On definition

Definitions, though logically and semantically constrained, are established for logical purposes. Many terms in natural language are attached to different senses by different people, including logically equivalent senses.  Thus the word 'circle' can have different senses for different people. In mathematics the same concept can be defined in different ways, the  equivalency between these different ways being often non-trivial. For instance 'Noetherian ring' in terms of i) satisfying the ascending chain condition or  ii) any ideal being finitely generated. A mathematician may well not know the equivalence between the two. So if we take the sense of Noetherian ring to be the sense of one of these definition we are lead to the 'paradox of analysis'. For instance from  '$A$ knows that a Noetherian ring satisfies the ACC' we could use Leibniz' rule for $=_I$ to obtain a falsehood.  This suggests that definitions should involve $=_N$ not $=_I$.  We just have to be careful with the introduction of new constants via $=_I$. For often not all people agree on the sense-attribution of terms. The paradox of analysis reveals itself to be a pseudo-problem. But note that it can pop up again in indirect discourse where there is a certain ambiguity between verbatim reported speech and looser reported speech. 

Problems with definitions are quite distinct from  substitutivity pseudo-problems such as Mates' puzzle which are merely about linguistic incompetency or individual divergence. Different agents may attach different senses to the same expression or no sense at all.  In CIL terms stand for senses, hence senses which a given agent attaches to CIL expressions.  We might even introduce a 'non-sense'  sense.  Groundhog $=_I$ Woodchuck means that the agent attaches the same sense to the expressions 'Groundhog' and 'Woodchuck'.  Groundhog $=_N$ Woodchuck means that even if the attached senses are different the reference is the same in all possible states-of-affairs. Other pseudo-problems could, as we saw above, arise from reported speech which hovers been sense and expression. He said 'here is a woodchuck !'  vs.  he said that there was a woodchuck there.  Obviously there is a perspective in which we cannot substitute 'woodchuck' for 'groundhog'.  CIL needs syntactic abstraction operations $[A]$ on terms  for which the meaning of $[A]$ is to be seen as the expression $A$ itself. But how can  an expression be a meaning ? But consider 'the letter coming after 'a''. This has both sense and reference.  So $[A]$ might be seen as the individual concept of the expression 'A'.