In book IV, Locke addresses the nature of knowledge itself, asking what knowledge is and in what areas we can hope to attain it. For Locke, knowledge is what the mind is able to perceive through reasoning out the connection, or lack of connection, between any two or more of our ideas. Because knowledge only has to do with relations between ideas, which are in the mind, the knowledge we are capable of is not actually knowledge of the world itself. Locke identifies four sorts of agreement and disagreement that reason can perceive to produce knowledge: (1) identity (blue is blue) and diversity (blue is not yellow), (2) relation (two triangles with equal bases located between the same two parallel lines are equal triangles), (3) coexistence (iron is always susceptible to magnets), and (4) realization that existence belongs to the ideas themselves and is not in the mind (the idea of God and of the self). Locke distinguishes between three grades or degrees of knowledge: intuition, when we immediately perceive an agreement or disagreement the moment the ideas are understood; demonstration, which requires some sort of proof; and sensitive knowledge, which is about the existence of an external world, roughly resembling the world as we perceive it.

Locke argues that we can never really develop a system of knowledge in natural philosophy. The best that we can do is to observe certain qualities in the world that tend to occur together on a regular basis. The kind of connection he demands is the sort that we find between properties occurring together regularly in geometrical figures. Although he doesn’t seem to think we will ever be able to know more about the true nature of things, Locke is hopeful that we can understand existence, and the properties of things that exist in the world, much more thoroughly.