Is cutting one head off a two-headed person a case of beheading?
Examples like this are normally used as illustrations of vagueness. It’s natural to think of cases like this as ones where we have a predicate defined over a domain and being applied outside it. Thus, “is being beheaded” is defined over n-headed animals that are being deprived of all heads or of no heads.
I don’t like vagueness. So let’s put aside the vagueness option. What else can we say?
First, we could say that somehow there are deep facts about the language and/or the world that determine the extension of the predicate outside of the domain where we thought we had defined it. Thus, perhaps, n-headed people are beheaded when all heads are cut off, or when one head is cut off, or when the number of heads cut off is sufficient to kill. But I would rather not suppose a slew of facts about what words mean that are rather mysterious.
Second, we could deny that sentences using predicates outside of their domain lack truth value. But that leads to a non-classical logic. Let’s put that aside.
I want to consider two other options. The first, and simplest, is to take the predicates to never apply outside of their domain of definition. Thus,
False: Cutting one head off Dikefalos (who is two headed) is a beheading.
True: Cutting one head off Dikefalos is not a beheading
False: Cutting one head off Dikefalos is a non-beheading.
True: Cutting one head off Dikefalos is not a non-beheading.
(Since non-beheading is defined over the same domain as beheading). If a pre-scientific English-speaking people never encountered whales, then in their language:
False: Whales are fish.
True: Whales are not fish.
False: Whales are non-fish.
True: Whales are not non-fish.
The second approach is a way modeled after Russell’s account of definite descriptors: A sentence using a predicate includes the claim that the predicate is being used in its domain of definition and, thus, all of the eight sentences exhibited above are false.
I don’t like the Russellian way, because it is difficult to see how to naturally extend it to cases where the predicate is applied to a variable in the scope of a quantifier. On the other hand, the approach of taking the undefined predicates to be false is very straightforward:
- False: Every marine mammal is a fish.
10: False: Every marine mammal is a non-fish.
This leads to a “very strict and nitpicky” way of taking language. I kind of like it.
Hello Dr. Pruss, I am struggling to see how your solution (and also Russels solution) works without an appealing to a non-classical logic. Using the first example:
ReplyDelete1. False: Cutting one head off Dikefalos (who is two headed) is a beheading.
2. True: Cutting one head off Dikefalos is not a beheading
3. False: Cutting one head off Dikefalos is a non-beheading.
4. True: Cutting one head off Dikefalos is not a non-beheading.
It seems as if this leads to a straight forward contradiction if a “non-beheading” is any action that is not a beheading. Statement 2 and 4 are clearing contradicting one another (assuming that I understood “non-beheading” correctly) seeing that 2 asserts that “ Cutting one head off Dikefalos is not a beheading” and that 4 sates “ Cutting one head off Dikefalos is not not a beheading”. The same would apply under Russell’s method (though in an inverse manner), resulting in the in the assertion of a proposition and it’s negation. Would you be able to clarify how this could be if you are sticking to classical logic (it seems to fall into an absurdity)? -Thank You