Descartes' First Meditation: Mathematics and the Laws of Logic

Descartes' First Meditation: Mathematics and the Laws of Logic MARK A. OLSON 1. INTRODUCTION DESCARTES' DECEIVING GOD ARGUMENT has long been criticized as incoherent. If the Deceiving God Argument casts doubt on all beliefs, then it also casts doubt on its own premisses and, thus, defeats itself. Furthermore, among the "eternal" truths Descartes includes the law of non-contradiction. 1 So, if the Deceiving God Argument casts doubt on all eternal truths, then the law of non-contradiction must be suspended. Descartes did hold the curious view that God freely created the eternal truths and could have made contradictories true.' So it seems that, if God is a deceiver, then the law of noncontradiction is dubitable. Thus, if God is a deceiver, no argument could be formulated. Indeed, all reasoning would have to cease. It appears that historical criticisms of the argument are just. Leibniz and Hume, for example, saw Descartes' antecedent skepticism as extending to all principles and thus to reasoning itself. Leibniz charged, "if this doubt could once be justly raised, it would be straightway insuperable."3 Hume objected, A list of abbreviations for the primary sources cited in this article and a bibliography of the secondary sources cited are given at the end of the essay. ' Among Descartes' published works, the law of non-contradiction is explicitly listed as an eternal truth, as far as I can tell, only in the Principles, 1.49 (AT, 8:24.1--2 ). However, it is mentioned or implied in several of the letters listed in note ~, below. 9 This view is stated in the Fifth and Sixth Replies, AT, 8:38o. 1-13 and 435.2~-436.s5. The main texts, however, are found in Descartes' letters to: Mersenne, ~5 April 163o, AT, ~:~45-7146 .19, PL 11; Mersenne, 6 May 163o, AT, 1:149.21-15o.~7, PL 13; Mersenne, ~7 May 163o, AT, I:151.1--153.3, PL 14; Mesland, 2 May 1644, AT, 4:118.6-119.14, PL 151;Arnauld, ~9Juty 1648, AT V:~3.31--~4.17, PL ~36-7. Leibniz 1969, 385. [407] 408 JOURNAL OF THE HISTORY OF PHILOSOPHY ~6:3 JULY 1988 "The Cartesian doubt.., were it ever possible to be attained by any human creature (as it plainly is not) would be entirely incurable."4 Descartes, too, thought the argument to be incoherent, but he considered the skepticism it engendered to be curable. He thought it incoherent simply because God is not a deceiver. The cure consists in attaining a clear and distinct perception of the essence of God. This cure, however, raises the problem of the "Cartesian circle." Given the apparent depth of the skepticism engendered by the Deceiving God Argument, the problem is acute. The circle would turn on supplying non-question-begging guarantees for both the truth of clear and distinct ideas and the validity of demonstrative reasoning. Thus, the Deceiving God Argument appears to force upon the meditator two sets of problems. If the meditator is to escape the argument's grip, he apparently must solve the problems posed by an aggravated circle and the problems raised by Dcscartes's doctrine of the creation of the eternal truths.5 However, these two sets of problems are forced on the meditator in the First Meditation only if a prior question is answered affirmatively. That question is, roughly, whether or not doubting the truths of mathematics implies doubting the laws of logic in the First Meditation. Broadly conceived, this problem is whether the Deceiving God Argument of the First Meditation casts doubt on all eternal truths. To twentieth-century eyes, it seems that it would. Surely any reasons which are sufficient for doubting some necessary truths are sufficient for doubting them all. So, if the truths of mathematics, which are necessary truths, are dubitable, then so are all necessary truths, including the laws of logic. However, this assumes that all necessary truths are of the same epistemic type. So, the prior issue is, more precisely, whether the "naive" meditator of the First Meditation assumes that mathematical truths and the laws of logic are of the same epistemic type, and, if so, whether he assumes them to be of...