An e-mail I recently sent to my philosophy of language prof:
Dr. Sidelle,A philosophy language question that’s been bothering me: What do we make of the sentence “A castrated bull is not a bull but an ox.” It seems true at first glance, but it also seems that any sentence of the form “Some members of a set are not members of that set” should be necessarily false. Key question: Is there any philosophical work on this subject? It occurs to me that you could treat it as a deviant use of the word “bull,” like Putnam’s “plastic lemon,” but this does not seem entirely satisfactory.
Thanks,
Chris
One of my math teacher (i studied math at university) once said
“In mathematics, a pink elephant is not always an elephant, and is not always pink”.
It is the “pink elephant principle” (loosely translated from french). And in a strange way, it is true. The meaning of this is that if we denote an abstract concept by some combination of words (here : pink elephant), it is a standalone definition and does not depend of the definitions of the various words involved. However, there should have some kind of link between the words and the new concept.
Is it really of the form “Some members of a set are not members of that set”?
I think it’s of the form “After a transformation, some members of a set cease to be members of the that set”.
Even if it really were equivalent to “some members of a set are not members of that set”, I think we explain it.
Some sentences can still convey information even though they are false. To cut a long story short, metaphors could be thought of this way. The sentence, “jealousy is a green-eyed monster that doth mock the flesh it feeds on” is false – jealousy isn’t, strictly speaking, a monster – but it still conveys information.
Anyway, I know this is controversial but if you have the Martinich anthology for your class, I suggest that you check out “On Metaphor” by Davidson.
Or does ‘bull’ equivocate? Most words do to some extent. I call a bull a cow most of the time, using the word ‘cow’ for ‘cattle’. A bull is a male cow, I say. Anyway, a bull with no head and no guts is not a bull but a lot of raw beef, we may also say. Is a dead human a human? It has few human rights; and what if it fossilised slowly? Would it go from human to rock? Is a fossil dinosaur even a dinosaur? I think there are bad metaphysical arguments aplenty here, if we want them! But in answer to your question, I read the quote as saying that a bull = male cow, is not a bull = uncastrated male cow, but an ox = castrated male cow. Similarly a magpie is a crow (a Corvid), but it is not a (common) crow.
John Morales is right, the issue is reconciling transformation with grouping. So the problem that that the sentence is badly phrased.
One might as well say, “A married bachelor is not a bachelor but a husband.” The essence of bachelorhood is being an unmarried adult male. Perhaps the essence of bullhood is being uncastrated.
It would be better to say “A castrated bull is no longer a bull, it has become an ox.” This makes clear that the relevant grouping makes bullhood mutually exclusive with oxhood. If the author insists on subgrouping, she might remind the reader that both oxen and bulls are subsets of cattle.
John Morales and Enigman both seem to have the kind of solutions we need, but they both depend on not being to bloodly literal about the matter. Not being to bloodly literal seems to be an under-studied phenomena in philosophy of language.
As for the suggestion that this is not a great sentence, I should explain that I generated it not while looking for a paradox, but while thinking about what Hilary Putnam has said about abnormal members of sets. My internal monologue went something like this, “It’s odd how some sets have very sharp boundaries. For example, a castrated bull is not a bull but an ox.”
Chris, you won’t leave us hanging, I hope, if your prof responds? I’d love to hear the explanation from an expert.
“Not being to bloodly literal seems to be an under-studied phenomena in philosophy of language.”
What does blood have to do with being literal?
But seriously folks… On the study of NBBL, Paul Grice is a good start.
(I wish HTML were less bloody literal.)
So how did your prof respond?
John: Dr. Sidelle said he didn’t know of any relevant literature, but suggested another guy in our department, Peter Vranas, might. Both of them, however, were inclined to say that the sentence was false.
Michael: Yes, reading more Grice (I’ve read some) seems like a good idea here.