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How does the Problem of the Many relate to the philosophical basis of Calculus, if at all?

J D
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bob myers
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  • Welcome to SE Philosophy! Thanks for your contribution. Please take a quick moment to take the [tour](https://philosophy.stackexchange.com/tour) or find [help](https://philosophy.stackexchange.com/help). You can perform [searches here](https://philosophy.stackexchange.com/search) or seek additional clarification at the [meta site](https://philosophy.meta.stackexchange.com/). Don't forget, when someone has answered your question, you can click on the arrow to reward the contributor and the checkmark to select what you feel is the best answer. – J D Oct 29 '21 at 06:43
  • Added links and a couple of qualifiers. – J D Oct 29 '21 at 06:44
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    A curious question. Willing to share your motivations? – J D Oct 29 '21 at 07:40
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    Unger's problem of the many has formal similarity to the ancient problem of one over many that Plato presents in *Parmenides*. Of course, in Plato's case the one is a form and the many are its instances, while in Unger's the one is a vague object and the many are precise aggregates. But in both cases there is a problem with reducing the many to the one. Zeno's paradoxes can be thought as playing on this reduction of many to one, and it is there that calculus is taken to give a solution, but see [Papa-Grimaldi](http://philsci-archive.pitt.edu/2304/) who argues that, in fact, it does not. – Conifold Oct 29 '21 at 08:46
  • A clear common theme of both is *vagueness*. A concept like cloud actually is extremely vague, similar to the concept of limit, infinity and infinitesimals which have all been rigorously defined and studied in modern math based on set theory and non-standard analysis... – Double Knot Nov 01 '21 at 05:38

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