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And you give me the choice between a description that is sure but that teaches me nothing and hypotheses that claim to teach me but that are not sure. — Albert Camus • The Myth of Sisyphus |
Re: R.J. Lipton and K.W. Regan • Zeno Proof Paradox
The classical paradoxes of change and motion really have to do with a disconnect that exists between two realms —
On the one hand we have the phenomenology. There is no problem there since we obviously observe all sorts of Achillean runners passing all sorts of Tortoises all sorts of times, the respective handicaps of heels and hulls notwithstanding.
On the other hand we have the logical theories and mathematical models that we bring to bear on the phenomena by way of trying to describe and explain them.
There’s the rub. Get a model or theory that “saves the appearances” (solves the phenomena) and the paradox disappears.
Transpose the phenomena from a classical mode to a quantum-mechanical, information-theoretic, or ordinary logical key — and the note that resolves the chord is a trifle harder to find.
In a related development, we could hardly complete this course without mentioning the logical version of Zeno’s Paradox given by Lewis Carroll —
Inquiry Into Inquiry 
Maybe this my comment is an offtopic, but I have a theological theory which resolves three-in-one paradox about Christian God: http://endofgospel.org/docs/god-as-civilization.html
Traveling today so a little scattered …
What I read of your essay so far reminds me of things I read many years ago in the work of Teilhard de Chardin — his notion of Humanity tending toward an “Omega Point” that marks the immanent aim or ultimate goal of life in the cosmos.
The primary narrative describing Zeno’s paradox is Plato’s “dialogue”, which is a monologue by Plato as the playwright. The paradox which is attributed to Zeno is presented as “multiple” paradoxes. It is clear upon examining the “dialogue” that the paradox which Zeno is assigned is actually Zeno pointing out the paradox built into Plato’s idealistic materialism. Plato is in effect defending his philosophy against two of the strongest philosophers who would have challenged Plato’s whole philosophic program. He frames the dialogue to make Parmenides and Zeno to seem enigmatic or wrong within Plato’s metaphysics. Plato was NOT beginning from a genuine straight up comparison and critique. This makes Plato probably a better playwright and rhetorician than a philosopher.