I Think, Therefore I Am

While methodic doubt has a nature, one need not hold that knowledge is impossible in order to apply the method of doubt. Indeed, Descartes’ attempt to apply the method of doubt to the existence of himself spawned the proof of his famous saying, “Cogito ergo sum” (I think, therefore I am). That is, Descartes tried to doubt his own existence, but found that even his doubting showed that he existed, since he could not doubt if he did not exist.

Criticisms

Cartesian skepticism advocates the doubting of all things which cannot be justified through logic. Some have claimed that the corresponding philosophical proposition fails the criterion of falsifiability that is associated with empirical theory.

Incontrovertible Evidence

Incontrovertible evidence is a colloquial term for evidence introduced to prove a fact that is supposed to be so conclusive that there can be no other truth as to the matter; evidence so strong it overpowers contrary evidence, directing a fact-finder to a specific and certain conclusion.

Luc Paquin

Descartes’ Method

René Descartes, the originator of Cartesian doubt, put all beliefs, ideas, thoughts, and matter in doubt. He showed that his grounds, or reasoning, for any knowledge could just as well be false. Sensory experience, the primary mode of knowledge, is often erroneous and therefore must be doubted. For instance, what one is seeing may very well be a hallucination. There is nothing that proves it cannot be. In short, if there is any way a belief can be disproved, then its grounds are insufficient. From this, Descartes proposed two arguments, the dream and the demon.

The Dream Argument

Descartes, knowing that the context of our dreams, while possibly unbelievable, are often lifelike, hypothesized that humans can only believe that they are awake. There are no sufficient grounds by which to distinguish a dream experience from a waking experience. For instance, subject a sits at the computer, typing this article. Just as much evidence exists to indicate that the act of composing this article is reality, as there is evidence to demonstrate the opposite. Descartes conceded that we live in a world that can create such ideas as dreams. However, by the end of The Meditations, he concludes that we can distinguish dream from reality at least in retrospect.

The Evil Demon

Descartes reasoned that our very own experience may very well be controlled by an evil demon of sorts. This genius is as clever and deceitful as he is powerful. He could have created a superficial world that we may think we live in.

In Meditation I, Descartes stated that if one were mad, even briefly, the insanity might have driven man into believing that what we thought was true could be merely our minds deceiving us. He also stated that there could be ‘some malicious, powerful, cunning demon’ that had deceived us, preventing us from judging correctly.

Descartes argued that all his senses were lying and since your senses can easily fool you, his idea of an infinitely powerful being must be true as that idea could have only been put there by an infinitely powerful being which would have no reason to be deceitful to him.

Luc Paquin

Cartesian doubt is a form of methodological skepticism or scepticism associated with the writings and methodology of René Descartes (1596-1650). Cartesian doubt is also known as Cartesian skepticism, methodic doubt, methodological skepticism, Universal Doubt, or hyperbolic doubt.

Cartesian doubt is a systematic process of being skeptical about (or doubting) the truth of one’s beliefs, which has become a characteristic method in philosophy. This method of doubt was largely popularized in Western philosophy by René Descartes, who sought to doubt the truth of all his beliefs in order to determine which beliefs he could be certain were true.

Methodological skepticism is distinguished from philosophical skepticism in that methodological skepticism is an approach that subjects all knowledge claims to scrutiny with the goal of sorting out true from false claims, whereas philosophical skepticism is an approach that questions the possibility of pure knowledge.

Characteristics

Cartesian doubt is methodological. Its purpose is to use doubt as a route to certain knowledge by finding those things which could not be doubted. The fallibility of sense data in particular is a subject of Cartesian doubt.

There are several interpretations as to the objective of Descartes’ skepticism. Prominent among these is a foundationalist account which claims that Descartes’ skepticism is aimed at eliminating all belief which it is possible to doubt, thus leaving Descartes with only basic beliefs (also known as foundational beliefs). From these indubitable basic beliefs, Descartes then attempts to derive further knowledge. It’s an archetypal and significant example that epitomizes the Continental Rational schools of philosophy.

Technique

Descartes’ Method

• 1. Accepting only information you know to be true
• 2. Breaking down these truths into smaller units
• 3. Solving the simple problems first
• 4. Making complete lists of further problems

Is also known as hyperbolic doubt or having the tendency to doubt, since it is an extreme or exaggerated form of doubt. (Knowledge in the Cartesian sense means to know something beyond not merely all reasonable, but all possible, doubt.) In his Meditations on First Philosophy (1641), Descartes resolved to systematically doubt that any of his beliefs were true, in order to build, from the ground up, a belief system consisting of only certainly true beliefs. Consider Descartes’ opening lines of the Meditations:

