Rationalism
The view that truths can be discovered through use of reason alone as the senses can deceive us.
Empiricism
The view that only through direct sensory observation that truth can be discovered as the imagination can delude us.
Scepticism
An attitude of questioning or doubt in response to things usually taken for granted, or to views accepted as fact by others. Philosophical scepticism requires an extreme level of rigour in argument and that all statements must be supported by indisputable evidence.
Cartesian Doubt
Descartes' describes his journey through a process of radical doubt.

His tactic is to distrust every belief as long as there is any chance it may be mistaken. The only way to find whatever certainty there might be is to doubt everything and find that one thing that cannot be doubted. The beliefs that cannot be doubted will be called truths or knowledge.

First Meditation Summary 1
"Many of the things I once believed turned out false, so how can I be sure that the things I believe now are true? I will seek out a solid foundation on which to secure the edifice of my belief system."
First Meditation Summary 2
"It would be too onerous to attempt to test every single belief. So, my method will be to consider broadly the ways that form the basis of my beliefs, and see if they can be doubted [this method is now know as 'hyperbolic doubt'].

If they can, I will disregard them holus bolus as viable foundations for my beliefs."

First Meditation: Summary 3
But if I can find something that cannot be doubted, then it would seem I have knowledge. The things I believe most strenuously are on the basis of experience via the senses. Yet the senses have deceived me in the past, and so perhaps shouldn't be trusted now.

First Meditation: Summary 4
Although the sense are liable to deceive under exceptional circumstances (e.g. vision over great or small distances), under normal circumstances they seem indubitable. One would have to be mad to doubt them on this ground.
First Meditation: Summary 5
Sometimes when dreaming, I take my experiences to be veridical perceptions of a mind-independent reality. But the experiential content of dreams are at least always reflections of reality; that is, dreams must always occur in some (albeit nondescript) passage of time, place, including numbers of extended objects with properties such as colour, etc.

First Meditation: Summary 6
"So we might concluded that beliefs regarding composite objects are capable of being doubted (e.g. physics, astronomy, medicine, etc.) But beliefs concerning the most simple and general principals are certain (e.g. geometry, arithmetic, etc.

)"

First Meditation: Summary 7
But people often go wrong in mathematics, so isn't it at least conceivable that I could similarly be going astray all the time? Granted, given my belief in God, it is incongruous that He should allow me be deceived in such a way, and yet...
First Meditation: Summary 8
".

.. despite my tendency to revert to my normal state of self-confidence, it is theoretically possible that my beliefs be unfounded or non-veridical. Let us suppose, then, that, instead of God, a malicious demon has created all my perceptions out of nothing, such that, while I have been led to believe in my perceptions of a mindindependent reality, no such reality exists."

Second Meditation: Summary 1
Let's continue on with the method of hyperbolic doubt in search of an indubtiable, Archemedian point I shall therefore doubt all my senses and all that has originated from them (i.e.

memories, dreams, etc.)

Second Meditation: Summary 2
But even if all of the things that I imagine I perceive aren't real, this doesn't mean I don't exist. So long as I am being deceived into thinking the world is such and such, I must at least exist to be in this way deceived.0
Second Meditation: Summary 3
Therefore 'I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind'. i.

e. I think, therefore I am i.e. cogito ergo sum i.e.

Je pense donc je suis

Second Meditation: Summary 4
Okay, but what is 'I'? Must be careful not to presume it's more or less than I can be certain of. So let's start again: Ask what did I suppose I was before the first meditation? Then apply the method of hyperbolic doubt to it
Second Meditation: Summary 5
A man. What's essential to that? Being a 'rational animal'? (c.f. Aristotle) Obviously too complex a notion to be impervious to the method of doubt.
Second Meditation: Summary 6
Try again: what's the most obvious thing I identify as myself ? My body (*thumps chest*).

But the nature and existence of the body is susceptible to the same doubts as all objects of the senses; no joy. The soul. But what is this? If we take it to mean the animating force ('nutrition and movement'), these things have no meaning without the body :(

Second Meditation: Summary 7
Thought? Eureka! 'I am, then, in the strict sense only a thing that thinks; that is, I am a mind, or intelligence, or intellect, or reason...'
Second Meditation: Summary 8
'What else am I?' Well, not a body, it seems.

And given that what is certain cannot be better understood by considering what is less well understood, there's no point thinking about the body any further (like dreaming to learn the truth)

Second Meditation: Summary 9
With this principle in mind, let's ask what is a thing that thinks? 'A thing that doubts, understands, affirms, denies, is willing, is unwilling, and also imagines and has sensory perceptions.' Because, none of these can exist seperate from thought and so must be identical to it.
Second Meditation: Summary 10
And yet, it still seems that the things I perceive are more distinct to me than these cognitive processes. So let's think it through again..

.

Second Meditation: Summary 11
Consider this piece of wax: When it's a candle, it has a particular set of sensory qualities; But once it's melted, it has a completely distinct and novel set; And yet it is still recognised as the same piece of wax (even if we left the room while it melted). How is this possible? Can't be the senses, for there's no two sensory qualities shared between the wax in its two states, and so there's nothing for the senses by themselves to link the two distinct perceptions together. Can't be imagination, for the later state of the wax could have turned out an infinite number of different possible ways, and yet the imagination is finite and so is inadequate to the task of recognising that it's the same piece of wax formed in an unpredictably new, particular state. Therefore, the only other option (in the trilemma) is that it's the mind that constructs my perceptions of the world!
Second Meditation: Summary 12
"Seems odd, for it feels that I see the wax immediately, unmediated by the workings of the mind.

..But admittedly, although I could swear I see men walking down the street, when I think about it, literally all my senses perceive are hats and coats."

Second Meditation: Summary 13
And so, by considering the wax (and the world), I am inevitably learning more about myself. But even so, there's also the mind itself to think about directly.

Sixth Meditation: Summary
Whatever can be understood clearly and distinctly is capable of being created by God so as to correspond exactly to the way it is understood. If two things can be understood as being clearly distinct then it is good evidence that they are distinct. A human can be understood as distinctly a thinking thing and as having a body, and thus can exist without a body.