I am reading a book about Aristotle. Aristotle lays out a potential argument against infinite divisibility by the Atomists, that infinite division would leave components of zero-magnitude which could not sum to the origin whole. In response, he differentiates actual and potential infinities, with a potential infinity simply meaning "endlessly divisible". Then he attempts to improve this argument, and this is where I'm at a loss. Here is the relevant passage:

He offers a distinction between different kinds of potentiality. A block of marble has the potentiality to become a statue: when this is realized, the statue will be there, all of it at once. But the parts into which a temporal period or series can be divided have a different kind of potentiality. They cannot be all there at once: when I wake up, the day ahead contains both morning and afternoon, but they cannot both occur at once.

(from Anthony Kenny's A New History of Western Philosophy: Ancient Philosophy, p. 181)

The author goes on to say this is the basis of a further argument against the Atomists, and that it is fallacious arguing erroneously from "if p or q are possible, p and q are possible". It isn't clear to me how this distinction could serve as an argument against Atomism or in defense of infinite divisbility, nor how it resembles this fallacious form.

1 Answer 1


Well, the fallacious reasoning that the author mentions is the Atomists' mistaken belief that if something is individually possible, then it must be possible for those things to happen together. In other words, if p or q (where p and q represent different parts) are possible, then the Atomists assume that p and q can both happen at the same time.

Aristotle's distinction challenges this assumption. He argues that while individual parts of a day may be possible, like morning and afternoon, they cannot occur simultaneously. This means that the Atomists' idea of infinite divisibility, where all parts can exist together, doesn't hold up.

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