The sorites paradox is the paradox of the heap, which is that if you have heap of grain and remove one grain, it is still a heap. If you continue to remove the grains one at a time, each time still leaving a heap, then one grain of sand is still a heap. Zeno’s paradox of Achilles and the Turtle says that even though Achilles moves forward, so does the turtle. Each time the turtle moves forward, Achilles moves forward to the turtle’s previous position. The turtle moves forward ½ of the previous distance, each time cutting the distance moved. However, even though Achilles gets closer and closer, he will never catch the turtle. It is a paradox because even though the representational logic appears to hold true, it defies common sense.
One might propose that Achilles could simply increase his speed to catch and surpass the tortoise. However, this paradox is not about speed, but about distance traveled. The paradox assumes speed as constant for both the Tortoise and Achilles. If this were real life, Achilles could simply speed up, but that is not the point of the paradox. The paradox is not about Achilles and the tortoise, it is only an illustration of a mathematical concept. In order to simulate the mathematical concept, speed must be assumed constant.
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"Zeno’s Paradox Of Achilles And The Tortoise".
The argument goes as such:
P1: Achilles must travel across an infinite number of distance divisions to reach the tortoise.
P2: Achilles cannot travel across an infinite number of divisions.
C: Achilles can never catch and pass the tortoise.
Paradoxes are useful for expanding our understanding of something because they use something with which we are familiar and can relate to in our world. They then make us look at things in a different way to gain a better understanding. They help to illustrate abstract concepts with concrete imagery. Concrete imagery is easier to relate to than abstract imagery. Paradoxes make complex concepts easier to grasp.
