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Published online by Cambridge University Press: 05 June 2012
VISUAL IMAGINATION – THE MEDITATOR'S PUTATIVE BODY (AT VII:72–8)
It remains for me to examine whether material things exist … I now know they are capable of existing, in so far as they are the subject matter of pure mathematics, since I perceive them clearly and distinctly.
(vii:71)Anything could exist, could be created by God, the Meditator decides, so long as there is no contradiction involved in the supposition that it is perceived distinctly. The notion of a material object that is regarded as the subject matter of pure mathematics is not self-contradictory, for there is no contradiction involved in my perceiving a geometrical object such as a triangle or a cube or a sphere distinctly. What is it, though, for a body to be regarded mathematically, to be “the subject matter of pure mathematics?”
Recall that the Meditator decided in Meditation Five that what was distinctly imagined in bodies was their “continuous quantity.” A body and its parts are characterized by the following attributes:
Extension in length, breadth, and depth
Division or divisibility into parts possessing various sizes, shapes, and positions
Motion of these parts, of various intensities and durations
Mathematics treats of objects of certain dimensions, certain sizes, shapes, and relative positions. A formula such as x + y = 2 can be represented as a line on a graph, and we can write the formula for a circle.
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