Method, Ordinality, Doubt, Mathematics

In #V of the Rules, Descartes asserts that "order" is the essence of Method.  Now, Order is typically expressed by Ordinal numbers, often represented as a sequence of Cardinal numbers.  Thus, his Method of Doubt is governed by Ordinality, not only as evinced by the passage in part II of the Discourse, in which he summarizes "The first . . . the second . . . the third . . . the last", but by his mere enumeration of chapters in both that work and the Meditations.  Furthermore, the Ordinal principle by which any nth term transitions to the (n + 1)th is the basis of Addition, and, hence, of all Arithmetical operations.  Thus, even as Descartes is subjecting Mathematics to his Method, he is presupposing the truth of its propositions.  Indeed, both his evil God and his good God, are likewise governed by Ordinality.

Clear and Distinct

Some scholars attribute to Descartes the thesis that being 'clear and distinct' is a characteristic of a 'true' idea, one which they analyze as being defended by 'circular' reasoning.  Now, that thesis is implicitly expressed in the Rules, and hence, without defense.  However, in part IV of the Discourse, he asserts that "things which we conceive clearly and distinctly are all true--remembering, however, that there is some difficulty in ascertaining which are those that we distinctly conceive".  Furthermore, in the Third Meditation, he explains that an idea that is perceived clearly and distinctly is a true idea only if it is not the product of a deceiving God.  So, at minimum, these passages suggest that his concept of 'clear and distinct' is dubious as an indication of Truth, and the difficulty is to glean from them whether or not it is wittingly so.  At face value, they do express a reconsideration of that status of the concept, in which case there is no circularity involved.

Deception and Incorporeality

The possibility that Descartes is an incorporeal being enters the Meditations in two ways--as an inference from the example of dreaming, and as a consequence of the hypothesis that God is evil.  But, the inference from dreaming is invalid.  For, the deception in dreaming consists in a discrepancy between two corporeal scenarios, e. g. between one running, and one sleeping in a bed with legs twitching.  Thus, the extrapolation to a discrepancy between a corporeal scenario and an incorporeal one is ungrounded, e. g. a brain in a vat is as much a corporeal entity as the full body that it is stimulated to imagine.  Furthermore, once the hypothesis that God is evil is refuted, in the Third Meditation, so, too, is part of the consequence of that hypothesis, namely, the thesis that Descartes is actually an incorporeal entity.  So, Mind-Body Dualism does not follow in the Meditations from a rigorous exercise of his Method, but it could reflect a prejudice central to his Theological affiliation, i. e. the separation of Soul and Body.

I Think, Therefore God Exists

Descartes' famous phrase, 'I think, therefore I am', appears in the Discourse on Method, but not in the Meditations, not adventitiously, but because it is a stage in the former, but not in the latter.  In the Discourse, 'I think', via the irreducibility of the application of the method of Doubting, is the first certainty at which he arrives., from which 'I am' follows.  In contrast, in the Meditations, the axiom is 'I exist', derived from 'An evil God may be deceiving me', via the irreducibility of the deceived 'me'.  From there in the Meditaitons, he next proves that 'I am a thinking being', which supplies him with the proposition 'I have a thought of God', which serves as the premise of both the Third and Fifth Meditations, in proofs of the existence of God.  Furthermore, the topic of the Fourth Meditation--"Of the True and the False", extends the one of the Theological concepts--Perfection--of the Third, i. e. in establishing that because God is perfect, and deception involves imperfection, God is not a deceiver..  So, while the staple in academic curricula is the more explicitly Theological of Descartes' two mature works, his greater influence, not only on the popular image of him, but in the primacy of Epistemological methodology--Empiricism, Rationalism, Phenomenalism, Transcendentalism, Phenomenology, etc.--in subsequent Modern Philosophy, stems from the other book.  In other words, the Discourse presents his Philosophical innovation, while the Meditations merely continues the Medieval tradition of subordinating Philosophical methods to Theological purposes, i. e. its primary theme can be expressed as 'I think, therefore God exists'.

Will, Thinking, Proof

Insofar as Will is a species of Thinking, as it is in the Meditations, it is bound by the laws of the Intellect.  So, for example, on the basis of that classification, it is logically impossible to doubt the existence of God once that is proven in the Third Meditation.  In contrast, insofar as Will is independent of Thinking, as it is in the Rules for the Direction of the Mind, its operations, e. g. Doubting, Disbelief, Denial, etc. are not bound by the Law of Contradiction.  So, for example, on that basis the result of the Third Meditation does not entail the indubitability of the existence of God.  Thus, though Descartes never explains the subsumption of Will under Thinking in the later work, it does eliminate from its development a profound complication.

Doubt and Freedom of Choice

As has been previously discussed, in the earlier Rules, Belief and Disbelief are modes of Will, which is independent of Thinking.  So, prior to the subsumption of the former under the latter, the Cognitive problem of Doubt vs. Certainty is a Volitional one of Freedom of Choice vs. Necessity.  Accordingly, the quest for Certainty is a quest for Necessity, with the result that Freedom of Choice is Necessary, anticipating Existentialism, especially Sartre, by several centuries.  Likewise, in hindsight, Descartes' subsequent reliance on the archaic, eventually repudiated, Proofs of the Existence of God, seems a crutch for his consequent innovations in Mathematics, though, more charitably, in the historical context, his Theology can be interpreted as functioning as parental assistance in a baby learning to walk.

Belief, Doubt, Will, Thinking

At first glance, the Rules for the Direction of the Mind and the Meditations are complementary--the former expounds the Axiomatic Method, i. e. the derivation of compound propositions from a simple one, while the Method of Doubt in the latter supplies the Axiom.  So, the introduction in the later work of the Cogito as that ground of all Knowledge constitutes no conflict with the Rules, in which it does not appear.  However, the status of Doubt seems to shift significantly between the two projects.  For, while in the later, it is plainly a cogitation, at the end of Rule III,  Belief or non-Belief is "an action not of our intelligence, but of our will."  Now, in the Second Meditation, a thinking being is one which "doubts . . . affirms, denies, wills . . . ".  So, apparently a fundamental difference between the two works is the classification of Will, i. e. as a species of Thinking, or not.  Still, the later subsumption, i. e. of Will under Thinking, does not, in itself, repudiate the earlier insight that withholding Belief, and, hence, Doubting, is Volitional.  It just indicates that the more immediate result of the Second Meditation is 'I will, therefore I am, via 'I cannot disbelieve that I am disbelieving', and prior to its generalization into 'I think, therefore I am'.