Changes

===2.4.  Syntactic Transformations===

===2.4.  Syntactic Transformations===

To discuss the import of the above definitions in greater depth, it serves to establish a number of logical relations and set-theoretic identities that can be found to hold among this array of conceptions and constructions.  Facilitating this task requires in turn a number of auxiliary concepts and notations.

We have been examining several distinct but closely related notions of ''indication''.  To discuss the import of these ideas in greater depth, it serves to establish a number of logical relations and set-theoretic identities that can be found to hold among their roughly parallel arrays of conceptions and constructions.  Facilitating this task requires in turn a number of auxiliary concepts and notations. The notions of indication in question are expressed in a variety of different notations, enumerated as follows:

The diverse notions of ''indication'' under discussion are expressed in a variety of different notations, in particular, the logical language of sentences, the functional language of propositions, and the geometric language of sets.  Thus, one way to explain the relationships that exist among these concepts is to describe the ''translations'' that they induce among the allied families of notation.

# The functional language of propositions

# The logical language of sentences

# The geometric language of sets

 

Thus, one way to explain the relationships that hold among these concepts is to describe the ''translations'' that are induced among their allied families of notation.

====2.4.1.  Syntactic Transformation Rules====

====2.4.1.  Syntactic Transformation Rules====