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46766.  Fri Jan 20, 2006 6:19 am Reply with quote

From Brewer's Dictionary of Phrase and Fable
Cogito, ergo sum. Descartes' axiom. This is a petitio principii.
" I think " can only prove this : that " I think."
And he might just as well infer from it the existence of thought as the existence of I.
He is asked to prove the latter, and immediately assumes that it exists and does something, and then infers that it exists because it does something.
Suppose I were asked to prove the existence of ice, and were to say, ice is cold, therefore there is such a thing as ice.
Manifestly I first assume there is such a thing as ice, then ascribe to it an attribute, and then argue back that this attribute is the outcome of ice.
This is not proof, but simply arguing in a circle.

46775.  Fri Jan 20, 2006 6:55 am Reply with quote

Not to discredit that "simplified" explanation, but it is far from correct.
Descartes uses three steps.
First he establishes that doubt exists, and that there is a subject that doubts.
The he looks for innate ideas. Ideas that can't have been constructed by this subject. (since everything the subject constructs must be doubted, it might be wrong. (malin genie)).
He finds the idea of infinity. Here is his mestake: He claims that the idea of infinity has to be caused by an infinite object: causality: a smaller cause can't create a bigger result.
He claims that God is this infinite object.
Then he says that there are ideas of objects, of the outside world, in the doubting (thinking) subject. These can't be caused by the subject itself (since they aren't all "wanted" by the subject). They can't be caused by God, because God is by definition good, and wouldn't caus an idea of something, if this something didn't actually exist.
Conclusion: there must be a world, outside of the subject, that causes the ideas in the mind of the subject.

Descartes goes further, by claiming that the only things we can be certain about this outside world are mathematical, as measurability is another innate idea. Qualities might still be misconceptions in the mind of the subject.

Therefor the "knowable" world becomes purely mathematical and scientific.

The quote you gave is a result from simplification of the theory, and a misunderstanding, or incomplete understanding, on the part of those who tried to simplify.
I'm not saying that what Descartes said was right. (mainly the causality thing, also the fact that he has no knowledge of the subconcious), but what he does say is more correct than what Brewers claims.

46778.  Fri Jan 20, 2006 7:21 am Reply with quote

Rene Descartes (b. March 31, 1596 (La Haye en Touraine, Indre-et-Loire, France, d. February 11, 1650 Stockholm, Sweden) was the originator of continental rationalism, a philosophical approach which asserts that all knowledge may be gained through a process of deductive reasoning from a set of intuitively understood principles. In practice he accepted that this was not the case except in certain areas such as mathematics but it is not entirely surprising that his other major interest, and indeed contribution, to the modern world came through mathematics in the form of analytic geometry.

It is Descartes who was responsible for the concept of mathematical models to explain natural phenomena (the fiend). If all art constantly aspires towards the condition of music* then for Descartes all science constantly aspires towards the condition of mathematics.

The work describes what Descartes considers is a more satisfactory means of acquiring knowledge than that presented by Aristotle's logic. Only mathematics, Descartes feels, is certain, so all must be based on mathematics.

Mathematical legacy
Descartes said, "Nature can be defined through numbers."
Mathematicians consider Descartes of the utmost importance for his discovery of analytic geometry. Up to Descartes's time, geometry, dealing with lines and shapes, and algebra, dealing with numbers, appeared as completely different subsets of mathematics. Descartes showed how to translate many problems in geometry into problems in algebra, by using a coordinate system to describe the problem.
Descartes's theory provided the basis for the calculus of Newton and Leibniz, by applying infinitesimal calculus to the tangent problem, thus permitting the evolution of that branch of modern mathematics [3]. This appears even more astounding considering that the work was just intended as an example to his Discours de la méthode pour bien conduire sa raison, et chercher la verité dans les sciences (Discourse on the Method to Rightly Conduct the Reason and Search for the Truth in Sciences, known better under the shortened title Discours de la méthode).
Descartes also made contributions in the field of optics, for instance, he showed by geometrical construction using the Law of Refraction that the angular radius of a rainbow is 42° (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°).

La Géométrie is by far the most important part of this work. In The Scientific Work of René Descartes (1987) Scott summarises the importance of this work in four points:-
1. He makes the first step towards a theory of invariants, which at later stages derelativises the system of reference and removes arbitrariness.
2. Algebra makes it possible to recognise the typical problems in geometry and to bring together problems which in geometrical dress would not appear to be related at all.
3. Algebra imports into geometry the most natural principles of division and the most natural hierarchy of method.
4. Not only can questions of solvability and geometrical possibility be decided elegantly, quickly and fully from the parallel algebra, without it they cannot be decided at all.


