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Locke opens the Essay Concerning Human Understanding with an attack on the notion of innate knowledge. He is particularly keen on demolishing the nativist position because it had recently gained renewed currency among intellectual circles, partially in response to René Descartes's philosophy. Descartes believed that inborn in our minds are certain mathematical ideas (such as the ideas of geometrical shapes), metaphysical ideas (such as the idea of God and of essences), and eternal truths (such as the truth that something cannot come from nothing).
Locke could not have disagreed more, and he spends the entire first book showing us why. He begins by attacking the possibility of innate principles, such as the principle whatever is is. He then moves on to attack the possibility of innate ideas, such as the idea of God and of infinity. Locke only wages this second attack in order to cover all of his bases. The meat of the argument against innate knowledge rests on an argument against innate principles, since only principles (statements of fact), and not ideas (which are the building blocks of these statements of fact, the sort of things that have names, such as "God," "Man," "blue," "existence"), can properly be called "knowledge." I can know (conceivably) that God exists, I cannot know that "God."
The structure of the argument against innate principles is very simple and can be summed up in three sentences:
(1) If, in fact, there are any innate principles, then everyone would assent to them.
(2) But there are no principles to which everyone assents.
(3) Therefore, there are no innate principles.
Locke, however, takes a long time making this simple argument because he is meticulous in establishing that there are no principles to which everyone would assent. His proof of this claim takes the form of a dialectic. He formulates a strong nativist position, objects to it, revises the nativist position, objects, and so on until the position left to the nativist is so weak as to be utterly trivial.