Marx adopts a triadic model of the concept of property and emphasizes how this concept assumes different historical forms, including private property. I seek to explain why Marx must be thought to commit himself to the complete abolition of private property by beginning with how he speaks of property, equality and freedom as forming a constellation of concepts within capitalist society. This approach enables me to show how, for Marx, private property functions within a social world structured by contractual relations established between allegedly free and equal rights-bearing persons, whose self-conception and relations to one another are determined by an abstract exchange value that finds legal and political expression in a purely formal notion of equality. I argue that there are two key elements in Marx’s critique of private property. The first concerns how individuals are unable to relate to themselves and to others as genuine individuals in an economic and social system governed by exchange value. The second concerns how a system of exchange governed by this form of value dominates individuals and is thus incompatible with ‘free’ individuality.