Now, consider the following identity statement:
Peter Parker = Spider-manThis identity statement is true in the world in which Peter Parker exists. But is it necessarily true (i.e., is it true in all possible worlds)?
Couldn't one conceive of a world in which the person who is bitten by a radioactive spider is not Peter Parker, but rather Harry Osborn? And if so, wouldn't it be the case that, in that possible world, 'Peter Parker = Spider-man' is false and 'Harry Osborn = Spider-man' is true? And if so, wouldn't it then be the case that 'Peter Parker = Spider-man' is not necessarily true even though 'Pater Parker' and 'Spider-man' are rigid designators?