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The entirety of the Essay Concerning Human Understanding builds up to Locke's theory of knowledge. The upshot of this theory is that knowledge is possible but limited. He is arguing here primarily against the rationalists, who believed that our capacity to know is virtually limitless, and the skeptics, who believed that we are incapable of knowing anything at all.
Locke gives a strict definition of knowledge, whereby one can only be said to know something when one sees why it is necessarily so. That is, knowledge depends on the perception of a necessary connection. This is much the same definition of knowledge that Descartes and the other rationalists used, but in Locke's empiricist hands, it has very different consequences for the human capacity to know.
According to the Cartesian Rationalists, the entire world is made up of a web of necessary connections that the mind, with its use of reason, can potentially unravel. Locke, however, does not believe either of these claims. First of all, he denies that the mind is capable of grasping every necessary connection there is because he thinks that our only source of information is experience and experience does not reveal all the necessary connections to us, as these lie in the unobservable underlying microstructures of object. In addition, he does not believe that there is a necessary connection behind every question; there is no necessary connection linking the unobservable microstructures to the secondary qualities we experience. There is no reason, for instance, why the microstructure that currently gives rise to our sensation of yellow had to give rise to our sensation of yellow, rather than our sensation of blue. The connection between the microstructure and the sensation it produces in us is based entirely on the arbitrary decision of God.
Since all of our access to the natural world is founded on observable properties and we cannot grasp the necessary connections that account for these (or, in the case of secondary qualities, not account for them), Locke concludes that we cannot have any knowledge regarding the nature of things. This is tantamount to saying that science (other than the purely mathematical sciences and the science of morality) can never result in knowledge.