall apart. Evaluating a paradox can help clear up ambiguous language or reveal logical flaws. The philosopher Søren Kierkegaard said that the paradox is the “passion of thought” and to study them is “to want to discover something that thought itself cannot think.”
