/sci/ - Science & Math

>Girard proposes replacing the idea of individuals with linear propositions (e.g. T,U,V), which can be thought of as atomic formulas that do not reference any specific objects. Equality between individuals can then be expressed as linear equivalence between these linear propositions.
Can you explain how equality of individuals is expressed with their properties? Does this quantify over more properties? Or are that uniquely specifying properties? I don't see why equality on individuals goes away. And how does linearity help with all of this?