Philosophy - 750 words essay (please read all the attached files)

Write an essay of about 750 words, double-spaced, Time New Roman 12.

Structure your essay in response to the all the questions below in the same sequence.

This essay is not looking for your opinion, but please justify your argument.

Introduction. What is a paradox? Briefly characterize our working notion of “paradox”. What is a strict (logical) paradox? What is a “paradoxical” claim, or philosophical “puzzle”?

Part A. On paradoxes of the infinite. Explain, succinctly, how Zeno’s paradox of motion is formulated. Explain, in your own terms, Zeno’s argument that motion is impossible. Why do we face a paradox if the argument works?

Part B. On Cantor’s notion of the “transfinite”. The mathematician Georg Cantor proved that:

the number N of “natural numbers” (0, 1, 2, 3, ... ) is less than

the number R of “points” on the “real line” between 0 and 1. Yet these numbers, N and R, are both “infinite” or “transfinite” measures of the size or “cardinality” of, respectively, the set of “natural” numbers and the set of “real” numbers. While Cantor’s mathematics itself is beyond the scope of our course, many philosophers hold that Cantor’s results show that Zeno’s “paradox” of motion is misconceived, so there is no genuine paradox. How does this critique strike you? (In the Sorensen text: Cantor’s ideas are addressed along the way, in relation to different problems, on pages 54 (hypertasks), 57 (infinities), 317 (continuity, the calculus), 322 (set theory, cardinality of sets), 345 (rule-following as in counting). Draw on Sorensen’s observations together with Lectures and Discussion sections.)

Part C. On the Trolley Problem. Judith Thomson assessed a moral dilemma for the “trolley” case described in her classic article. How do you respond, intuitively, to this dilemma? If you were able to direct the trolley, what do you think you would choose to do? Do you think the Trolley “dilemma” constitutes a type of philosophical “paradox”? (Though much has been written, the text for your essay is Judith Jarvis Thomson, “The Trolley Problem”. Focus your discussion only on this essay.)