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How to Fall in Love with Math, Manlil Suri

Reflection Paper Feb/15

Sarah Myers

Math is something I make a point of staying away from because it’s terrifying. I begin to see math as rational thought, not just drill after drill after drill like I was previously taught. So much emphasis is put on math as something to get through and get over with, not to understand below surface level by applying its rules to surroundings.

Do we all crave math? I never thought I had craved math. Maybe what he means is I crave a rational understanding of the world around me. I had never been comfortable with numbers or wanted to get to know them. But knowing things like Fibonacci numbers and how this relates to nature puts sorts of things into perspective. This relation between nature and mathematics gives reason to simple pattern and therefore increases my appreciation for math. I recognize this order in pinecones and flowers but then I notice I start to seek the pattern elsewhere in the world, this could be one way that someone would crave math. Not strictly in a numbers sense, but in pattern.

It is curious to know numbers themselves and their properties. For example: natural number, prime number, rational number, and irrational numbers. I don’t know exactly how knowing this helps but I feel that it does. I think the familiarity with the numbers themselves makes math more playful then when taught as sets of cold fact.

Not needing to understand complicated derivations is something I had not considered. Math was usually taught that you learn one thing so you know it and can move on to next, more complicated formula after. There is not time given to appreciate the simple formula because the bigger one is waiting. For whatever reason, there is some kind of structure set up that implies learning basics math is not enough. It is relief to know that basic math is just as important. Such things like the pigeonhole principle, this we may intuitively know but never have been aware that math was the reason behind it. This is how profound insights can be found at an uncomplicated level. (….though I sort of find the basics of basics math complicated). And therefore at any level, math can be appreciated. I think this is something what Manlil was getting at.

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Western Final Essay

Ideas about the Role and Education of Women

The purpose of this paper is to talking about the developing ideas concerning women’s role and education in society. The sources I will be drawing ideas from are Castiglione’s, Book of the Courtier (1528), Wollstonecraft’s A Vindication of the Rights of Woman (1792), and Condorcet’s, Future Progress of the Mind (1882).

A woman’s role in the Courtier was one of the lady of the court. She was required of many things. There were no opportunities for women of other classes at this time. Two hundred years later Wollstonecraft calls upon society to bring forth gender equality and to provide educational opportunities for women of all classes. Another twenty years later, and along the same lines, Condorcet endorses that gender equality is important and necessary for society as well as equal educational opportunities for both men and women.

In the Book of the Courtier, following ‘How To Be A Man’ there is, ‘How To Be A Lady,’ and the following is what was expected of an aristocratic woman during the 16th century. The characteristics are not in order of importance, though it is important to remember that above all a lady of the court must be a wife and a mother;1 among being formally educated; among other things.

It is already assumed that a woman be a mother, and a wife. The main occupation for a lady of the court is that she be entertaining. This is her main function, as hostess and that entails that she needs to be good at ‘knowing the audience.’1 In other words, she needs to know who is talking to, what they should be talking about, and when. She must be, do, and know everything about what a man is, does, and knows; not so she can perform but so she can talk about these things.1 In accordance with this, she must be able to keep a conversation going, and in order to do so; she must be well educated in a broad range of subjects.1 The woman of the 16th century is defined by her femininity in a way that the man is not. “…so it is well for a woman to have a certain soft and delicate tenderness, with an air of feminine sweetness in her every movement, which, in her going and staying and whatsoever she does, always makes her appear a woman, without any resemblance to a man.”1 (Castiglione, 211)

In addition to these requirements a woman must be concerned about her appearance. She should be conscious which garments enhance her grace and wear them in accordance with to the occasion. She should also be skilled in music and dance.1 There were no opportunities for education at this time for peasant women.

In Condorcet’s Future Progress of the Mind, he tells us in which direction our thoughts will expand. Condorcet’s aim was to predict which faculties of the mind would in the future be explored. “Among the progress of the human mind…”2 Condorcet begins, and then goes on to suggest we destroy the prejudices between sexes. (He believes this is necessary for happiness.) It is relevant because it calls into question what is expected of a lady of the court. Condorcet is saying that the qualifications of a man and a woman must equal one another.2 Although I did not discuss what was required of a man, I did say that the woman has to know all that is required of a man, plus be a wife, plus be a mother. In order for them to have equal expectations, the man would have to be required of more, or the women would have to be lessened of a few. The outcome, Condorcet believes, is that education will be more uniform across genders, and opportunities may be created for those to receive education other than those belonging to a higher class.2 These are the future ideas of education that he has presented.

