So far, I have shown that theoretical knowledge is the highest form of knowledge, that knowledge is unified if it is about the same thing and that knowledge of a things purpose is the highest form of knowledge. But how is our knowledge of things related to each other? There are three possibilities: the knowledge is independent and separate, it is interdependent and equal or it is dependent and unequal.

Knowledge of one thing is not necessarily separate from knowledge of another thing. This is fairly obviously true. For example, the more we learn about mammals, the more we learn about human beings. When a ball breaks a window, we learn that the window is breakable and that the ball is hard. There are plenty of other examples as well. But some items of knowledge are separate. Knowing that 2 + 2 = 4 has no bearing on whether or not reptiles are cold-blooded. So complete independence is not possible, but some knowledge is separate from other knowledge.

When knowledge is dependent in some way, it is not necessarily equal. Knowing that animals have senses requires that human beings have senses because human beings are animals. The reverse form of reasoning is wrong though. That human beings are mammals does not mean that all animals are mammals. This is an inequality in knowledge. It happens because animals is a broader category than human beings, so whatever is true of the broader category will always be true of the narrower categories, but the reverse is not necessarily true.

In order to avoid examples of equal knowledge or independent knowledge it is best to stick to what we have proven so far. I will mention only theoretical knowledge and only knowledge of a thing’s purpose. With these restrictions in place, knowledge of things is either knowledge of the thing as an individual or knowledge of a thing as belonging to a particular category. We cannot speak about a thing in any other way if we are speaking about the purpose of a thing.

If we are speaking about an individual thing, then its particular purpose is unknown to us. In order to understand a particular thing in that way, we would have to know what the thing as an individual is. But this is impossible. To know what a thing is we would have to give a definition of that thing. But we cannot give a definition of any individual. Any supposed definition would describe it as belonging to a particular genus and having a certain difference from other things in that genus. But no matter what we described as the difference, it is possible that something else also has the same difference. So since there is no difference that would of necessity describe the individual and only that individual, it is impossible to give a definition for any individual.

If we are speaking of a kind of thing, then we are speaking of genus and difference. In that situation, the knowledge is of two kinds: it is either unequal or it is separate. If the knowledge is of two kinds of things that lack any genus in common – such as whiteness and mammals – then the knowledge is separate. If the knowledge is of two kinds of things that share a genus in common, then knowledge of that genus will improve our knowledge of both kinds of things.

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