Key Arguments

• After bounding increase and quantifying the just maximum, he asks about the nature of this residual right: "Nevertheless, the account is not finished, and the laborer is still ignorant of the full extent of his rights. What is the right of increase when confined within just limits? A recognition of the right of occupancy." redefining it not as a privilege of a separate class, but as an expression of occupancy.
• He universalizes this: "But since all have an equal right of occupancy, every man is by the same title a proprietor. Every man has a right to an income equal to a fraction of his product." extending the logic of increase to every worker.
• From this symmetry he infers reciprocity of obligations: "If, then, the laborer is obliged by the right of property to pay a rent to the proprietor, the proprietor is obliged by the same right to pay the same amount of rent to the laborer;" thereby eliminating any asymmetry between classes.
• He draws the algebraic conclusion: "and, since their rights balance each other, the difference between them is zero." so any net 'right of increase' vanishes once equal occupancy is acknowledged.
• In the Scholium, he generalizes to fragmented ownership: "If farm-rent is only a fraction of the supposed product of the proprietor, whatever the amount and value of the property, the same is true in the case of a large number of small and distinct proprietors. For, although one man may use the property of each separately, he cannot use the property of all at the same time." indicating that the mutual cancellation of rents applies even with many small owners.
• He concludes the section by summarizing the annihilation of property’s core: "To sum up. The right of increase, which can exist only within very narrow limits, defined by the laws of production, is annihilated by the right of occupancy. Now, without the right of increase, there is no property. Then property"—leaving the final deductive step (property’s non‑existence) to be completed in the following lines.

Source Quotes

It is something of a reduction, to take nine hundred and ten millions from the burdens which weigh so heavily upon the laboring class! Nevertheless, the account is not finished, and the laborer is still ignorant of the full extent of his rights. What is the right of increase when confined within just limits? A recognition of the right of occupancy. But since all have an equal right of occupancy, every man is by the same title a proprietor.

A recognition of the right of occupancy. But since all have an equal right of occupancy, every man is by the same title a proprietor. Every man has a right to an income equal to a fraction of his product. If, then, the laborer is obliged by the right of property to pay a rent to the proprietor, the proprietor is obliged by the same right to pay the same amount of rent to the laborer; and, since their rights balance each other, the difference between them is zero.

Every man has a right to an income equal to a fraction of his product. If, then, the laborer is obliged by the right of property to pay a rent to the proprietor, the proprietor is obliged by the same right to pay the same amount of rent to the laborer; and, since their rights balance each other, the difference between them is zero. Scholium.⁠—If farm-rent is only a fraction of the supposed product of the proprietor, whatever the amount and value of the property, the same is true in the case of a large number of small and distinct proprietors.

If, then, the laborer is obliged by the right of property to pay a rent to the proprietor, the proprietor is obliged by the same right to pay the same amount of rent to the laborer; and, since their rights balance each other, the difference between them is zero. Scholium.⁠—If farm-rent is only a fraction of the supposed product of the proprietor, whatever the amount and value of the property, the same is true in the case of a large number of small and distinct proprietors. For, although one man may use the property of each separately, he cannot use the property of all at the same time.

For, although one man may use the property of each separately, he cannot use the property of all at the same time. To sum up. The right of increase, which can exist only within very narrow limits, defined by the laws of production, is annihilated by the right of occupancy. Now, without the right of increase, there is no property. Then property

Key Concepts

• Nevertheless, the account is not finished, and the laborer is still ignorant of the full extent of his rights. What is the right of increase when confined within just limits? A recognition of the right of occupancy.
• But since all have an equal right of occupancy, every man is by the same title a proprietor. Every man has a right to an income equal to a fraction of his product.
• If, then, the laborer is obliged by the right of property to pay a rent to the proprietor, the proprietor is obliged by the same right to pay the same amount of rent to the laborer; and, since their rights balance each other, the difference between them is zero.
• Scholium.⁠—If farm-rent is only a fraction of the supposed product of the proprietor, whatever the amount and value of the property, the same is true in the case of a large number of small and distinct proprietors.
• To sum up. The right of increase, which can exist only within very narrow limits, defined by the laws of production, is annihilated by the right of occupancy. Now, without the right of increase, there is no property. Then property

Context

Conclusion of the Third Proposition, where Proudhon interprets his quantitative limitation on increase as simply recognizing a universal right of occupancy; because all have this right, proprietors and laborers are symmetrically entitled and indebted, so rents cancel out and the economic core of property—the right of increase—is 'annihilated', paving the way for his final conclusion that property itself is impossible.