He presents his reestablishment of reality as a series of proofs, like proving a mathematical formula. What is the first conclusion he reaches in this search? What is the second?

Descartes first finding is that he exists because he is a thinking being, hence his famous statement: 'I think, therefore I am.' The second is that his mind is distinct from his body, that his mind stands apart from what he perceives with is senses.

Descartes - the Melted Wax

In the discussion of the melted wax, how do we "know" the wax candle at the start? What happens when the candle melts?

We know the wax by its properties, yet as the wax changes and melts, it changes its physical properties.

How do we know the melted wax is the same wax as the candle was?

Through our ability to rationally analyze the situation -- hence although our sense knowledge may produce an immediate faulty first impression that the wax has changed into something entirely different, the mind, as distinct from the body, can still obtain correct information.

What does this example help us to know better?

This establishes the true basis of all knowledge, not the body, not the imagination, but the mind alone.

What do you think of Descartes' idea of the relation between the senses and the mind?

The problem with Descartes' theory is that it goes against much of what we have learned from modern neuroscience. The mind is not separate from the body. The 'mind,' or at least the brain, can be caused to perceive or sense things in a faulty manner, for example, if the brain is physically damaged after someone...

Also, what Descartes calls the mind seems distinct from the brain, and more of a sense of the thought process in general rather than 'gray matter.' But sensory information can cause people to feel and think things incorrectly, such as in optical illusions that make a room seem larger or smaller than it is.
Attracted to Opposites

Both Socrates and Descartes use radical and extreme forms of doubter to justify the need for rational thinking. They begin assuming nothing is true, and attempt to establish 'truth' through the process of a step-by-step process. In the case of Socrates, this is accomplished through a dialectical process of discussion with a student, where the student's common sense assumptions are questioned, virtually word-by-word. Descartes uses mathematical proofs, and engages in a dialect with his mind, or with what he has established over the course of his previous writings. By showing what cannot be true, for example it cannot be true that there is no 'mind' doing the thinking, or that a piece of wax is transformed into an entirely different substance when it is melting in a candle, Descartes proves the superiority of the mind through deduction. Socrates is less systematic, rather he confronts different people, who have different assumptions about what is true, and he attempts to show why their perceptions are faulty, in his own quest for truth.

Works Cited

Descartes, Rene. Discourse on Method and the Meditations. Translated by Lafleur.

Macmillan Publishing Co.

Plato. Great Dialogues of Plato. Translated by H.D. Rouse. New American

Library/Mentor Books.