In the first Meditation, Descartes writes:
"arithmetic, geometry, and other such disciplines, which treat of nothing but the simplest and most general things... are indifferent as to whether these things do or do not in fact exist, contain something certain and indubitable."I should look more into this apparent 'truth-independent-of-reference' position, that mathematical truth is independent of the existence of mathematical entities, especially as an alternative to the Quine-Putnam indispensibility argument for the reality of mathematical objects.
Relevant secondary literature:
- Gregory Brown (in "Vera Entia: The Nature of Mathematical Objects in Descartes" Journal of the History of Philosophy, 1980:23-37) contains a nice discussion of the kind of existence mathematical objects have for Descartes, esp. section III:
"mathematical objects in particular, have a "being" that is independent of their actual existence in (physical) space or time, and that is characterized by what Descartes calls 'possible existence'"(p.36).
- Brown quotes Anthony Kenny ("The Cartesian Circle and Eternal Truths," Journal of Philosophy, 1970):
"the objects of mathematics are not independent of physical substances; but they do not support the view that the objects of mathematics depend for their essences on physical existents... . Descartes held that a geometrical figure was a mode of physical or corporeal substance; it could not exist, unless there existed a physical substance for it to exist in. But whether it existed or not, it had a kind of being that was sufficient to distinguish it from nothing, and it had its eternal and immutable essence."