Zeno’s Reductio ad Absurdum

Zeno was a student of Parmenides, and his paradoxes were crafted as logical weapons to defend Parmenides’ radical claim:

“All is One. Change, motion, and plurality are illusions.”

Zeno used paradoxes to show that if we believe in motion and multiplicity (like most people do), we end up with contradictions and absurdities — therefore, Parmenides must be right.

Zeno’s Goal: Reductio ad Absurdum

He used reductio ad absurdum: taking common beliefs (like “things move”) and showing they lead to impossible conclusions. The aim was to prove motion and plurality are impossible, and that only a single, unchanging “Being” exists.

The Most Famous: Achilles and the Tortoise

Paradox:

Achilles gives a tortoise a head start in a footrace. Achilles runs faster, but Zeno argues he will never catch up.

Why?

When Achilles reaches the tortoise’s starting point, the tortoise has moved a bit ahead.
When Achilles reaches that next point, the tortoise has again moved slightly forward.
This continues infinitely, so Achilles is always chasing — but never overtaking.

The Deeper Point:

Zeno’s argument hinges on the idea that space and time are infinitely divisible. If you divide the space Achilles must travel into an infinite number of steps, he can never complete them in finite time — even though in reality, we see people overtake others all the time.

Conclusion (Zeno): Motion is logically impossible.

Other Paradoxes

1. The Dichotomy Paradox

Before reaching any destination, you must get halfway there.
But before that, you must get halfway to halfway.
This goes on infinitely.
So, you can never start moving, let alone finish.

2. The Arrow Paradox

An arrow in flight is actually at rest at every single instant in time.
Time is made up of individual instants.
So, if the arrow is motionless at every instant, it’s not moving at all.

3. The Stadium

Imagine two rows of objects passing each other in opposite directions.
The time it takes for them to pass appears inconsistent depending on how you measure it, which challenges assumptions about relative motion and time.

What Was Zeno Really Getting At?

Zeno wasn’t stupid or denying our experience — he was pushing the limits of logic to expose contradictions in how people thought about space, time, and motion.
His paradoxes forced philosophers to think deeply about the nature of infinity, continuity, and the foundations of mathematics.

Legacy and Resolution

Later thinkers like Aristotle critiqued Zeno’s assumptions.
Modern calculus, developed by Newton and Leibniz, uses limits to resolve the paradoxes: it shows that the sum of an infinite series can be finite, allowing Achilles to overtake the tortoise.

But even with modern math, Zeno’s paradoxes still puzzle and inspire debate in physics, philosophy, and metaphysics.

Reductio ad Absurdum meaning

Reductio ad absurdum is Latin for “reduction to absurdity.”

It’s a way of arguing where you:

Assume something is true,
Then show that it leads to a ridiculous or impossible result,
So the original assumption must be false.

Example:
Zeno assumes that motion is real.
→ But then he shows that if motion were real, Achilles could never pass a tortoise.
→ That’s absurd.
→ So, motion must be an illusion.

It’s like saying: “If your idea leads to nonsense, your idea can’t be right.”

explain achilles and the tortoise as simple as possible. idk why this is so hard for me to understand

Totally fair — and honestly, you’re not alone. Zeno’s paradox trips up a lot of people, even smart ones, because it messes with your intuition using something that feels simple but hides deep logic.

Let’s break it down like you’re explaining it to a 5-year-old:

Imagine This:

A super fast guy (Achilles) is chasing a super slow turtle (the tortoise).
The turtle gets a little head start.
Achilles starts running.

Now, here’s the trick Zeno plays:

Achilles runs to the turtle’s starting spot.
But in that tiny bit of time, the turtle moves a tiny bit ahead.
Achilles runs to that new spot.
The turtle moved again — just a tiny bit.
Repeat… forever?

Zeno says:

“Since there are infinite little steps to catch up, Achilles never actually catches the turtle.”

But here’s the catch:

Zeno isn’t describing real life.
He’s pointing out a weird thing about dividing space and time into infinite pieces.

What he’s really saying is:

“If you believe motion is just an infinite number of tiny steps, then things start to sound wrong.”

But we now know:

Infinite steps can still add up to a real, finite distance.
(That’s what calculus explains.)

So if you’re confused…

That’s okay. Zeno wants to confuse you. That was his whole vibe — break your brain, so you start asking bigger questions about what’s real.

If you’d like, I can turn this into a single cartoon strip-style diagram that explains it visually. Sometimes that helps everything click. Want that?

so… as a thought experiment, even if a really fat guy who gets a head start is being chased by a really fast guy, under zeno’s assumption, the fat guy will always be ahead of the fast guy because the fat guy already technically moved through space and time before the fast guy

Yes — you totally get it now.

That’s exactly Zeno’s weird logic:

If someone gets a head start, then by the time the faster person reaches the first spot, the slower person has already moved a bit ahead — and this happens forever.

So under Zeno’s assumptions about space and time being infinitely divisible, the fat guy (tortoise) would always stay slightly ahead of the fast guy (Achilles) — even if it’s just by a hair.

But remember:

This is just a thought experiment. Zeno knows the fast guy wins in real life. He’s just saying:

“If motion means crossing infinite points, how do you ever finish moving?”

It’s a way of saying:

“Maybe something about how we understand motion, space, or infinity is flawed.”

And that’s what sparked 2,000 years of debate… until calculus came along and said:

“Yeah, infinite steps are fine — they can add up to a finite distance.”

So yes:
Under Zeno’s logic, the fat guy stays ahead. But in real life, Achilles smokes him.

so this is why the ionian school makes more sense to me. they deal with real physics. the eleatics were more metaphysical which is harder to understand. without the metaphysical conversations, though, breakthroughs wouldnt have occurred