You will reflexively answer in the affirmative. But the names on grave stones are proper names for only so long as the memories of survivors are extant to supply reference-fixing context. With the passing of the survivors the names revert to commonality. After a while the dead may as well lie in a common grave.
No matter how unusual the name, every so-called proper name either actually has, or could have had, more than one bearer. A name that has more than one bearer is surely not proper, but common. Thus so-called proper names are not properly so-called. If a name has exactly one bearer in actuality, but could have had more than one, then it does not designate either one.
Names are rigid designators in Kripke's sense.
What lies below the stone is not Patrick J. McNally, but a Patrick J. McNally. And not even this; rather, the bodily remains of a Patrick J. McNally. The person has fled or else no longer exists.
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