Question

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.

Answer 1

Aristotle's differentiation between types of potentiality in relation to infinite divisibility is used to counter the Atomists' claim of indivisible building blocks. He argues using the logic that just because parts can exist potentially, it doesn't mean they can exist all at once, which highlights a fallacy in Atomist argumentation.

Step-by-step explanation:

In Aristotle's critique of Atomism, he distinguishes between actual and potential infinities, and within potential infinities, he differentiates between different kinds of potentiality. This delves into the substance's chances of becoming its purpose. The atomists believed in a priori reasoning, asserting that things must be reducible to indivisible building blocks, opposing the notion of infinite divisibility.

However, Aristotle's concept differs in that he believes a substance can be divided endlessly - a potential infinity - but parts of a temporal series can't all exist at once, such as the morning and afternoon.

The passage cited points out the fallacy in the argument from the Atomists which erroneously infers that if separate possibilities exist independently (p or q are possible), then they must be able to co-exist jointly (p and q are possible), which Aristotle finds logically unsound.