Descartes' First and Second Meditations
This is a pretty quick summary of Descartes' first
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I. Descartes' Method of Doubt
In his Meditations, Rene Descartes sets out to determine what sorts of things he knows and how he knows them. In order to determine this, he puts forth the following two methods of doubt:
(i) He need not examine all of his beliefs, one by one (for this may well be a never-ending task); he need only examine the very foundational beliefs--e.g., whether he can trust sensory beliefs, mathematical beliefs, etc.
(ii) If there is even the slightest possibility of a belief being false, he will reject the belief as a candidate for knowledge.
So, Descartes is trying to determine what sorts of things he knows
that his criteria for knowledge is infallibility. If there is any way
he could be mistaken about something, he will discount it as knowledge.
II. Methods Applied
Descartes applies his method in the following three ways:
1. The Senses Sometimes Deceive: Descartes reflects on the fact that our senses sometimes deceive us. When we are looking at something very small or far away, we can often be mistaken about the size or shape of the thing in question, For example, a tall building at a distance can look smaller than a short tree in the foreground. Some small things that appear to be smooth around the edges can be discovered to be jagged or curved upon closer inspection. In addition to these kinds of phenomena, there are also hallucinations, optical illusions, and after-images. E.g., a straight stick might look bent when sticking halfway out of water; pink elephants might seem to abound if you've had a sip of acid kool-aid; and a red-orange after-image can appear for awhile in your field of vision if you've just stared at the sun too long. However, Descartes admitted that even though the senses can sometimes deceive in these ways, they are usually pretty reliable. So at this point he thought that we should rule out knowledge through our senses only when it came to things that are very small or far away, or under certain abnormal conditions. This still leaves us with much that we do know (e.g., that there is a computer screen in front of you, that you have hands, etc.)
2. You Could Be Dreaming!: Descartes next questions whether we can distinguish dreaming from being awake. For example, in your dreams you are usually quite convinced that you are not dreaming. No matter how crazy your dreams may be (e.g., you may fly or breath under water in your dreams), you are usually quite convinced in your dreams that you are not dreaming. So how, Descartes asks, could you possibly be able to determine whether you are dreaming or awake right now? Thus, since it is possible that you may be dreaming right now, Descartes is going to discount many of our beliefs as candidates for knowledge. For example, you do not know that there is a computer screen in front of you, you do not know that you have hands, etc. For if you were in fact dreaming right now, then none of these things would be true. However, Descartes allows that perhaps you still know about colors and math and logic, since these will remain unchanged whether you are dreaming or not.
3. The Evil Demon: Lastly, Descartes entertains the possibility that he is being deceived by an evil demon. This evil demon could deceive him into thinking just about anything--e.g., that 2+2=4 even if in fact it didn't; that red is a particular color even if it weren't; and that tautologies (e.g., that A is not identical to A) are actually false. To illustrate: you can imagine that every time you try counting the sides of a triangle, the evil demon makes you think there are only three sides there when in fact there are, say, four. All Descartes really needs is that the evil demon could get you to do this once or twice, and your foundation for mathematical knowledge will be destroyed. For remember that Descartes' criteria for knowledge is infallibility; so if you are wrong about something once, then you could be wrong again, and so you cannot be counted as knowing it. (Modern versions of the evil demon hypothesis include: (a) brains in vats manipulated by evil scientists, (b) The Matrix hypothesis (go see the movie), etc.
After applying his methods of doubt, Descartes concludes that there is only one thing that he knows for certain. This is his famous cogito ego sum, which is roughly translated as "I think, therefore I am." For Descartes, a thinking thing is "a thing that doubts, understands, affirms, denies, is willing, is unwilling, and also imagines and has sensory perceptions." Since the demon would have to deceive something in order to carry out his deception, the deceived must exist.
Rene Descartes, Meditations on First Philosophy, Third Edition, Translated by Donald A. Cress.