ESSAY I: On philosophical paradoxes Write an essay of about 3 pages, or 750 words. (Printed in double-spaced format.) Structure your essay in response to the specific questions below. Your TA will instruct you on how to turn in your essay (in electronic or hard copy, etc.). First: What is a paradox, i.e., a strict (logical) paradox? What is a “paradoxical” proposition, or philosophical “puzzle”? How does a strict paradox differ from such a puzzle? Second: By way of example, what is Zeno’s paradox of motion? Explain how this particular paradox is formulated. Third: By way of philosophical critique: What do you make of Zeno’s paradox of motion? Is there a true paradox in the phenomenon of motion itself? Or in the nature of space, or in the nature of time: given that motion is defined as change in spatial location over time? Is Zeno’s paradox arguably solved (or resolved or dissolved) by drawing on more recent ideas from mathematics or philosophy? Our main text is Sorensen’s A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind. We draw ideas from Sorensen’s observations and extend our analysis of paradoxes as in Lecture and Discussion. We have extended our analysis of Zeno’s paradox in terms drawn from Cantor’s theory of “transfinite” numbers (formulated in terms of his mathematical development of set theory). And, subsequently, we consider McTaggart’s theory of time (as McTaggart argues that time itself is unreal). You may consider how Cantor’s mathematical theory of measures of “infinity” may impact Zeno’s argument. Or you may consider how the nature of action, in “hypertasks”, impacts Zeno’s argument. Or you may consider how McTaggart’s theory of time itself may impact Zeno’s argument. Or you may consider how exactly these more idealized technical models — of motion or space or time — apply to the concrete phenomenon of motion. After clearly expounding Zeno’s paradox of motion itself, your task in the third part of your essay is to focus on a particular aspect of Zeno’s paradox that you think revealing, and to analyze Zeno’s paradox further in terms of that aspect. 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). McTaggart’s ideas are addressed on pp. 173-176 and again 184-196.
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