After careful consideration I have decided that 'Anakin Skywalker' is a rigid designator. This means that regardless of who Anakin Skywalker is, he is identical with himself, and the term 'Anakin Skywalker' refers to Anakin Skywalker. Now, it's possible that Anakin Skywalker could have been called 'Jim Jones' but Anakin Skywalker would still have all the properties of Anakin Skywalker, even if he were named 'Jim Jones'. This is what a rigid designator is, it is a name that refers to an object itself, but a rigid designator is not a description of the object. If we try to describe Anakin Skywalker as the person who became Darth Vader, it is possible that Anakin Skywalker never turned to the dark side, so that would be a incorrect description of Anakin Skywalker. Or if we said that Anakin Skywalker is the father of Luke Skywalker it is possible for Luke to have never been born so this would be an incorrect description if Luke were never born. Thus, a rigid designator is not a description, it is a term that picks out an object. 'Anakin Skywalker' (picks out) refers to Anakin Skywalker and the term 'Anakin Skywalker' does not have any descriptive content.
Now if two different rigid designators refer to the same object then the rigid designators are identical. Here is an example: Mark Twain is identical with Samuel Clemons. Two objects are identical if they share all of the same properties. Here is the problem with Anakin Skywalker being identical with Darth Vader. It is not a necessary property of Anakin Skywalker to have turned to the dark side of the force. Yet, by definition Darth Vader is a sith and all sith necessarily have turned to the dark side of the force. So, Darth Vader and Anakin Skywalker do not share all the same necessary properties. Using the dark side of the force is a contingent property of Anakin Skywalker. It appears that 'Anakin Skywalker' is a rigid designator, but 'Darth Vader' is not.
I propose that 'Darth Vader' is a partially descriptive desginator. 'Darth' implies that something is a sith lord. So, this is how Darth Vader can be identical with Anakin Skywalker because 'Darth Vader' is not a rigid designator but a partially descriptive designator.
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