Take the following syllogism :
John believes that green people should be killed.
Mushmush is a green person, a neighbour of John.
Thus, John believes that Mushmush should be killed.
Formally, the argument seems valid. However, in reality it doesn't work. A persona can believe that all people with quality X should be killed, but not think it about a specific person he knows. So is there a logical contradiction here? What happens?
Thank you, Sam
Whoa! With all due respect to Professor Nahmias, he is mistaken. The syllogism is NOT valid and here is why. Propositions that are "in the scope" of words like belief can't be manipulated while preserving validity. So while, Green people should be killed. Mushmush is a green person. ergo, Mushmush should be killed is valid, embedding the first premise in the scope of belief ('John believes that green people should be killed') will destroy the argument's validity. Words like 'believes' (and related ones such as 'knows', 'wants', 'fears') create what is known as opaque contexts, in which inferences that would otherwise be valid are no longer valid. The reason is that what a person believes (knows, wants, fears) depends not only on what is implied by the propositions he believes, but also on whether he *realizes* that these things are implied. Alas, we are all too often unaware of what is implied by the things that we believe. The point here has been discussed in detail by...