Key Arguments

• He formulates the proposition as: "Property is impossible, because, with a given capital, Production is proportional to labor, not to property." thereby explicitly opposing the logic of property to the quantitative law of production.
• He recalls his previous numerical model: "To pay a farm-rent of one hundred at the rate of ten percent of the product, the product must be one thousand; that the product may be one thousand, a force of one thousand laborers is needed." hence the payment of a given rent presupposes a corresponding volume of labor.
• When one hundred laborer‑proprietors stop working to live as rentiers, the number of active laborers falls from one thousand to nine hundred, so "the production is also reduced to nine hundred, one-tenth of which is ninety." thus the community can no longer generate the farm‑rent of one hundred.
• From this he concludes that either "ten proprietors out of the one hundred cannot be paid⁠—provided the remaining ninety are to get the whole amount of their farm-rent⁠—or else all must consent to a decrease of ten percent," i.e. there is a necessary loss borne by proprietors.
• He insists that the loss cannot justly fall on workers: "For it is not for the laborer, who has been wanting in no particular, who has produced as in the past, to suffer by the withdrawal of the proprietor. The latter must take the consequences of his own idleness." shifting the burden logically to the idle owner.
• Thus, "the proprietor becomes poorer for the very reason that he wishes to enjoy; by exercising his right, he loses it; so that property seems to decrease and vanish in proportion as we try to lay hold of it⁠—the more we pursue it, the more it eludes our grasp," showing the self‑undermining character of property when its beneficiaries stop working.
• He notes that when the laborer‑proprietor continues working, he both creates and then loses the very tenth that disappears: "By taking part in the production, he was himself the creator of this tenth which has vanished; and while he thought to labor only for himself, he unwittingly suffered a loss in exchanging his products, by which he was made to pay to himself one-tenth of his own farm-rent. Like everyone else, he produced 1, and received but 0.9." demonstrating that whether the proprietor works or not, the structure of property causes his claims to shrink relative to production.
• He generalizes the relationship: "If, instead of nine hundred laborers, there had been but five hundred, the whole amount of farm-rent would have been reduced to fifty; if there had been but one hundred, it would have fallen to ten." so rent mechanically falls as laborers are withdrawn into idleness.
• He asks rhetorically: "What sort of a right is that which is governed by numerical relations, and which an arithmetical calculation can destroy?" insinuating that a 'natural' or 'absolute' right should not collapse under simple arithmetic, whereas property does.

Source Quotes

Third Proposition Property is impossible, because, with a given capital, Production is proportional to labor, not to property. To pay a farm-rent of one hundred at the rate of ten percent of the product, the product must be one thousand; that the product may be one thousand, a force of one thousand laborers is needed.

Third Proposition Property is impossible, because, with a given capital, Production is proportional to labor, not to property. To pay a farm-rent of one hundred at the rate of ten percent of the product, the product must be one thousand; that the product may be one thousand, a force of one thousand laborers is needed. It follows, that in granting a furlough, as we have just done, to our one hundred laborer-proprietors, all of whom had an equal right to lead the life of men of income⁠—we have placed ourselves in a position where we are unable to pay their revenues.

It follows, that in granting a furlough, as we have just done, to our one hundred laborer-proprietors, all of whom had an equal right to lead the life of men of income⁠—we have placed ourselves in a position where we are unable to pay their revenues. In fact, the productive power, which at first was one thousand, being now but nine hundred, the production is also reduced to nine hundred, one-tenth of which is ninety. Either, then, ten proprietors out of the one hundred cannot be paid⁠—provided the remaining ninety are to get the whole amount of their farm-rent⁠—or else all must consent to a decrease of ten percent.

In fact, the productive power, which at first was one thousand, being now but nine hundred, the production is also reduced to nine hundred, one-tenth of which is ninety. Either, then, ten proprietors out of the one hundred cannot be paid⁠—provided the remaining ninety are to get the whole amount of their farm-rent⁠—or else all must consent to a decrease of ten percent. For it is not for the laborer, who has been wanting in no particular, who has produced as in the past, to suffer by the withdrawal of the proprietor.

The latter must take the consequences of his own idleness. But, then, the proprietor becomes poorer for the very reason that he wishes to enjoy; by exercising his right, he loses it; so that property seems to decrease and vanish in proportion as we try to lay hold of it⁠—the more we pursue it, the more it eludes our grasp. What sort of a right is that which is governed by numerical relations, and which an arithmetical calculation can destroy?

By taking part in the production, he was himself the creator of this tenth which has vanished; and while he thought to labor only for himself, he unwittingly suffered a loss in exchanging his products, by which he was made to pay to himself one-tenth of his own farm-rent. Like everyone else, he produced 1, and received but 0.9. If, instead of nine hundred laborers, there had been but five hundred, the whole amount of farm-rent would have been reduced to fifty; if there had been but one hundred, it would have fallen to ten.

Like everyone else, he produced 1, and received but 0.9. If, instead of nine hundred laborers, there had been but five hundred, the whole amount of farm-rent would have been reduced to fifty; if there had been but one hundred, it would have fallen to ten. We may posit, then, the following axiom as a law of proprietary economy: Increase must diminish as the number of idlers augments.

But, then, the proprietor becomes poorer for the very reason that he wishes to enjoy; by exercising his right, he loses it; so that property seems to decrease and vanish in proportion as we try to lay hold of it⁠—the more we pursue it, the more it eludes our grasp. What sort of a right is that which is governed by numerical relations, and which an arithmetical calculation can destroy? The laborer-proprietor received, first, as laborer, 0.9 in wages; second, as proprietor, 1 in farm-rent.

Key Concepts

• Third Proposition Property is impossible, because, with a given capital, Production is proportional to labor, not to property.
• To pay a farm-rent of one hundred at the rate of ten percent of the product, the product must be one thousand; that the product may be one thousand, a force of one thousand laborers is needed.
• the productive power, which at first was one thousand, being now but nine hundred, the production is also reduced to nine hundred, one-tenth of which is ninety.
• Either, then, ten proprietors out of the one hundred cannot be paid⁠—provided the remaining ninety are to get the whole amount of their farm-rent⁠—or else all must consent to a decrease of ten percent.
• the proprietor becomes poorer for the very reason that he wishes to enjoy; by exercising his right, he loses it; so that property seems to decrease and vanish in proportion as we try to lay hold of it⁠—the more we pursue it, the more it eludes our grasp.
• Like everyone else, he produced 1, and received but 0.9.
• If, instead of nine hundred laborers, there had been but five hundred, the whole amount of farm-rent would have been reduced to fifty; if there had been but one hundred, it would have fallen to ten.
• What sort of a right is that which is governed by numerical relations, and which an arithmetical calculation can destroy?

Context

Opening of the Third Proposition in Chapter IV, where Proudhon applies his earlier numerical models of a community with rent to show that, for a fixed capital, production scales with the number of laborers; when proprietors stop working to live from rent, total production falls and their own rent necessarily declines, indicating that the institution of property contradicts the quantitative laws of production.