If 'Adams' is a rigid designator that presupposes its referent's existence, then (a=a) is not a pure logical truth but a metaphysically loaded one, making the derivation of necessary existence question-begging.
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A statement that is true just because of the rules of logic itself, with no need to know anything about the real world—like 'either it's raining or it's not raining.'
derivation(Used to distinguish arbitrary proofs from proofs grounded in agreed and plausible premises)
A logical proof of a proposition produced from a set of premises and rules of inference
A charge leveled against anti-skeptical arguments that assume what they set out to prove, particularly in Putnamian externalist arguments
referent(what Russell says is the sole meaning of proper names)
The actual thing in the real world that a word points to or stands for—for example, the referent of 'Abraham Lincoln' is the actual historical person.
rigid designator(Term due to Kripke (1972); used to distinguish expressions whose reference is fixed across circumstances from those whose reference varies.)
An expression which, relative to a context of utterance, refers to the same object with respect to every circumstance of evaluation at which that object exists, and never refers to anything else with respect to another circumstance of evaluation.