Mary Wollstonecraft’s Vindication of Women’s Rights is a political treatise. It defends the rights for women. It brings attention to women and calls upon women to take a stand. In her title the word vindication means to justify, to defend the right of, and this is what she does. Mary believes if women are going to be good wives and mothers, they first women should be intelligent and educated citizens.3 She claims society would be better off if things were this way. Mary rejects the traditional idea of defining a women by her femininity as we see illustrated by the 16th century lady of the court. Mary does not claim women are a better gender, but instead she is asserting that men and women must be treated equal. Women do not have the same opportunities men do at this time. Mary acknowledges this fact, wants to see a change, and therefore brings the problem to light in the face of other women. She does they by calling out to women to start acting like responsible adults and demands them to quit letting others treat them like children.3 This revolutionary act was the beginning of someone telling the world to give girls a chance.

Sources:

1.Castiglione, Baldassarre. The Book of the Courtier. Garden City, N.Y.: Doubleday, 1959. Print. (207-222)

2.Marie Jean Antoine Nicolas Caritat, marquis de Condorcet, Esquisse d’un tableau historique des progrès de l’esprit humain (Paris: Masson et Fils, 1822), pp. 279­-85, 293-­94, 303­5.

3.Wollstonecraft, Mary, and Sylvana Tomaselli. A Vindication of the Rights of Men ; with A Vindication of the Rights of Woman, and Hints. Cambridge [England: Cambridge UP, 1995.

In J.S. Mill’s “On Liberty,” Mill supports the freedom of speech.9 By supporting freedom of speech, Mill supports freedom of thought, and expression. Included in free thought, and expression, is our capability to form an opinion. Is it reasonable to suppress an opinion that we disagree with? Mill argues that neither perceived nor contrary opinion should be suppressed.9 He gives us one exception, in a case where opinion brings harm to another.9 Mill is speaking of expressed opinion rather than written or published opinion.11 He is considering opinion held by all rational human beings, meaning, children are excluded from his argument. 9

I would like to argue against Mill by searching for and finding a case where other than infliction of harm, opinion should be suppressed. I will begin by explaining that there are two types of opinion. The received opinion, which is the individual’s held belief, and contrary opinion; which is opposite the held opinion.17 I could not find a good reason (other harm done to others) why opinion should be suppressed, and I agreed with Mill, because I found that despite whatever disagreement I may find in a contrary opinion, I am losing more than I can gain when I close myself off from potential truth.

Why might we want to suppress opinion? To take away power from individuals and to control society.13 We may not want to hear our opinion is wrong or we may believe with confidence that it is true.50 There is more than one reason for wanting to suppress opinion. Take the case where I am confident my opinion is absolutely true, and therefore perfect. Humans aren’t perfect yet I sometimes think I can have a perfect opinion.17 I do not think it is a good enough reason to say opinion should be suppressed if it can never be perfect. Though perfect opinion is impossible, there is something to learn from opinion.50 Mill says we can learn truth, and we can learn to refine our own beliefs.51 We refine our beliefs we seeing truth in others or falsity in our own.50 And as long as there is room for error, there is room for error to be corrected.19 I cannot disagree that I should not want to correct my error if I am searching for the truth. That would be like saying I want to have a true opinion, but I don’t want to go about the process it takes to find truth.

Mill believes opinion should not be suppressed because it may hold a small truth to it despite what falsity we might percieve.50   Any opinion I perceive at first as false, after careful consideration, may not be entirely so. 18 I cannot disagree with Mill until I have gone out and tried this for myself. Mill brings up the importance of discussion. He says in discussion we can realize our mistakes and correct our judgment when it is wrong.19 I am in agreement with Mill opinion that in suppressing opinion we lose the ability to correct its falsity. By suppressing opinion we are losing discussion; the element we need to discover new ideas.19   We are suppressing what truth an individual is able to share.

Mill believes even if we could find an opinion that was truly false, suppressing it would still be evil (bad). 18 Having an opinion that is truly false is not enough to stifle it.18 Mill’s argument is that by stifling an opinion we are stifling some sort of truth no matter how small it is or whether or not we can see it. By stifling truth we are suppressing new ideas and the ability to challenge an already perceived opinion.18

I cannot disagree with Mill because I believe the importance of being able to challenge a perceived truth and being wrong is better than not being able to challenge a perceived truth at all. Mill supports this by saying the prevailing opinion is rarely the whole truth.50

