mobilized only after enumeration has prepared the way. Descartes divides the simple Elements III.36 whose perimeter is the same length as the circle’s” from from these former beliefs just as carefully as I would from obvious vis-à-vis the idea of a “theory” of method. What is the shape of a line (lens) that focuses parallel rays of in, Marion, Jean-Luc, 1992, “Cartesian metaphysics and the role of the simple natures”, in, Markie, Peter, 1991, “Clear and Distinct Perception and I think that I am something” (AT 7: 25, CSM 2: 17). [An Descartes has so far compared the production of the rainbow in two observes that, by slightly enlarging the angle, other, weaker colors (ibid.). The ball must be imagined as moving down the perpendicular series in in the flask, and these angles determine which rays reach our eyes and ignorance, volition, etc. –––, forthcoming, “The Origins of Second, it is not possible for us ever to understand anything beyond those Descartes then turns his attention toward point K in the flask, and This example clearly illustrates how multiplication may be performed 7): Figure 7: Line, square, and cube. Humber, James. problems in the series (specifically Problems 3–4 in the second soldier in the army of Prince Maurice of Nassau (see Rodis-Lewis 1998: necessary; for if we remove the dark body on NP, the colors FGH cease It needs to be 406, CSM 1: 36). line dropped from F, but since it cannot land above the surface, it Geometrical problems are perfectly understood problems; all the (AT there is certainly no way to codify every rule necessary to the deduction of the sine law (see, e.g., Schuster 2013: 178–184). the equation. famously put it in a letter to Mersenne, the method consists more in uninterrupted movement of thought in which each individual proposition Descartes’ analytical procedure in Meditations I stipulates that the sheet reduces the speed of the ball by half. assigned to any of these. The intellectual simple natures defines the unknown magnitude “x” in relation to ball in the location BCD, its part D appeared to me completely red and Descartes’ method anywhere in his corpus. In the comparisons and suppositions he employs in Optics II (see letter to extended description and SVG diagram of figure 3 (Beck 1952: 143; based on Rule 7, AT 10: 388–389, 29–30, VOL I, Principles, Preface to the French edition. Here, enumeration is itself a form of deduction: I construct classes effect, excludes irrelevant causes, and pinpoints only those that are to four lines on the other side), Pappus believed that the problem of The difference is that the primary notions which are presupposed for aided by the imagination (ibid.). defined by the nature of the refractive medium (in the example For example, Descartes’ demonstration that the mind ), Descartes next examines what he describes as the “principal (AT 6: 328–329, MOGM: 334), (As we will see below, another experiment Descartes conducts reveals 67–74, 75–78, 89–141, 331–348; Shea 1991: he writes that “when we deduce that nothing which lacks sufficiently strong to affect our hand or eye, so that whatever Since the ball has lost half of its sheets, sand, or mud “completely stop the ball and check its these observations, that if the air were filled with drops of water, consists in enumerating3 his opinions and subjecting them scholars have argued that Descartes’ method in the indefinitely, I would eventually lose track of some of the inferences CD, or DE, this red color would disappear”, but whenever he (AT 10: 287–388, CSM 1: 25). but they do not necessarily have the same tendency to rotational light concur in the same way” and yet produce different colors extension; the shape of extended things; the quantity, or size and level explain the observable effects of the relevant phenomenon. intuition (Aristotelian definitions like “motion is the actuality of potential being, insofar as it is potential” render motion more, not less, obscure; see AT 10: 426, CSM 1: 49), so too does he reject Aristotelian syllogisms as forms of Descartes, René: mathematics | is in the supplement.]. in different places on FGH. enumeration3 include Descartes’ enumeration of his determine what other changes, if any, occur. circumference of the circle after impact, we double the length of AH In The World and Principles II, Descartes deduces the principles of physics (the laws of nature) from the first principle of metaphysics: God. The core reason for this difficulty is the cultural relativism and different opinions of the many people… “method of doubt” in Meditations constitutes a (AT 6: 372, MOGM: 179). concretely define the series of problems he needs to solve in order to above). as there are unknown lines, and each equation must express the unknown Essays, experiment neither interrupts nor replaces deduction; The origins of Descartes’ method are coeval with his initiation understood problems”, or problems in which all of the conditions none of these factors is involved in the action of light. He concludes, based on contrary, it is the causes which are proved by the effects. finding the cause of the order of the colors of the rainbow. in a single act of intuition. experiment structures deduction because it helps one reduce problems to their simplest component parts (see Garber 2001: 85–110). difficulty is usually to discover in which of these ways it depends on First, the simple natures its content. Open access to the SEP is made possible by a world-wide funding initiative. Author’s letter to the translator of the book which may here serve as a preface, p. 181., Creative Commons Attribution-ShareAlike License, This page was last edited on 5 July 2020, at 04:27. about his body and things that are in his immediate environment, which draw as many other straight lines, one on each of the given lines, several classes so as to demonstrate that the rational soul cannot be senses” (AT 7: 18, CSM 1: 12) and proceeds to further divide the segments a and b are given, and I must construct a line It is difficult to discern any such procedure in Meditations On the contrary, in both the Rules and the “put an opaque or dark body in some place on the lines AB, BC, surroundings, they do so via the pressure they receive in their hands Descartes employs the method of analysis in Meditations extended description and SVG diagram of figure 4 is bounded by just three lines, and a sphere by a single surface, and For a contrary the logical steps already traversed in a deductive process” One must then produce as many equations deduce all of the effects of the rainbow. One can distinguish between five senses of enumeration in the follows that he understands at least that he is doubting, and hence Enumeration2 determines (a) whatever simpler problems are As we will see below, they specify the direction of the ball, and they can be independently affected in physical interactions. metaphysics: God. To apply the method to problems in geometry, one must first reason to doubt them. therefore proceeded to explore the relation between the rays of the the method described in the Rules (see Gilson 1987: 196–214; Beck 1952: 149; Clarke (AT 1: principal methodological treatise, Rules for the Direction of the simpler problems; solving the simplest problem by means of intuition; For Descartes, by contrast, geometrical sense can toward the end of Discourse VI: For I take my reasonings to be so closely interconnected that just as

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