By a weak reading, I mean viewing a concept as overdetermined, revealing a ream of constituent dialogues and discourses which destroy a particular conceptual framework surrounding said concept. By implanting one discursive form upon such a concept, an ideological system is created which hides the truth of what underlies something. In the case of private property, capitalist definitions provide a concept as something privately owned, yet the reality is that much of modern private property came out of the enclosures, of feudal and modern eras, and large tracts of private property have been gifted to vested interests by the state. The capitalist discourse of private property is an ideological lie masking systemic theft.
However, private property as a concept can be thought as having many different elements that aren’t defined by the capitalist discourses that entrap the modern definition. These alternative discourses include things like commonly-owned property, usufructory property rights, Lockean proviso systems and social ownership. A weak reading means these can be placed in the idea of private property as property owned by those who use and control it. A unifying definition of private property allows such disparate systems to be conceived as under a rubric of similar conceptualisations. All recognise ownership and control. Yet each is not simply a totality. All are systems that historically have found themselves in variable systems. The commons of Torbel combined individual ownership for small-farms with commons for herding and pasture. A community funded via a land-value tax means full private property rights tempered by a tax on ground-rent. Here there is a recognition of full ownership in the improvement upon land, but with the belief that land as an unimproved resource is a gift of nature, non-replicable by man, and thus unjustified in being owned purely by man.
The variability of this Panarchy means that private property as a concept of anarchism takes on many forms, which are borne out of the social relations of each community, and the relations between such communities. It’s not simply non-proviso Lockean property, encompassing all the concepts I’ve mentioned and many others. The unification of these diverse concepts comes from understanding private property as ownership through private means. That means in opposition to the state, and can mean collective ownership or customary rights over land. In understanding this, we see that much corporate ownership and control of land and labour is through the illegitimate function of the state (a system of theft) that create the wage labour and land monopolies. Without this function, labour becomes the ownership of its creator, equalising economic relations between capital and labour. Land ownership becomes open to legitimate claims by those it was stolen from, with corporations illegitimately profiting from the state being open to homesteading by stakeholders. And most importantly, intangible property (in the form of intellectual property) is unsustainable in its monopoly form. This eliminates the rentierism of the modern corporate economy. A weak reading of private property allows for the variety of existent systems and theoretical concepts to be seen as legitimate, private ownership by individuals and communities of individuals. This rejects the current capitalist discourses which legitimate theft and extortion by the state.
 Ostrom, E. Governing the Commons, 1990
 Paine, T. Agrarian Justice, 1797