Intersubjectivity and Intensionality

 Let the world consists of a collection of subjects $\{A_1,A_2,...\}$. To each subject $A_i$ we associate a unique UDIL model $M_i$.  These models can be different.  For each model $M_i$ we can take the quotient $M_i/{\cong }_N$ under necessary equivalence when $D$ is restricted to coarsed-grain elements. We require that all these quotient models be isomorphic. 

Constants are either primitive or defined. But does substitution of a constant for its definition preserve fine-grained equality, in particular for propositional attitudes ? What is this opaqueness vs. transparency of defined constants ? In ordinary language we do not fix definitions for many constants. But in scientific or sophisticated language we do. The 'paradox of analysis' is an expression of cognitive-linguistic dis-coordination. But is has to do with a larger problem, that of hyper-fine-grainedness in definitions which was already pointed out by Aristotle in the Topics.

Another argument for hyper-fined-grainedness involves arithmetic or algebraic calculations.