Knowledge

If two things are the same thing under one concept, and yet two distinct things under another concept, is it logically possible that things of the second concept are things of the first concept? For example if two people have the same belief, but one has knowledge and the other doesn't, is it logically possible that knowledge is belief?

Comments

Are you imagining a situation in which x is F and y is F, but x is G and y is not G? And then are you asking whether all things that are G might also be F? If so, I think the answer is Yes: let x be Fido, your dog, let y be Kitty, your cat, let F be the property of being a mammal and let G be the property of being a dog. Fido is a mammal, as is Kitty; Fido is also a dog, but Kitty isn't; and also, all dogs are mammals.

The last question asked here can be treated more generally. When we speak of two people's having the same belief, what we mean is that they believe the same thing, where what they both believe is, say, that Margaret Thatcher likes hot dogs.

Belief is usually regarded as a relation between a person and a "proposition", which characterizes the "content" of the belief. So to say that two people have the same belief is to say e.g. that both Bill and Sue stand in the belief-relation to the same proposition, say, that Bill has been unfaithful. Knowledge, too, is a relation between a person and a proposition. So the fact that Bill knows that he is unfaithful, whereas Sue does not, simply means that Bill stands in the knowledge-relation to this proposition, whereas Sue does not. There's no logical problem here, even though if is also true, as most philosophers think, that, to stand in the knowledge-relation to some proposition, you must also stand in the belief-relation.

There is some controversy over whether the following situation is possible: X is the same F as Y, but X is not the same G as Y. Good examples are hard to come by, but here is the one I find most impressive. Consider this expression: Bob. The first letter of that expression is, in one sense, the same as the last letter; but it is, in another sense, different from it. This fact is reflected in our willingness to answer the question "How many letters does 'Bob' contain?" in two different ways. Perhaps, then, we should say that the first letter is the same type as the last one, but is not the same occurrence. If you're attracted to this view, then you are attracted to the view that identity is relative to a "covering sortal concept", as it is put. See the article on this topic on the Stanford Encyclopedia.

Most philosophers and logicians have not gone that route, because it has a large cost. Identity is usually taken to be governed, logically speaking, by Leibniz's Law of the Indiscernability of Identicals, which says that, if X is the same as Y, then Y has every property that X has. If identity is relative, Leibniz's Law is violated, and it has never been clear how it should then be re-formulated. That is to say, relative identity theorists lack a convincing logic of identity.

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