Observations on CIL

The individual concept of an individual is not a kind of infinitary logic conjunction of descriptions which denote this individual. For each one of such descriptions may be modally conditioned. Rather it is a special essence which describes what is unique, essential and invariant to the individual under any state-of-affairs or possible world.  But this essence perhaps does contain contingent definite descriptions suitable specified by the state-of-affair. In this way the description 'the tutor of Alexander' plus the data of the actuality of a certain possible state-of-affairs (world history or something of the sort) are enough to attach the sense of the description to the individual concept and thus to reference the individual.

For Frege the reference of propositions are truth-values, for Husserl they are states-of-affairs or a kind of equivalence class of such, situation-of-affairs.  CIL takes a kind of medium ground, although the extension function for propositions yields truth values, many equivalence classes on propositions can be defined which might accommodate Husserlian references.

The concrete world, the spatio-temporal world,  the world of generation and corruption, the realm of shadows and images, of change,  uncertainty, possibility, vagueness and indetermination. When we move from the realm of pure sense, of ideality, to this world, what must happen ?  

Physics has its method.  This concrete world is captured through the geometry of phase spaces.  In philosophy we should consider moduli spaces, spaces of deformations and variations of structures. What is is what can be defined in a moduli space.  Thus an individual concept is a logically determined form within a space of possibilities $\mathcal{S}$. This form is perhaps continuous, connected and compact in $\mathcal{S}$. Thus the individual concept of 'Aristotle' is a continuous spectrum of individuals spanning deformations of the current world sufficiently like it - its domain of definition.  Thus a definite description is like an indexical, you must input a world in a domain of definition. 

We have at last decided to let $D_{-1}$ consist of individual concepts $i$ for which $Hi = i$. Then we have a function

\[  desc: \mathcal{H} \times D_{-1} \rightarrow \mathcal{P}D_1 \]

which for a given state-of-affairs $H$ and individual concept $i$ yields the set of properties which characterize $i$ uniquely in $H$.  There are situations $H$ in which the individual concept $i$ does not have an existence or embodiment, this is translated by the fact that $desc(H,i) = \emptyset$.