  But the PC does more work for Du Châtelet than just separating out the possible from the impossible, and on this point, she leans more toward Leibniz's use of this principle than toward Wolff's use of it, for the PC secondarily divides the category of the possible into truths that are necessary from those that are contingent. At this second stage, she seems to be employing a new conception of the PC. To show this, we examine her way of distinguishing between necessary and contingent truths. Necessary truths are ‘truths which can only be determined in a single way, for this is what is meant by the term necessary’ (IP §7). Immediately after this (admittedly odd) definition she contrasts necessary truths with contingent truths, ‘that is to say, when a thing can exist in various ways’ (IP §7), indicating that necessary truths are claims about things that can exist in only one way. To use her own examples to further clarify (IP §8), geometrical truths are necessary because, for example, a triangle (generally conceived) can exist in only one way, i.e., it is a figure whose three angles added together are equal to the sum of two right angles. We cannot conceive of it in any other way. Conversely, truths about the posture Du Châtelet finds herself in are contingent because she can exist in many ways, i.e., standing, sitting, lying down and so forth. Implicit here is a version of the PC which states that for any proposition P if P is or is reducible to an identical proposition, then P is necessarily true (6 above, with the modality of necessity added). For ‘triangle’ and ‘a figure whose three angles added together are equal to the sum of two right angles’ can be reduced to an identity statement (triangles can exist only in that one way) while ‘Du Châtelet’ and ‘sitting down’ cannot be reduced to an identity statement (Du Châtelet can exist in many other ways).[7] A crucial lesson to be drawn from her approach just outlined is that she takes the human's everyday experience—including our psychological inability to imagine, for example, necessary geometrical truths differently than how they are—as telling us something metaphysically true about the world itself. That is, like Wolff, she starts with a psychological rendition of the PC, but draws ontological conclusions from this starting point.