I need to make an argument map for Achilles and the Tortoise with the conclusion at the top and premises and undisclosed premises coming out of it 5-10nodes. Im stuck and dont know how to go about it if anyone can help it would mean alot. This is an example of how I have to do it.


  • Regarding your example: anyone who talks about brain-in-a-vat without mentioning the burden of proof, explanatory power or parsimony (Occam's razor) is not someone I'd trust when it comes to philosophy. Those are the main reasons people reject brain-in-a-vat. Most people (with some philosophy exposure) would trivially agree that we have no evidence against it, so it's questionable to focus on that instead of focusing on why we shouldn't reject things we don't have evidence for (but for an Intro to Philosophy exercise, that focus might make sense).
    – NotThatGuy
    Commented Feb 6 at 20:25

2 Answers 2


WHAT I HAVE RN BUT I FEEL IS WRONG 1. Premise 1: Achilles and the Tortoise engage in a race. 2. Premise 2: The Tortoise is given a head start. 3. Reason (Green Bracket): The Tortoise covers a fraction of the distance Achilles must run. - Claim: The Tortoise covers 1/10th of the distance. - Claim: Achilles is faster and covers the remaining 9/10th of the distance. 4. Objection (Red Bracket): Achilles must cover an infinite number of smaller distances to reach the Tortoise. - Claim: Before Achilles reaches the Tortoise, he must cover half of the remaining distance. - Claim: This process repeats infinitely, making it impossible for Achilles to overtake the Tortoise. 5. Implicit Premise: The infinite division of distance leads to an infinite series. - Claim: An infinite series cannot be completed. 6. Conclusion: The paradox challenges the possibility of completing an infinite number of tasks.


Here is how to proceed.

Prepare a chart with horizontal distance travelled on the x (horizontal) axis and elapsed time on the y (vertical) axis. Mark the tortoise's position with little dots and the hare's position with little crosses.

The tortoise starts at the starting line which is at the intersection of the x and y axies. The finish line point is a vertical line somewhere to his right. He travels at a small speed and so his world line is an almost vertical line which does not cross over the finish line for a long time.

The hare doesn't start until the tortoise has had a chance to get a head start. He doesn't leave the starting line (vertical line through the x, y origin point) until sometime after the tortoise did. So the hare's world line departs from the origin line somewhere up the time axis, but since he is traveling faster (farther per unit time) than the tortoise his his world line is flatter on the chart and these two world lines will inevitably cross, at which point the hare will overtake the tortoise.

If the hare is fast enough and the tortoise's head start is brief enough, the hare will overtake the tortoise before the finish line and win the race.

The inevitability of the crossing point is a simple fact of geometry and no infinite series is needed to establish that fact!

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