Zeno’s Paradoxes

Zeno of Elea

Zeno of Elea was a mathematician and a Greek philosopher whom Aristotle referred as the inventor of dialectic. He was born in 495BCE and died on 430BCE (Abelard, n.d.). Zeno is famous for his invention of some ingenious paradoxes. He advocated against the commonsense assumption that there are various things by illustrating how it resulted in a contradiction (Palmer, 2017). I think Zeno developed his famous mysteries to defend the paradoxical monism of his Eleatic mentor, Parmenides. His arguments problematize the application of quantitative conceptions to physical bodies; thus, they may have originated in reflection on Pythagorean efforts to adopt mathematical philosophies to the natural world.

Zeno’s Paradoxes and Reduction ad Absurdum

Zeno’s paradoxes were one of the examples of a method proof called “reduction ad absurdum” which was a dialectical syllogism or proof by contradiction (Palmer, 2017). He had devised arguments against both motion and multiplicity although they are variations of one case applying to time or space. Zeno argued that any quantity of space must either be divided ad infinitum or be composed of terminal indivisible units. The amount of time must, therefore, have magnitude if it is comprised of indivisible units resulting in contradiction of scale which cannot be divided (Palmer, 2017). However, if it divisible ad infinitum, I think an individual can also encounter a different opposition of supposing an infinite number of parts can be added to create a finite sum.

Zeno’s Paradox Variations

Zeno had 40 versions of the paradox (Palmer, 2017). For example, in the arrow paradox, he argued that if it is fired from a bow, then it is either where it is or where it is not. If it moves in its space, then it must be still, and if it runs where it is not, then it cannot be there (Abelard, n.d.). Therefore, he meant that the arrow could not move in any situation. The dichotomy paradox, on the other hand, illustrates that a moving object must get halfway before traveling a certain distance. The sequence continues to infinity thus demonstrating that an infinite number of points must integrate, which is logically impossible in a finite period hence the range will never be covered.

Criticism of Zeno’s Paradoxes

I disagree with Zeno’s ideas and disprove some of his versions such as the dichotomy paradox. In my thought, as the distance decreases, the time required to cover that length also reduces. Additionally, some scholars such as Kant, Hegel, Leibniz, and Hume have also offered solutions to Zeno’s paradoxes (Palmer, 2017). The paradox may have a false assumption that it is impossible to complete an infinite number of discrete tasks in finite time but Zeno’s paradoxes have continued to stimulate and clown thinkers and learners.

Zeno’s Arguments and Their Purpose

Zeno’s arguments had a specific structure and purpose, opposing the reasonable assumption that there are a variety of things. The general pattern of his argumentation was: if there are many things, these must be both F and not -F; but it cannot be both F and -F (Palmer, 2017). The description has inspired various scholars to attempt to accommodate the real paradoxes within a unified architecture that would have provided the plan for Zeno’s original book. However, if he wrote only one argument, none of these attempts have proved convincing. His arguments challenged the conventional assumptions about plurality and motion. His ideas are paradoxes and opinions for conclusions contrary to what people may ordinarily believe.

Contradiction and Contradictory Magnitude

Zeno also designed some ideas to illustrate how the claim that there are many things resulted in contradiction. He demonstrated that if there are many things, they are both large and small: large to be unlimited in magnitude, and little to the extent of having no significance (Palmer, 2017). The argument shows that no object can exist without either size or thickness as what would be added or eliminated would be non-existence. Zeno explains this as each of the various things has magnitude and is infinite (Abelard, n.d.). Therefore, if there are many things, they must be large or small as Zeno concludes that ”none have a magnitude because each of the many is the same as itself and one.”

Paradox of the Millet Seed and Paradox of Place

He also argues, in the paradox of the millet seed, that every portion of millet seed whatsoever produces a sound (Palmer, 2017). In my thought, this argument is not reliable and is incorrect. Zeno could have engaged in a fictional discussion with Protagoras where he argues that a large number of millet seeds would produce a sound and every seed should produce its sound. The evidence suggests that Zeno anticipated reasoning that related to the paradoxes that were invented more than a century later after his argument (Abelard, n.d.).

Additionally, Zeno argues in the paradox of place that ”if a place is something, it will be in something.” He illustrates that if a site is something, then it must be in something and the same reasoning applies and continues and each successive place to infinity (Palmer, 2017). Therefore, according to his argument, if there is such a thing in the area, there must be limitless places everywhere, which is illogical. Zeno’s opinion could have formed part of a more elaborate argument against the perception that there are a variety of things thus there is somewhere in some place. However, this was an assumption, therefore, should not be believed.

Conclusion

In conclusion, Zeno’s arguments or paradoxes seems illogical. His puzzles, however, can contribute to the development of logical and mathematical rigor through the development of concepts of continuity and infinity. The paradoxes are generated by the assumption that it is not possible to touch infinitely variety of points in a finite amount of time. The solution could be to deny that space is infinitely divisible. Zeno also advocated against his actual opponents, Pythagoreans, who believed in a plurality composed of numbers that were extended units.

Reference

Abelard, P. (n.d.). Zeno of Elea. Retrieved from The Basics of Philosophy: https://www.philosophybasics.com/philosophers_zeno_elea.html

Palmer, J. (2017, December 21). Zeno of Elea. (E. N. Zalta, Editor) Retrieved from Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/archives/spr2017/entries/zeno-elea/