Presumably we are talking about something like....
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What the difference between a goat and cancer?
Jade Goody can't milk a goat.
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Actually I think it is quite funny.
Personally, I don't think a joke like this is offensive in Goody's case as she chose to have a high profile, media led death. A similar joke about a private, decent "nice" person - say Wendy Richards for example - would, I think upset me. This just goes to prove how difficult this subject is.
I think people who filter jokes through the "political correctness" filter and respond appropriately are missing the point. A joke is something unexpected and outrageous and a response to a joke should be visceral. If you have to think about a joke it isn't really a joke and isn't funny. It's just "clever". A genuine joke doesn't offend, even if it is barbed.
The modern trend by government to put certain areas off limit to jokers is appalling mind control and must be resisted.
Joking is a way of publically airing difficult issues, and trying to find ways of dealing with those issues. Congratulations again to our out of touch, interfering, witless government for stifling this important avenue of discussion.
PS: I didn't get the Liam Neeson joke above