Discourse on Method for Reasoning Well and for Seeking

Truth in the Sciences

Rene Descartes

(1637)

Malaspina Great Books

Original Discourse

• Optics• Meteorology• Analytical Geometry – this work is familiar to

students of modern science. It ranks with Isaac Newton’s Principia as the most important contributions to mathematical reasoning from the 17th century and the most important contribution to geometrical reasonong since Euclid

Descartes’ Epistemology

• Descartes’ Method represents a new attitude towards reasoning – an approach that if applied judiciously towards the right subjects does bare fruit.

Fundamental Questions

• What is unique about the Method?

• Does it work?

• How does it work?

• What evidence is there that the Method does work?

• What opportunities and what application areas did Descartes’ Epistemology open up?

Response

Compare the Method to conventional modalities

Examine the rules in detailOffer examples of Descartes’ reasoning as

applied to historical and contemporary problem solving

Alternate Modalities

• Descartes Method represents an early and “classical” attempt to model how systematic knowledge occurs.

• Descartes’ conjecture is that this process is formulaic or subject to a computational strategy

• Non-classical modern theorists have argued recently that there can be no such method – as such – because cognition or consciousness itself involves the action of intellectual processes that are impossible to formalize – because (simplistically) they are non-classical – meaning subject to quantum phenomena – phenomena that were unknown in Descartes’ era.

• In simple terms such processes do not adhere to the normal rules of traditional logic.

Historical Approach to “Knowing”

• Scientific – Greek Platonism

• Non-Scientific – Judeo-Christian

The Greek View

• Knowledge is a kind of “recollection” of universal ideas (or forms). These ideas are accessed through a process of reasoning called dialectic.

The Hebraic View

• Knowledge is revealed. Knowledge resides in authority and acquired through Faith (capital F)

The Competition

• Francis Bacon (1620) – admired greatly by Descartes - provided a systematic inductive mode of scientific reasoning in Novum Organum.

• This Method was very successful (and

fundamental to modern empirical approaches) but relies on sense perception

Cartesian View

• Greek & Judeo-Christian based epistemologies are set aside

• Distrust sense – Greek view relies on this• Put God aside – no a priori God• The Cartesian Approach is rooted in skepticism.

There are no forms; there is no authority; faith is inadmissible

• Unlike Bacon’s inductive approach, the Cartesian Method is fundamentally deductive

Background on Cartesian Method

• Descartes’ Method profoundly influenced by Galileo’s success and by Galileo’s censure

• Descartes intended to publish a substantive defense of the heliocentric model in 1633 in Le Monde

• Galileo was condemned by the church in the same year• Descartes (like Galileo) did not believe that Galileo’s

heliocentric views were prejudicial to religion but he worried that his own work might also be censured

• Descartes withdrew his manuscript on heliocentric reasoning

• The Discourse on Method was published in 1637 – 5 years later

Radical Nature of the Cartesian Method

• Descartes asserts that the world is knowable – God intends we know it – but the Method used must be proper

• Objective of Method: eliminate influences of opinion or systemic bias – (modern idea)

• Refuse to accept the authority of Aristotelian and Scholastic philosophies

• Refuses to accept the “obvious” authority of his own “obvious” senses

• Accept only that which is “clear and distinct”

The Matrix

• Dream or Reality

First Rule

• The first rule was that I would not accept anything as true which I did not clearly know to be true. That is to say, I would carefully avoid being over hasty or prejudiced, and I would understand nothing by my judgments beyond what presented itself so clearly and distinctly to my mind that I had no occasion to doubt it.

Second Rule

• The second was to divide each difficulty which I examined into as many parts as possible and as might be necessary to resolve it better.

Third Rule

• The third was to conduct my thoughts in an orderly way, beginning with the simplest objects, the ones easiest to know, so that little by little I could gradually climb right up to the knowledge of the most complex, by assuming the same order, even among those things which do not naturally come one after the other.

Fourth Rule

• And the last was to make my calculations throughout so complete and my examinations so general that I would be confident of not omitting anything.

Intellectual Operations in the Method

• Intuition – apprehension of simple natures

• Deduction – inference of necessary connections between simple natures

• Enumeration – process of review designed to avoid intellectual “copying” errors

• A system designed to be simple, clear, orderly and self-checking

Radical

• Clarity – all aspects of an idea when reduced to simplest form are seen

• Distinctness – the limit or boundary of simple idea is discerned; and therefore all relationships between two or more simple ideas are clearly seen as relationships between ideas and not part of the simple idea itself.

• Innate Ideas – Only innate ideas (God, first principles, etc.) can be certain; adventitious (sensation) and fictitious ideas never certain

The Foundation of the Method

• Descartes’ Method rests on a foundation built from three incontrovertible (not susceptible to doubt) and interconnected elements: 1) The doubter is; 2) Reason is; 3) God is.

• These elements are interconnected in that 3) acts as guarantor for 1) & 2)

• This explains why Descartes offers three separate “proofs” for 3)

Proofs of the Existence of God

• It is impossible to have an idea of perfection unless that idea placed by a perfect nature (p. 22).

• Proof from geometry. Existence of god more certain than existence of geometric object (p. 23).

• It is unreasonable to deny insufficiency of evidence for God’s existence. There is thus sufficient evidence for the existence of God (p. 24)

The World Exists - Dualism

• Extension (space-time) and extended substance (res extensa) represent a clear and distinct idea. The world is mechanistic and its motions (placed by god) determine phenomena.

• Dualism: thinking substance (res cogitans) – God and soul – is distinct from the world

A Hypothetical Example of Cartesian Method

• A question on the nature of the world susceptible to Cartesian method: What is the world? Is it finite? Is it infinite?

• Whatever conjecture reason currently offers will be subject to doubt (first rule)

• Divide this question into as many parts as necessary to resolve it better (second rule).

• Seek an orderly architecture to unify the distinct elements (third rule)

• Develop a mathematical description that prescribes this unity and serves as a check for the reasoning (fourth rule).

A Solution

• The world is comprised of space, time and matter (clarity). Seek distinctness with respect to these three clearly reduced elements.

• Infinite matter, time and space generate indistinct contradictions

• Bring distinctness to space and time by redefining these as bounded yet counter-intuitive elements (i.e. elements not based on senses)

• Modern relativistic physics achieves this end by defining space and time as finite and bounded and then devising a non-intuitive non-euclidian mathematical formalism to bring order to those redefined elements

Problems Unsolved by Descartes

• Relationship between infinite substance (God) and finite substance (the world)

• Relationship between the thinking soul (or mind) and the body

• Subsequent attempts to offer solutions: 1) unify Plato & Descartes (Spinoza); 2) Unify Augustine & Descartes (Malebranche); Unify Aristotle & Descartes (Leibniz).

Legacy

• Cartesian coordinate system (divide problem into simplest parts – first rule)

• Histogram• Analytic Geometry• Foundation for infinitesimal calculus (climb

up to knowledge of the most complex – third rule)

• Never accept as true unless clear – skepticism at base of modern science.