Achilles paradox, in logic, an argument attributed to the 5th-century-bce Greek philosopher Zeno, and one of his four paradoxes described by Aristotle in the treatise Physics. … The paradox
concerns a race between the fleet-footed Achilles and a slow-moving tortoise.
What are Zeno’s 4 paradoxes?
Zeno’s paradoxes are a set of four
paradoxes dealing with counterintuitive aspects of continuous space and time
. can converge, so that the infinite number of “half-steps” needed is balanced by the increasingly short amount of time needed to traverse the distances.
What is the point of Zeno’s paradox?
Thus Plato has Zeno say the purpose of the paradoxes “is to show that
their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one
.” Plato has Socrates claim that Zeno and Parmenides were essentially arguing exactly the same point.
What is the race paradox?
The paradoxes of race/ethnicity are that: it is
a common-sense idea that everyone under- stands, yet is impossible to define
; it is a universal concept that only has local meaning; and it is the only way we can describe certain social and political inequalities, but its very use reproduces these divisions.
What is Zeno’s paradox simplified?
In its simplest form, Zeno’s Paradox says
that two objects can never touch
. The idea is that if one object (say a ball) is stationary and the other is set in motion approaching it that the moving ball must pass the halfway point before reaching the stationary ball.
What is wrong with Zeno’s paradox?
No matter how small a distance is still left, she must travel half of it, and then half of what’s still remaining, and so on, ad infinitum. With an infinite number of steps required to get there, clearly she can never complete the journey. And hence, Zeno states,
motion is impossible
: Zeno’s paradox.
What is the most famous paradox?
Russell’s paradox
is the most famous of the logical or set-theoretical paradoxes. Also known as the Russell-Zermelo paradox, the paradox arises within naïve set theory by considering the set of all sets that are not members of themselves.
What are Zeno’s paradoxes supposed to prove?
Zeno’s Arrow and Stadium paradoxes demonstrate that
the concept of discontinuous change is paradoxical
. Because both continuous and discontinuous change are paradoxical, so is any change. Eudemus, a student of Aristotle, offered another interpretation.
What was Zeno trying to prove?
First, Zeno sought to
defend Parmenides by attacking his critics
. Parmenides rejected pluralism and the reality of any kind of change: for him all was one indivisible, unchanging reality, and any appearances to the contrary were illusions, to be dispelled by reason and revelation.
How do you identify a paradox?
- Here are the rules: Ignore all rules.
- The second sentence is false. The first sentence is true.
- I only message those who do not message.
What is the first known paradox?
The first known paradoxes were given by
the ancient Greek School of philosophy at Elea
. Parmenides (c. 515-c. 450 B.C.E.) had held that motion is an illusion and that existence is one indivisible whole.
Why is Achilles paradox wrong?
Achilles’ task seems
impossible
because he “would have to do an infinite number of ‘things’ in a finite amount of time,” notes Mazur, referring to the number of gaps the hero has to close. But not all infinities are created the same. There are divergent series and convergent series.
Who is the slowest Achilles or tortoise?
The tortoise
goes 0.8 meters per second. Pretty fast—for a tortoise, that is; Achilles is 10 times as fast, i.e., he goes 8 meters per second!
Is a paradox true?
A paradox is a
logically self-contradictory statement
or a statement that runs contrary to one’s expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
How many paradox are there?
Read on to see our favorite Catch-22s from Wikipedia’s epic list of
more than 200 types of paradoxes
.
What is the mistake in Zeno’s logic?
The faulty logic in Zeno’s argument is often seen to be the
assumption that the sum of an infinite number of numbers is always infinite
, when in fact, an infinite sum, for instance, 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 +…., can be mathematically shown to be equal to a finite number, or in this case, equal to 2.
