The Chicken and the Egg
— J. Chr. de Vries
Let us speak of the paradox.
Everything I say is a lie.
If I say that the chicken came before the egg because the chicken must exist first to lay an egg, then that is a lie. After all, the chicken is born from an egg. But an egg, in turn, must first be laid by a chicken. Voilà, a vicious circle — or, a paradox.
Zeno of Elea is famous for his paradoxes, though they are actually aporia.
- A paradox is a situation that can exist in reality but lacks a strictly logical explanation within the framework of the ideal model used.
- An aporia is a logical deduction from a particular theory that cannot exist in reality.
Zeno’s aporia (or apory) of Achilles and the Tortoise goes as follows:
The tortoise challenges Achilles to a hundred-meter race and claims he will win, provided Achilles gives him a ten-meter head start. “Then you will definitely lose,” the tortoise declares. Achilles rolls his eyes and asks the tortoise how that could possibly be true since the demigod is far faster than the slow reptile. The tortoise explains:
“Every time you cover a meter, I will have covered, say, a centimeter. So you will have to cover another extra distance. You will cover that extra distance much faster than I will, but in the meantime, I will have advanced a little further. This goes on infinitely, so you can never catch up to me, and that is why I win the race.”
Achilles concedes defeat.
This apory can be easily refuted. The tortoise’s logical error lies in the premise that the subdivision of the lead can indeed be divided into an infinite number of infinitely small units. The number of so-called irrational numbers (those are the numbers after the decimal point) between, for instance, 0 and 1, or 1 and 2, is infinite:
0.000…1 — 0.000…2 — 0.000…3 — etc.
However, the difference between 0 and 1, or 1 and 2, is a finite number, namely: 1. Achilles overtakes the tortoise with ease.
My father had his own way of refuting the vicious circle of the Chicken and the Egg. When I confronted him with this paradox, he said: “Show me the chicken, and show me the egg, and I’ll tell you which came first.”
The paradox is often defined as an ‘apparent contradiction’. Aristotle and other thinkers from Greek antiquity paid much attention to it. Most paradoxes are, indeed, resolved. The question remains whether truly insoluble paradoxes exist. For example, there is the Grandfather Paradox, a fictional paradox from science fiction literature: “A time traveler goes back in time and kills his grandfather before the latter has conceived a child. At that moment, the time traveler can no longer exist and therefore cannot kill his grandfather.” However, if time travel is impossible, then the paradox dissolves.
If everything I say is a lie, then this entire story is a lie. Zeno has formulated no aporia, my father never made his statement about the chicken and the egg, and the Grandfather Paradox does not exist. If all of this is true, then the claim that I always lie is true — except for the claim itself, which is then false. But if the story above is true, then the claim is false. My statement is thus true if it is not true.
Now, I am left with one final argument to close the vicious circle. Paradoxes like the Grandfather Paradox and Zeno’s apory can only exist as contradictions in a fictional world; they dissolve in reality. Other paradoxes, such as the Liar Paradox (my opening sentence), dissolve in fiction and can only exist as contradictions in reality. Fiction and reality form an unbreakable paradox. Our dreams are a magnificent example of this.
— J. Chr. de Vries, Loosduinen, December 25, 2024