• Several years have now elapsed since I first became aware that I had accepted, even from my youth, many false opinions for true, and that consequently what I afterward based on such principles was highly doubtful; and from that time I was convinced of the necessity of undertaking once in my life to rid myself of all the opinions I had adopted, and of commencing anew the work of building from the foundation…

  – René Descartes , Meditation I, 1641

Luc Paquin

Cartesianism is the name given to the philosophical doctrine (or school) of René Descartes. Descartes is often regarded as the first thinker to emphasize the use of reason to develop the natural sciences. For him, the philosophy was a thinking system that embodied all knowledge, and expressed it in this way:

Cartesians view the mind as being wholly separate from the corporeal body. Sensation and the perception of reality are thought to be the source of untruth and illusions, with the only reliable truths to be had in the existence of a metaphysical mind. Such a mind can perhaps interact with a physical body, but it does not exist in the body, nor even in the same physical plane as the body.

In general, Cartesian thought divides the world into three areas of existence:

• That inhabited by the physical body (matter),
• That inhabited by the mind, and
• That inhabited by God.

Geographical Dispersal

In The Netherlands, where Descartes had lived for a long time, Cartesianism was a doctrine popular mainly among university professors and lecturers. In Germany the influence of this doctrine was not relevant and followers of Cartesianism in the German-speaking border regions between these countries (e.g., the iatromathematician Yvo Gaukes from East Frisia) frequently chose to publish their works in The Netherlands. In France, it was very popular, and gained influence also among Jansenists such as Antoine Arnauld, though there also, as in Italy, it became opposed by the Church. In Italy, the doctrine failed to make inroads, probably since Descartes’ works were placed on the Index Librorum Prohibitorum in 1663.

In England, because of religious and other reasons, Cartesianism was not widely accepted. Though Henry More was initially attracted to the doctrine, his own changing attitudes toward Descartes mirrored those of the country: “quick acceptance, serious examination with accumulating ambivalence, final rejection.”

Notable Cartesians

• Antoine Arnauld
• Balthasar Bekker
• Johannes Clauberg
• Michelangelo Fardella
• Antoine Le Grand
• Adriaan Hereboord
• Nicolas Malebranche
• François Poullain de la Barre
• Edmond Pourchot
• Pierre-Sylvain Régis
• Henricus Regius
• Jacques Rohault
• Christopher Wittich

Luc Paquin

Writings

• 1618. Musicae Compendium. A treatise on music theory and the aesthetics of music written for Descartes’ early collaborator, Isaac Beeckman (first posthumous edition 1650).
• 1626-1628. Regulae ad directionem ingenii (Rules for the Direction of the Mind). Incomplete. First published posthumously in Dutch translation in 1684 and in the original Latin at Amsterdam in 1701 (R. Des-Cartes Opuscula Posthuma Physica et Mathematica). The best critical edition, which includes the Dutch translation of 1684, is edited by Giovanni Crapulli (The Hague: Martinus Nijhoff, 1966).
• 1630-1631. La recherche de la vérité par la lumière naturelle (The Search for Truth) unfinished dialogue published in 1701.
• 1630-1633. Le Monde (The World) and L’Homme (Man). Descartes’ first systematic presentation of his natural philosophy. Man was published posthumously in Latin translation in 1662; and The World posthumously in 1664.
• 1637. Discours de la méthode (Discourse on the Method). An introduction to the Essais, which include the Dioptrique, the Météores and the Géométrie.
• 1637. La Géométrie (Geometry). Descartes’ major work in mathematics. There is an English translation by Michael Mahoney (New York: Dover, 1979).
• 1641. Meditationes de prima philosophia (Meditations on First Philosophy), also known as Metaphysical Meditations. In Latin; a French translation, probably done without Descartes’ supervision, was published in 1647. Includes six Objections and Replies. A second edition, published the following year, included an additional objection and reply, and a Letter to Dinet.
• 1644. Principia philosophiae (Principles of Philosophy), a Latin textbook at first intended by Descartes to replace the Aristotelian textbooks then used in universities. A French translation, Principes de philosophie by Claude Picot, under the supervision of Descartes, appeared in 1647 with a letter-preface to Princess Elisabeth of Bohemia.
• 1647. Notae in programma (Comments on a Certain Broadsheet). A reply to Descartes’ one-time disciple Henricus Regius.
• 1648. La description du corps humaine (The Description of the Human Body). Published posthumously by Clerselier in 1667.
• 1648. Responsiones Renati Des Cartes… (Conversation with Burman). Notes on a Q&A session between Descartes and Frans Burman on 16 April 1648. Rediscovered in 1895 and published for the first time in 1896. An annotated bilingual edition (Latin with French translation), edited by Jean-Marie Beyssade, was published in 1981 (Paris: PUF).
• 1649. Les passions de l’âme (Passions of the Soul). Dedicated to Princess Elisabeth of the Palatinate.
• 1657. Correspondance. Published by Descartes’ literary executor Claude Clerselier. The third edition, in 1667, was the most complete; Clerselier omitted, however, much of the material pertaining to mathematics.

