Actual Versus Potential Infinity- extension Oct. 22,2013

Actual versus Potential Infinity

Extension: Oct. 22, 2013

The Ancient Greeks generally referred to infinity as “formless, characterless, indefinite, indeterminate, chaotic, and unintelligible” (Dowden). At the time, the term was perceived negatively because it was vague and it had no clear criteria to differentiate finite from infinite. Among various philosophers, Aristotle was one who made an attempt to this confusion by creating terms for infinity, “actual infinite” and “potential infinite” (Dowden). Aristotle developed this clarification through Zeno’s paradoxes about infinite divisibility. His observations led him to defining actual infinity as “an endlessness fully realized at some point in time” (Daring). Furthermore, he defined potential infinity as something that could be “manifested in nature [and could be used in a technical sense]” (Dowden). For example, a potential swimmer can learn to become an actual swimmer, but a potential infinity cannot become an actual infinity. According to Dowden, Aristotle argued, “all the problems involving reasoning with infinity are really problems of improperly applying the incoherent concept of actual infinity instead of the coherent concept of potential infinity” (Dowden). During that era, viewing infinity through these terms was a way to comprehend Zeno’s paradoxical statements such as the Dichotomy paradox. Within the Dichotomy paradox, suggesting that a fixed destination could be infinitely divided, conveys how actual and potential infinity creates a contradicting statement (Waterfield). However, Zeno made the mistake, according to Aristotle, of supposing that “this infinite process needs completing when it really doesn’t; the finitely long path from start to finish exists undivided… and it is the mathematician who is demanding the completion of such a process…Without that concept of a completed infinite process there is no paradox” (Dowden).

Even though Aristotle promoted the belief that “the idea of the actual infinite−of that whose infinitude presents itself all at once−was close to a contradiction in terms…” (Moore, 40) various philosophers and theorist contradicted Aristotle’s idea. Archimedes, Duns Scotus, William of Ockham, Gregory of Rimini, and Leibniz each had there own ideas and questions concerning Aristotle theory (Dowden). Therefore, it almost seems impossible to define infinity because there are various perspectives that it can be viewed from.

Through looking at Aristotle connotations of infinity, it shows how there can be another dimension to defining infinity among various other theories that we have already studied. Moreover, do you think Aristotle’s actual and potential infinity would make a difference in how we categorized the manifestations that we produced as a class?

Works Cited:

Darling, David. "Infinity." Encyclopedia of Science. The Worlds of David Darling, n.d. Web. 01 Nov. 

            2013.

Dowden, Bradley. "The Infinite." Internet Encyclopedia of Philosophy. ISSN 2161-0002, 6 Sept.           

           2013. Web. 28 Oct. 2013.

Moore, A. W. The Infinite. Second edition, New York: Routledge, 2001. Print. 

Waterfield, Robin, trans. Aristotle Physics. Comp. David Bostock. London: Oxford UP, 1996. Print.

           ISBN # 0-1995-4028-4.