# IV explained — What Is Property?

> Chapter companion for What Is Property? by Pierre-Joseph Proudhon.

## What happens

Proudhon argues that property is not only unjust but also impossible, using mathematical and numerical reasoning to demonstrate that equality of conditions is the only viable and natural state. He challenges the common objection that equality is a chimera and asserts that property contradicts arithmetic and logic.

## Themes in this chapter

### Property as Theft

Proudhon extends his critique by arguing that property is not only unjust but also impossible, using arithmetic to prove its inherent contradiction.

### Equality and Justice

The chapter centers on the necessity and possibility of equality, countering claims that equality is unattainable and linking justice to mathematical truth.

## Character check-ins

### Pierre Joseph Proudhon

Author and primary voice; presents the argument that property is impossible through mathematical proof.

## Key lines

> If I show that property itself is impossible⁠—that it is property which is a contradiction, a chimera, a utopia; and if I show it no longer by metaphysics and jurisprudence, but by figures, equations, and calculations⁠—imagine the fright of the astounded proprietor!

Proudhon announces his intention to prove property's impossibility through mathematical and numerical reasoning rather than abstract philosophy or law.

_This sets up the chapter's central method: using arithmetic to demonstrate that property is inherently contradictory._

> Property is physically and mathematically impossible.

Proudhon concludes that property cannot exist in reality or in logical terms.

_This is the chapter's definitive thesis, linking impossibility with injustice._

## Links

- HTML: https://www.betterreads.online/discover/what_is_property_se/chapters/iv
- Book: https://www.betterreads.online/discover/what_is_property_se
- All chapters: https://www.betterreads.online/discover/what_is_property_se/chapters