In January 2010, a previously unknown letter from Descartes, dated 27 May 1641, was found by the Dutch philosopher Erik-Jan Bos when browsing through Google. Bos found the letter mentioned in a summary of autographs kept by Haverford College in Haverford, Pennsylvania. The College was unaware that the letter had never been published. This was the third letter by Descartes found in the last 25 years.

Luc Paquin

Historical Impact

Emancipation from Church Doctrine

Descartes has often been dubbed the father of modern Western philosophy, the philosopher that with his skeptic approach has profoundly changed the course of Western philosophy and set the basis for modernity. The first two of his Meditations on First Philosophy, those that formulate the famous methodic doubt, represent the portion of Descartes’ writings that most influenced modern thinking. It has been argued that Descartes himself didn’t realize the extent of his revolutionary gesture. In shifting the debate from “what is true” to “of what can I be certain?,” Descartes shifted the authoritative guarantor of truth from God to humanity. (While the traditional concept of “truth” implies an external authority, “certainty” instead relies on the judgment of the individual.) In an anthropocentric revolution, the human being is now raised to the level of a subject, an agent, an emancipated being equipped with autonomous reason. This was a revolutionary step that posed the basis of modernity, the repercussions of which are still ongoing: the emancipation of humanity from Christian revelational truth and Church doctrine, a person who makes his own law and takes his own stand. In modernity, the guarantor of truth is not God anymore but human beings, each of whom is a “self-conscious shaper and guarantor” of their own reality. In that way, each person is turned into a reasoning adult, a subject, and agent, as opposed to a child obedient to God. This change in perspective was characteristic of the shift from the Christian medieval period to the modern period; that shift had been anticipated in other fields, and now Descartes was giving it a formulation in the field of philosophy.

This anthropocentric perspective, establishing human reason as autonomous, provided the basis for the Enlightenment’s emancipation from God and the Church. It also provided the basis for all subsequent anthropology. Descartes’ philosophical revolution is sometimes said to have sparked modern anthropocentrism and subjectivism.

Mathematical Legacy

One of Descartes’ most enduring legacies was his development of Cartesian or analytic geometry, which uses algebra to describe geometry. He “invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c”. He also “pioneered the standard notation” that uses superscripts to show the powers or exponents; for example, the 4 used in x4 to indicate squaring of squaring. He was first to assign a fundamental place for algebra in our system of knowledge, and believed that algebra was a method to automate or mechanize reasoning, particularly about abstract, unknown quantities. European mathematicians had previously viewed geometry as a more fundamental form of mathematics, serving as the foundation of algebra. Algebraic rules were given geometric proofs by mathematicians such as Pacioli, Cardan, Tartaglia and Ferrari. Equations of degree higher than the third were regarded as unreal, because a three-dimensional form, such as a cube, occupied the largest dimension of reality. Descartes professed that the abstract quantity a2 could represent length as well as an area. This was in opposition to the teachings of mathematicians, such as Vieta, who argued that it could represent only area. Although Descartes did not pursue the subject, he preceded Leibniz in envisioning a more general science of algebra or “universal mathematics,” as a precursor to symbolic logic, that could encompass logical principles and methods symbolically, and mechanize general reasoning.

Descartes’ work provided the basis for the calculus developed by Newton and Gottfried Leibniz, who applied infinitesimal calculus to the tangent line problem, thus permitting the evolution of that branch of modern mathematics. His rule of signs is also a commonly used method to determine the number of positive and negative roots of a polynomial.

Descartes discovered an early form of the law of conservation of mechanical momentum (a measure of the motion of an object), and envisioned it as pertaining to motion in a straight line, as opposed to perfect circular motion, as Galileo had envisioned it. He outlined his views on the universe in his Principles of Philosophy.

Descartes also made contributions to the field of optics. He showed by using geometric construction and the law of refraction (also known as Descartes’ law or more commonly Snell’s law) that the angular radius of a rainbow is 42 degrees (i.e., the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow’s centre is 42°). He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law.

Influence on Newton’s Mathematics

Current opinion is that Descartes had the most influence of anyone on the young Newton, and this is arguably one of Descartes’ most important contributions. Newton continued Descartes’ work on cubic equations, which freed the subject from the fetters of the Greek and Macedonian perspectives. The most important concept was his very modern treatment of independent variables.

Contemporary Reception

Although Descartes was well known in academic circles towards the end of his life, the teaching of his works in schools was controversial. Henri de Roy (Henricus Regius, 1598-1679), Professor of Medicine at the University of Utrecht, was condemned by the Rector of the University, Gijsbert Voet (Voetius), for teaching Descartes’ physics.

Luc Paquin