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
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 —