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In Book 2 Locke distinguishes two very different relations that can hold between an idea and a quality out on the world. Our ideas of primary qualities (size, shape, and motion) resemble the qualities actually in the world; there really is such a thing as shape, size, and motion in the objects we perceive. Our ideas of secondary qualities (color, smell, taste, and sound) do not resemble any qualities in the world. In actual objects there is only size, shape, and motion, and the arrangement of invisible corpuscles somehow causes in us the sensation of such things as color, taste, and smell.
The most accurate way of stating this distinction is in terms of explanation. In order to explain why a piece of wood looks square to me (even if the wood is in fact trapezoidal, and the appearance of squareness is merely an optical illusion), I must refer to shape. An explanation would go something like this: "The wood is shaped like a trapezoid, but because of where I am standing the angles appear so and so." Shape in the external world is always the cause of my sensation of shape, even if the shape out in the world is not exactly the shape I perceive it to be. On the other hand, color in the external world is never the cause of my sensation of color. The size, shape, and motion of insensible particles cause the sensation of color. In explaining why a flower looks blue, there is no reference to blueness out in the world, only to the size, shape, and motion of pieces of matter.
Locke's primary argument for this claim rests on what he calls the "best science of the day": Boyle's Corpuscular Hypothesis, in which all events and states of the natural world can be explained in terms of the motion of tiny indivisible particles of matter called corpuscles. Given this view of the world, all of our sensation can be explained in terms of size, shape, and motion. There is therefore no reason, Locke claims, to assume that there is anything but these qualities in the external world and so we should not make such an assumption. An argument like this one, which rests on the claim that there is simply no need to posit something (rather than on any conclusive proof that the something in question does not exist), is often referred to as an argument from parsimony.