Paradoxical Perplexities Trivia Quiz

Answer: Parmenides

Zeno of Elea was a pupil of the philosopher Parmenides. His paradoxes were designed to defend Parmenides' belief that reality is unchanging and that motion and change are illusions. By showing that everyday ideas about motion seemed to lead to logical contradictions, Zeno hoped to support his teacher's philosophy.

Although modern mathematics provides ways to resolve many of the paradoxes, they remain influential because they challenged later thinkers to examine the nature of infinity, space and motion.

Answer: You must first reach the halfway point

To reach any destination, you must first travel half the distance. Before you can do that, you must reach half of the halfway point, and so on. Zeno argued that because there are always more halfway points, a journey can never be completed.

It raises the question of whether motion is possible if a journey can be divided into infinitely many smaller steps. It has played an important role in discussions about infinity, mathematics and philosophy.

Modern mathematics shows that an infinite series of ever-smaller distances can still add up to a finite distance, allowing the journey to be completed.

Answer: False

Imagine an arrow flying through the air. At any single instant, it occupies one position. Zeno argued that if the arrow is at rest at every instant, it cannot truly be moving.

This argument examines the relationship between time and motion. It continues to be studied by philosophers and mathematicians interested in the nature of change.

Modern physics and mathematics treat motion as something that happens over intervals of time rather than at a single instant, so the arrow can still be moving.

Answer: Achilles and the Tortoise

In this paradox, the fast runner Achilles races a tortoise that has been given a head start. Each time Achilles reaches the tortoise's previous position, it has moved a little farther ahead. Zeno used this example to question whether motion is really possible.

The idea of dividing time and distance into infinitely many parts is explored in this paradox. It remains one of Zeno's best-known arguments.

Mathematics, particularly calculus, now shows that an infinite series can have a finite total, so Achilles eventually overtakes the tortoise.

Answer: A logical contradiction

This paradox describes three rows of objects moving past one another. Zeno argued that comparing their movements leads to conflicting results about time and distance. He used it to challenge the idea of motion.

Consider three rows of equal objects. One row is stationary while the other two move in opposite directions at the same speed. Zeno claimed this creates a contradiction, as one moving row passes twice as many objects in the stationary row, as in the other moving row in the same time, which he used to argue against the reality of motion.

Most philosophers agree that the paradox relies on mistaken assumptions about time and relative motion, so it is no longer regarded as a true contradiction.

Answer: One grain of millet seems silent, while a whole bushel makes a noise

A single grain of millet makes no sound when it falls, but a bushel of grain does. Zeno asked how adding together grains that each make no sound could suddenly produce a noise.

Unlike Zeno's other arguments, this one is sometimes considered more of an observation about perception than a true logical paradox. Aristotle himself said Zeno's argument on this point 'is not correct'. Just because the observer cannot hear the sound, that does not mean there is no sound produced, just that its volume is too low to be audible.

Modern science points out that many tiny sounds can combine to produce one that is loud enough for us to hear.

Answer: A place

Everything exists in a place, but where does that place exist? If every place must also be in another place, the chain never ends. Zeno used this argument to question the nature of place itself.

Aristotle argued that not everything needs to exist in a place; only physical bodies do. The paradox became an early example of infinite regress reasoning, but most philosophers now reject Zeno's conclusion.

Answer: If things are made of infinitely many parts, they may be infinitely large

Zeno argued that if an object is made of infinitely many parts with size, the whole object would also have to be infinitely large. He used this argument to question whether many separate things can exist.

It challenges the idea that objects can be divided endlessly without creating contradictions. The argument forms part of Zeno's case against plurality.

Mathematics now distinguishes between infinite division and physical size, avoiding the contradiction Zeno described.

Answer: No size

What if the smallest parts of an object have no size at all? Zeno argued that adding together parts with no size should still produce something with no size. This creates a contradiction with the objects we see around us.

This argument complements the 'Unlimited Size' paradox to create a double bind, because if the ultimate parts of things have size, the whole is infinitely large; if they have no size, the whole has no size either. Either conclusion seems impossible.

Modern mathematics and physics do not describe objects as being built from dimensionless parts in the way Zeno imagined.

Answer: Similar and dissimilar

This argument asks whether many things can be alike and different at the same time. Zeno claimed that if many things exist, they must be both similar and dissimilar. He used the contradiction to challenge the idea of plurality.

It highlights the difficulties that arise when describing many separate things. The argument forms part of Zeno's wider case against plurality and the nature of reality.

Later philosophers argued that things can be similar in one respect and different in another, so there is no contradiction.