# Section II: Of the Infinite Divisibility of Space and Time explained — A Treatise of Human Nature

> Chapter companion for A Treatise of Human Nature by David Hume.

## What happens

Hume argues against the infinite divisibility of space and time, asserting that our ideas of extension and duration are composed of indivisible parts or moments. He contends that any demonstration of infinite divisibility is sophistical, as it conflicts with the clear and distinct ideas we form of these concepts. He also applies his maxim that whatever is clearly conceived is possible, thereby defending the notion of mathematical points and indivisible moments.

## Themes in this chapter

### Empiricism and the Primacy of Impressions

Hume grounds his argument in the idea that our concepts must be derived from clear and distinct impressions, and that what we cannot conceive cannot be possible.

### Skepticism About the External World

By questioning the infinite divisibility of space and time, Hume challenges the nature of external reality and our ability to know it.

## Character check-ins

### David Hume

Hume presents arguments against infinite divisibility, using his empirical principle that clear ideas imply possible existence.

## Key lines

> It is an established maxim in metaphysics, That whatever the mind clearly conceives, includes the idea of possible existence, or in other words, that nothing we imagine is absolutely impossible.

A fundamental principle: if we can clearly imagine something, it is possible for it to exist; nothing we can conceive is inherently contradictory.

_Hume uses this maxim to argue that since we can conceive of indivisible points, they must be possible, thus undermining the doctrine of infinite divisibility._

> It is certain then, that time, as it exists, must be composed of indivisible moments.

Time, in reality, must consist of indivisible instants, because if it were infinitely divisible, there would be an infinite number of coexistent moments, which is contradictory.

_Hume argues that the successive nature of time requires indivisible moments, paralleling his argument for space._

## Links

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