-=Dark_Angel=-, P.I.4 Apr 2005

I knew you'd say that. I'm not trying to trap you or catch you out. When you consider the problem of extracting information from a Liar, it becomes clear that there are two sorts of liars. To give you an idea of why Liar-Confusers were introduced to the discussion, consider the question "What did you have for breakfast?"

Someone who is a liar answering your question could give two sorts of answer. The first is of the form "I didn't have baked beans". This is an informative lie, because you instantly know the liar had baked beans. In our formulation, this is what a Liar would say. The other possible answer is of the form "I had Ely Cathedral for breakfast." This lie is an answer to the question, but it is completely uninformative, because we don't get any closer to finding out what the liar actually had for breakfast. That is the sort of thing a Liar-Confuser would say.

I have not added any new rules that weren't already obvious. If you insist that Liar-Confusers don't have to answer the question, then they could just lock themselves in a cupboard and parp the national anthem. That's not answering the question. It's also academically an utterly useless example.