math sucks

I read and reread paragraph 4 of the Third Meditation probably about 10 times and could not really get an opinion about whether one can doubt if 2 + 3 = 5. However, after reading Hatfield I landed where I thought I would on the issue.

Paragraph 4 begins by considering simple arithmetic and geometry and how the meditator seemed to see these things clearly enough to affirm their truth. She then recalls her only reasoning for doubt in such matters at 2+3=5 was the deceiving god hypothesis. It seems that when she considers the DGH she must admit how easy it would be for the deceiving god to convince her of these simple truths when they were in fact false. But then she goes into this line of reasoning that confuses the issue. She states that when she thinks about things that are so clear to her (such as her existence and 2+3=5) let whoever deceive her because he can never make it so these things are not true. Given this it seems that she does not think 2+3=5 can be doubted. However, even after this, she maintains that there is still a possibility for a small metaphysical doubt due to the deceiving god hypothesis that she still must investigate and dispell. Given this last point I feel that 2+3=5 is still slightly able to be doubted. The cogito reasoning as Hatfield points out, is able to blanket this DGH concern because of the fact that thinking about the DGH automatically proves ones existence. However, 2+3=5 is not saved in this same way. Therefore, even if it is only a slight reason for doubt, 2+3=5 can still be doubted at the end of paragraph 4. So long as the DGH survives (and it has thus far even though the meditator doubts it heavily), 2+3=5 is possible to be brought under doubt.

Wax on, wax off

Descartes poses the proposition that we know our mind better than we know the body. Initially it seems that we would know the body of something more clearly due to our sensational perception of bodily objects (pun intended). However, Descartes wishes to dispose of this notion and aims to do so by proposing first that perhaps we do know the nature of body better and using an example to eventually show that this is not the case.

Now for the wax. The meditator considers a piece of wax as an example of an bodily object in order that the investigation will be able to represent the nature of all bodies. In considering the wax, it is obvious to the meditator at first that it contains certain properties such as sound when tappen, scent, and color. However, she notices the fact that the wax's scent, shape, and sound when tapped are dispelled if the wax is melted. In addition, the newly melted wax maintains it's inherent "waxness" despite this fact. Thus, it must be something else that causes the wax to be wax. Eventually the meditator lands on only standing properties of the wax being something "extended, flexible, and changeable".

The meditator now must consider how these properties are known. The knowledge that the wax may take an infinite number of forms allows the meditator to eventually make certain conclusions as to how we know the mind more clearly. This is done as she notes that the knowledge of the wax's infinite possibilities could not be known from the imagination as one cannot imagine each and every different possibility. However, one does grasp that the wax is capable of infinite shape and it must be known by some other faculty, the mind. Hatfield lays this out in 5 steps.
1. I can grasp that this melted wax is flexiable and changeable so as to be capable of innumberable changes of shape.
2. Imagination could allow me to grasp this fact only by representing these changes by an image of each possible shape.
3. My imagination cannot represent the innummerable shapes required.
4. It is not the imagination that allows me to grasp this capability of the wax.
5. But I do grasp this capability, so it must be by a faculty other than (sense or) imagination: call it the mind itself.
Given that it is the mind itself grasping the capabilities of the wax, it is noted that whenever one learns about the nature of a body it is the mind that grasps it. Each time it is the mind grasping the concept the cogito reasoning can be taken into account and one discovers once again the existence of self as a thinking thing. Thus, in a sense, knowledge of the mind's existence is always a precursor to the knowledge of the nature of body, and the claim is made that one must know the nature of the mind better than the nature of body.
For those unconvinced of the mind discovering the nature of bodily objects, Descartes discusses the cloaked men in which we cannot see the man himself but we use our mind to infer that it is a man under the cloak. In the same way we use our mind to discover many things that our senses and imagination to not directly show us.
The conclusion drawn from the whole mess of wax is essentially that due to the nature of body being derived from the mind allows us precursory knowledge of the nature of the mind, which in essence is saying that we know the nature of the mind better. This reasoning seems to work out pretty well, however, I still am wrestling with a couple of the arguments Wilson brought up. The main argument that I could not see the answer to was that if our knowledge of the nature of the body was incorrect, why wouldn't the knowledge of the nature of our mind be even moreso incorrect? However, I suppose that argument fails when one considers that the nature of the body and mind cannot be analyzed in the same scientific fashion. Thus, Descartes' reasoning lives to see another day.

Sensation vs. Perception

In the Second Meditation it seems that the meditator states that she both does not and does have sense perception. However, a difference can be brought out between what she is referring to in paragraphs 6 and 9. For my purposes I will consider this the difference between sensation and perception. Sensation is sensing in the actual bodily definition. Perception, however, refers to the thoughts that arise in one's mind due to sensations.
In paragraph 6 the meditator states that sense perception surely does not occur without a body. Since the body has been doubted, she is stating that sense perceptions do not occur. However, it seems that she implies here that sensations as I have defined them do not occur. Clearly, without a body, one cannot physically hear, smell, touch, see, or taste. However, come paragraph 9 she is not referring to this same idea.
In paragraph 9 the meditator discusses the sense perceptions she has but recognizes she could be dreaming and thus they are all false. However, she does state that she seems to see and hear. In this sense, she is having sense perceptions as her mind tells her she is having these experiences. That is, she is having what I defined as perceptions. Whether or not she is having physical sensations, she is still having perceptions as in her thoughts she seems to have these sense experiences.
Although it seems that the meditator is being inconsistent, she is able to state both that she has and does not have sense perceptions in that she is defining them in different ways. This similar divide between the physical and intellectual sides of sense-perception is drawn out in both Hatfield and Wilson. Hatfield seems to concentrate on the idea of the mind’s experience of the senses, and Wilson notes further sensations as either a mode of thought or matter. These two ideas are separable and thus allow the meditator to discuss both without contradiction.

