Wolfgang Schwarz

Rigidity and Hyper-Essentialism

According to the epistemic account of vagueness, there aren't really any vague statements: When we're uncertain whether to call somebody bald that's not because he is a borderline case of baldness. There are no borderline cases. The border between being bald and not being bald is perfectly precise. It's only that we don't quite know were it runs.

Not many people believe in this account. That's surprising, because many people do believe that there are rigid designators -- terms denoting the same thing in every possible world --, and this seems to imply something that looks to me just like (an application of) the epistemic account of vagueness.

Suppose "Saul Kripke" is a rigid designator. Then a statement of the form "necessarily, Saul Kripke is F" is true iff in every possible world where Saul Kripke exists he is F. Now let F be a perfectly determinate property, like (perhaps) weighing more than 10 kg. Consider all the worlds where Saul Kripke exists. Either he weighs more than 10 kg in all of them or not. If he does, "necessarily, Saul Kripke weighs more than 10 kg" is true, otherwise it is false. If it is true, we can also express this by saying that weighing more than 10 kg is an essential property of Saul Kripke.

Note that there is no room for vagueness or indeterminacy here: for every determinate property F and every thing x, either x is determinately essentially F, or determinately not essentially F. Let's call this view "hyper-essentialism".

I have no quarrels with a modest form of essentialism. Perhaps Saul Kripke is essentially human, or at least essentially not a prime number. Let's assume for simplicity that we intuit he essentially weighs more than 1 g. But he might well have weighed only 40 kg. (If the example doesn't work for you, replace the mass properties with some other scale of determinate properties, like origins or species or DNAs.) In between, there are properties for which we don't have any clear intuitions: Could he weigh less than 10 kg? less than 100 g? Modest essentialism can treat these questions as lacking a determinate answer, just as questions about whether a bordeline instance of baldness is bald. Not so hyper-essentialism. Hyper-essentialism assumes that there is a determinate weight in between 1 g and 40 kg, say 1.0786230394 kg such that Saul Kripke definitely could have weighed only that much, while he definitely couldn't have weighed less: he couldn't have weighed, say, only 1.078620393 kg. When we're uncertain whether he could have had some mass, that's not because this mass is a borderline case of essentially belonging to Saul Kripke. There are no borderline cases. The borders are perfectly precise. It's only that we don't quite know were they run.