When philosopher and mathematician Rene Descartes reached his mid-30s, he decided it was time to clear his mind. He decided to go through all his beliefs and list the ones he was sure of. For this he used the 'method of doubt'. By this he ment he would throw out any belief that he could doubt -- even if the doubt was only the smallest, most unlikely possibility.
This ment that he could not trust the past, as his memories, even of the recent past, could be wrong.
He could not trust the future, as even the most predictable things could conceivably not happen.
He could not be sure of his physical environment, because dreams and hallucinations can be mistaken for reality.
Maybe even such basic truths as 2+2=4 could be false -- if the universe were ruled by an Evil Demon, it could be placing this misinformation directly into your mind! He couldn't even trust basic thought processes.
But the one thing that the method of doubt could not attack was the fact that he was thinking. Even the questioning of the actuality of his thinking was a thought.
And if he could think... He must exist!
This is where we get one of the most famous Latin phrases to ever enter into the English language: Cogito Ergo Sum.
It was a start. He wrote up his reasoning process in his book Meditations of a first philosophy. But he didn't stop there.
I think, therefore I am... But what am I? A thing which thinks.
He believed that starting with this one unarguable statement he could deduce certain other things about the universe. (Here's where we give up on logic.) He believed that some things needed to exist before you could think -- namely, God. And God (being all-good and all-knowing) wouldn't let a demon mess with your head... So he decided that you could be sure of the basic laws of math and logic. But what about your senses? They aren't part of your mind, they're part of your body. So, onto the The mind/body problem.