What the Tortoise Said to Achilles

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In summary, "What the Tortoise Said to Achilles" by Lewis Carroll is a short dialogue between Achilles and a tortoise about the nature of logic and the rules of inference. The tortoise argues that in order to accept any logical proposition as true, one must first accept the rules of logic as true. This leads to an infinite regress of accepting rules, which the tortoise sees as a problem. Some sources refer to this as the Carroll paradox or the Paradox of Inference.
  • #1
murshid_islam
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"What the Tortoise Said to Achilles"

"What the Tortoise Said to Achilles" by Lewis Carroll: http://www.ditext.com/carroll/tortoise.html

What exactly is wrong with the logic here? Is anything wrong at all?
 
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  • #2


No error. It is just noting that in order to accept any logical proposition as true, you must first accept the "rules of logic" as true. And, in order to do that, you must accept the rules used to construct those rules, etc.

That is why mathematical logic (I can't speak for philosophers) always starts with "given" rules and axioms.
 
  • #3


Also see the Wikipedia article on this topic.
 
  • #4


I don't understand what makes this story paradoxical. Can anyone enlighten me as to where there is a contradiction or otherwise?
 
  • #5


I see nowhere any mention of "paradox". Where did you get the idea that the story was "paradoxical"?
 
  • #6


Wikipedia refers to it as the Carroll paradox. It is included in Micheal Clark's book Paradoxes from A to Z as the Paradox of Inference. Thus I get the idea that the story was paradoxical.
 

1. What is the "Tortoise and Achilles" paradox?

The "Tortoise and Achilles" paradox is a thought experiment created by philosopher Lewis Carroll in his 1895 paper "What the Tortoise Said to Achilles." It explores the concept of infinite regress, where a statement or argument leads to an infinite chain of reasoning.

2. How does the paradox work?

In the paradox, the Tortoise challenges Achilles to a race, with the condition that Achilles must give the Tortoise a head start. However, as Achilles reaches the point where the Tortoise started, the Tortoise has moved ahead slightly. This process repeats infinitely, making it impossible for Achilles to ever catch up to the Tortoise.

3. What is the significance of this paradox?

The paradox highlights the concept of infinite regress and the limitations of human logic. It shows that even seemingly simple statements or arguments can lead to an infinite chain of reasoning, making it impossible to fully comprehend or prove.

4. What are some real-life examples of this paradox?

One real-life example of this paradox is Zeno's Dichotomy paradox, where the act of walking an infinite distance is broken down into infinitely smaller distances, making it impossible to ever reach the destination. Another example is the "chicken or the egg" dilemma, where the question of which came first leads to an infinite regression of causation.

5. How is this paradox relevant in modern science?

This paradox is relevant in modern science as it challenges the concept of causality and the limitations of our understanding of the universe. It also raises questions about the validity of mathematical proofs and the use of logic in scientific theories.

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