The first time I read this section, it seemed that Descartes’ observations, although reasonable, were not free from doubt. For example, Descartes claims that although most of wax’s physical properties—taste, shape, smell, color, size, solidity—change when the wax is heated, the same wax still remains. “It must be admitted that it does; no one denies it, no one thinks otherwise” (20, AT30). Perhaps as we heat our piece of wax, invisible wax gnomes are secretly replacing bits of the solid wax with some other kind of non-wax liquid, tricking us into thinking we are holding molten wax. Is this objection ridiculous? Of course, but they remain logical possibilities; thus we could doubt that we ever hold the same piece of wax at any two times.
The second time I read this section, I realized that I was being sophistical and missing the point. Descartes isn’t trying to establish any claims about the external world, but our perception of things in the external world. We do not perceive the “thinghood” of a piece of wax through sight or feeling, but through thought. For example, we know that wax is a corporeal body, and thus extended in space.* Extension is not a property that we perceive by sight, for we will only experience but a few of the countless ways the wax can be arranged in space while still retaining its wax-ness. Indeed, we cannot even imagine all the ways the wax can be arranged: “I would not be making a correct judgment about the nature of wax unless I believed it capable of being extended in many more different ways than I will ever encompass in my imagination” (21, AT31). The thinghood of the piece of wax is not something we can see, but we instead perceive it in the unity of the wax’s appearances. This unity is something we perceive with our mind: “The perception I have of [the wax] is a case not of vision or touch or imagination… but of purely mental scrutiny” (21, AT31).
Now, if invisible wax gnomes exist, we are still perceiving incorrectly. But the clarity and distinctness that seems to accompany sensory experience (even if it is misleading) actually comes from the mind, not the senses.
*EDIT: A classmate approached me this morning to ask what I meant by "extension." As far as I can tell, extension for Descartes refers to the existence of the wax in three-dimensional space, and thus includes what we normally call "size" and "shape."
I agree. Extension is not perceived by the senses. "Body" is similar. We perceive bodies but not "body". Indeed extension often just seems to be the more general term for the realm of bodies, since the basic attribute of body is "extension". Somehow, it is this thought - that we can think body in the pure intellect even when the sense are doubted- that leads D. to realize that the pure space of mathematics and the pure space of the intellectual consideration of body is one and the same. Voila! Analytic geometry describes the real intrinsic properties of the physical world.
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