Archimedes point for knowledge

Archimedes sought “one firm and immovable point in order to shift the entire earth”. The idea is that given this immovable point and a long enough lever he could move anything. The narrator claims that equally great things may be achieved in the realm of knowledge if he is able to find a similar firm and immovable point. Following the First Meditation it seems that there is nothing left to be used as this point. However, the Second Mediation lays out the cogito reasoning. He realizes that no matter how much of a deceiver his malignant demon is, he is still having thoughts that are deceived. Although there may be no senses or body, as long as there is thought of these things there has to be existence. This notion of “I think, therefore I am” is to the narrator necessarily true. One’s existence is a necessity as long as he or she is thinking. This necessity is the certainty the narrator was seeking. The narrator finds no in way this reasoning could be false, which lends it to be the firm and immovable point he can achieve great things through. Now that he has his Archimedes point he can build upon it a host of knowledge. He begins to do this as he considers the wax and how he relates to it through the senses. He realizes that the senses ultimately reduce to the intellectual. In this way, the senses are built off of thought and his immovable point. So long as he has the cogito reasoning as a certainty for the foundation of his knowledge he does not have to fear the collapse of the knowledge he builds upon it.

what it is to deceive

In laying out the Deceiving God Hypothesis (DGH), the narrator discusses the possibility of an all-powerful malicious demon deceiving us by leading us to have false beliefs about ourselves and the world. For instance, we may think we have hands and that the sky is blue, but in actuality this is not the case. This possibility in turn should lead us to doubt all our prior beliefs. The question then is raised of whether this argument in turn causes us to doubt the existence of beliefs or thought itself. I find it contradictory that the argument could cause such a doubt. To deceive is to make one believe something that is not true. Beliefs in turn are thoughts. Thus, we could not be deceived if we had no thoughts. In order for the DGH to call thoughts themselves into question, the deceiving god would have to make us think that thoughts were real when they are not in fact real. However, the fact that the deceiving god makes us think this, means there must be some sort of thought to work with. The fact that the deceiving god is all powerful leads people to think that the god could make it so thoughts were not real. Perhaps this is true. However, if the all powerful being made it so thoughts were not real, he could not deceive us because deception requires the deceived being to have thoughts and beliefs. Thus, so long as the malicious demon is attempting to deceive us in all factions of our being, he cannot use his all-powerfulness to negate the existence of thoughts. If he were to do this, we could no longer be deceived.

What survives our dreams?

The dream argument interpreted either way we discussed in class relates to the idea of a painter. The narrator discusses how painters tend to paint pictures based on things that exist. However, it may be possible that a painter paints a picture of something that is completely fictitious. Even if this is the case the colors which the painter uses would still be real. Here is where the narrator sees the dream argument to end. It seems that while we may be able to dream of something completely fictitious there is a certain category of things that we dream that are indubitable facts. This class according to the narrator includes color, shape, quantity, time, etc. Thus, it seems that studies of composite ideas such as “physics, astronomy, and medicine” do not survive the dream argument, disciplines such as “arithmetic, geometry, and other subjects of this kind” survive the dream argument. This is because they consist of the most basic things. In other words, the narrator feels that we may be able to dream up fictitious beings or objects and thus we cannot trust any beings or objects to be real. However, the most basic concepts such as shape and number is not something that can be dreamt up. We cannot dream of a fictitious number or shape. Thus, when considering shape and number while awake, we have no reason to doubt the reality of it. This works even with either interpretation of the dream argument. One the one interpretation, the narrator states that we cannot tell if we are awake or not. However, if one cannot doubt these basic things in a dream it does not matter if we are awake or not. On the other interpretation we again do not have reason to doubt these things in our dreams, so there is no consideration of whether we should doubt these things in the same way we doubt them in our dreams. Thus, “arithmetic, geometry, and other subjects of this kind” seem to survive the dream argument.

Certainty: Is It Even Attainable?

It may sound like an avoidance of the question, but I find that certainty is only necessary when one wants to be certain, which is not very often. Life tends to be unpredictable as a rule. Thus, people have learned to accept knowledge that is less than absolutely certain. If certainty was often called for, progress would rarely be made. Science tests and retests theories and drugs in order to be as sure about findings as possible. However, certainty in the sciences seems unattainable. In the legal system, society often wishes to be as sure as possible about a verdict. Once again, indubitable truths are a far reaching goal. We live in a world of uncertainty. It is a part of being human. While certainty would be convenient at times, it is not necessary. We have been able as a species to progress immensely based on being relatively certain about truths and having faith in people. Descartes finds that in order to form anything lasting in the sciences he must tear down all his previous opinions in order to rebuild from the foundations of his knowledge and to ensure certainty. However, much has been found in the sciences without this certainty Descartes seeks. In actuality I am not fully convinced that absolute certainty exists. On the one hand, I am certain that 2 + 2 = 5, but on the other hand, I question what that means given that the number system was developed by man. I could say I am certain that I ate a bagel at brunch today, but what does that matter? I find that while one may be certain about simple facts, when it comes to general propositions in the world it may be unattainable. Attainable or not, however, I feel that certainty is not necessary.