René Descartes
René Descartes ( Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 - 11 February 1650) was a French philosopher, mathematician, and scientist who spent most of his life in the Dutch Republic.
Contents
Overview
He has been dubbed the father of modern philosophy, and much subsequent Western philosophy is a response to his writings, which are studied closely to this day.
In particular, his Meditations on First Philosophy continues to be a standard text at most university philosophy departments.
Descartes's influence in mathematics is equally apparent; the Cartesian coordinate system -- allowing reference to a point in space as a set of numbers, and allowing algebraic equations to be expressed as geometric shapes in a two- or three-dimensional coordinate system (and conversely, shapes to be described as equations) -- was named after him.
He is credited as the father of analytical geometry, the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus and analysis.
Descartes was also one of the key figures in the scientific revolution and has been described as an example of genius.
Descartes refused to accept the authority of previous philosophers, and refused to trust his own senses.
He frequently set his views apart from those of his predecessors. In the opening section of the Passions of the Soul, a treatise on the early modern version of what are now commonly called emotions, Descartes goes so far as to assert that he will write on this topic "as if no one had written on these matters before".
Many elements of his philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th century, or in earlier philosophers like Augustine.
Differs from Scholasticism
In his natural philosophy, he differs from the schools on two major points:
- First, he rejects the splitting of corporeal substance into matter and form
- Second, he rejects any appeal to final ends -- divine or natural -- in explaining natural phenomena.
In his theology, he insists on the absolute freedom of God's act of creation.
Influences of later thought
Descartes laid the foundation for 17th-century continental rationalism, which was later:
- Advocated by Baruch Spinoza and Gottfried Leibniz
- Opposed by the empiricist school of thought consisting of Hobbes, Locke, Berkeley, and Hume.
Leibniz, Spinoza and Descartes were all well versed in mathematics as well as philosophy, and Descartes and Leibniz contributed greatly to science as well.
Cogito ergo sum
His best known philosophical statement is "Cogito ergo sum" (Template:Lang-fr; I think, therefore I am), found in part IV of Discourse on the Method (1637 – written in French but with inclusion of "Cogito ergo sum") and §7 of part I of Principles of Philosophy (1644 – written in Latin).
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.
Universal mathematics
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.
Calculus
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.
Rule of signs
His rule of signs is also a commonly used method to determine the number of positive and negative roots of a polynomial.
Conservation of momentum
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.
Optics
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 Isaac 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.
See also
External links
- René Descartes @ Wikipedia