In 1618, at the age of twenty-two, he enlisted in the army of Prince Maurice of Nassau. It is not known what his duties were exactly, though Baillet suggests that he would have very likely been drawn to what would now be called the Corps of Engineers
Though there are reasons for thinking that he may have been a soldier, the majority of biographers argue that it is more likely that his duties were oriented more towards education or engineering.

While in the school his health was poor and he was granted permission to remain in bed until 11 o'clock in the morning, a custom he maintained until the year of his death.
In 1649 Queen Christina of Sweden persuaded Descartes to go to Stockholm. However the Queen wanted to draw tangents at 5 a.m. and Descartes broke the habit of his lifetime of getting up at 11 o'clock. After only a few months in the cold northern climate, walking to the palace for 5 o'clock every morning, he died of pneumonia.

When The World had become ready for publication in 1633, upon hearing of the Church's condemnation of Galileo (1564-1642) in the same year, Descartes decided against its publication. For, the world system he had adopted in the book assumed, as did Galileo's, the heliocentric Copernican model. In a letter to Mersenne, dated November 1633, Descartes expresses his fear that were he to publish The World, the same fate that befell Galileo would befall him.

Around 1635, Reneri began to teach "Cartesian" physics. Also during this year, a domestic servant by the name of Helene gave birth to a baby girl, Francine. According to a baptismal record, dated 28 July 1635, Descartes is named the father
In a letter dated 30 August 1637 we find him apparently working out an arrangement for Francine, but strangely refers to her as his "niece"-which suggests that he did not want certain people to know that he was a father. Gaukroger suggests that despite this apparent denial of paternity, Descartes not only corresponds with Francine, but in 1637 brings her and Helene to his new home at Santpoort or Egmond-Binnen

Omnia apud me mathematica fiunt.
With me everything turns into mathematics.

It is very certain that, when it is not in our power to determine what is true, we ought to act according to what is most probable.
Discours de la Méthode

. . . thus each truth discovered was a rule available in the discovery of subsequent ones.
Discours de la Méthode

*Walter Horatio Pater (1839-94)

47289.  Mon Jan 23, 2006 12:58 pm Reply with quote


47339.  Mon Jan 23, 2006 5:20 pm Reply with quote

Nihil tam absurdum, quod non dictum sit ab aliquo. CICERO

47340.  Mon Jan 23, 2006 5:23 pm Reply with quote

Ceci, n'est pas une pipe. MAGRITTE

Last edited by mckeonj on Mon Jan 23, 2006 6:34 pm; edited 1 time in total

47350.  Mon Jan 23, 2006 5:41 pm Reply with quote

Ceci n'est pas une pipe - surely that's Magritte, not Manet?

47353.  Mon Jan 23, 2006 5:46 pm Reply with quote

Je pense, donc, je suis.

That's my translation of it...anyone know if it's true or not?

47354.  Mon Jan 23, 2006 5:49 pm Reply with quote

Natalie, it says that earlier on in the thread ;)

47355.  Mon Jan 23, 2006 5:49 pm Reply with quote

It was in Latin originally, but it sounds credible as a translation to me; and yes, it was Magritte.

47358.  Mon Jan 23, 2006 6:36 pm Reply with quote

samivel wrote:
Ceci n'est pas une pipe - surely that's Magritte, not Manet?

Yes, and I fixed it. Lapsus memoriae.

47365.  Mon Jan 23, 2006 7:23 pm Reply with quote

OK :)

47366.  Mon Jan 23, 2006 7:46 pm Reply with quote

and whilst we're on that subject...

If someone produced an illusion of a mirage what would you believe you were seeing?

Quaintly Ignorant
47367.  Mon Jan 23, 2006 8:34 pm Reply with quote

If it were an illusion of a mirage, it would not be a mirage hence being 'real' and whether it were a mirage or it were 'real' one would still believe it to have form as that is the 'function' of a mirage.

I need a paracetamol, real or placebo as long as it works the same.

47368.  Mon Jan 23, 2006 8:59 pm Reply with quote

I figure that the mirage thing is usually that shimmering, 'looks-like-water-on-the-ground-reflects-the-sky-heat-haze-phenomenon' and if you "knew what you were doing" you'd think it was just a mirage and keep moving even though the illusion might be covering something, like an actual oasis!


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