If I am in disagreement with an opinion and I want to suppress it, should I or shouldn’t I? I don’t see any truth in it, or I don’t like it, or maybe I find the opinion unreasonable. Mill has said that I won’t be able to refine my own beliefs if I do not consider the beliefs of others. Whether or not I want to hear a contrary opinion, I will be cutting out a lot of ideas by suppressing it.19 Those ideas contain an element of truth. So by suppressing opinion I miss the opportunity to gain truth.18 What if I am just not hearing any truth in a contrary opinion? I am in agreement with Mill because if I strive to find a truth with in a false opinion then I will have to keep looking for one. After he has proven that there is no perfect opinion because humans are infallible, I know there must be a truth somewhere, and it is just that I have not found it. I cannot disagree with this. A variety of opinion is of value if we wish to know about a subject in its entirety. 19

In the case where harm is inflicted on another person because of opinion, Mill agrees the opinion should be suppressed, such as the case of collective opinion in violent protest.20 In a case where life is in danger, the value of life becomes more important. This is the only example where suppressing the opinion does good. Suppression opinion for reason of disagreement is not a good reason to suppress opinion. There is more value for truth to be sought and for challenged ideas to rise than it is to stifle an opinion because of disagreement, or mild intemperance.

What if harm is not severe but intemperate? If someone is just yelling in my face about their opinion then they are not expressing it in a temporal manner. Maybe I would have to wait until we both can speak our opinions temporally, otherwise I would have a hard time hearing what is being expressed. In this case, no good is being done because neither of us understands one another; neither hears truth. Mill argues that we are inclined not to listen to opinion less temperate than our own.50 But is this a good reason to stifle the opinion? No, the opinion is still valuable. The person shouting may not realize his opinion is not being heard. He must realize his mistake so his opinion may be heard. There is much more to consider, but I did not come up with a good reason to prove Mill wrong.

Source:

Mill, John Stuart. On Liberty. Raleigh, N.C.: Hackett, 1978. 6-52. Print.

So there is a problem with advancing technology and morals…the possibility for technology advancement is unequal to our moral energy…Well I agree with this but I would like some examples. My perspective of this is only on an individual level. I actually don’t even know what it means to have moral energy.. collectively? As a species? What would that look like? Have I ever seen it before? …I thought the part about Enlightenment Culture was interesting but I did not understand it that well…could that culture reflect what is taught is being taught in Universities today? For example, it is important for me to take a course in European Renaissance but a course in Ancient African Civilizations holds little to no importance.

Mary Wollstonecraft

Western Imagination

11/13/14

Sarah Myers

Mary Wollstonecraft is arguing rights for women. She believes women should be intelligent and educated citizens first and foremost, if they are going to be good wives and mothers. She claims society would be better off if things were this way. She does not claim women are better. She claims men and women must be treated equal. Mary calls to women to start acting like responsible adults and demands them to quit letting others treat them like children. This was revolutionary because it was the beginning of someone telling the world to give girls a chance.

Philosophy 203

Nov. 11, 2014

In T.S. Mill’s “On Liberty,” Mill argues that no opinion should be suppressed regardless of certainty or falsity for there may contain a small percentage of truth to it. There are no other cases where opinion should be suppressed except for those that inflect harm on others. I will defend this argument against objections by replying to objections.

Let us consider the belief in God as an opinion. An opinion is defined by a viewpoint of some kind. Belief in God suggests one’s viewpoint. The belief in God is a valid opinion. This is the held opinion. Let us take this also as the received opinion or the opinion that we believe is true. The belief opposite the held opinion or view is known as the contrary opinion. In this case, the contrary opinion would be the disbelief in God or no belief in God. Opinions are separate but equal. They are separate for each must represents its own unique case. The contrary opinion is opposing the held opinion, but in no way is either opinion held in higher regard. What this means is no opinion is better than the other.

I have just defined the two types of opinions. Now I will make an objection against suppressing an opinion that does not involve harm to others and say why that objection is wrong. Why should we acknowledge false opinion? First, Mill argues that we should acknowledge all opinion regardless of certainty (truthfulness) or falsity. He reasons that by acknowledging all opinion I am using my judgment to the best of my ability. Secondly, there may be some truth within a false opinion. By not hearing all opinions I am suppressing not only all true opinions but also false opinions that may hold a grain of truth to them. So not only will the truth be hidden but in doing so I have compromised my judgment. For this reason opinion should not be suppressed.

What if the opinion is true but has no good reason, meaning, and accurate justification? First, we must reflect on the validity of the held opinion. We need to know why we think our opinion is true. Knowing why we think our opinion is true means having a reason to support the opinion. Support strengthens the opinion. A strong opinion communicates more convincingly its truth than does a weak opinion. Second, it is more important to know a reason than not. The reason does not need to be good, but their needs to be a reason, for the sake of supporting the held opinion. A reasonless opinion renders the opinion weak and defenseless. It is also offensive; the opinion will be communicated as if the person holding the opinion doesn’t know why he believe it to be true, and doesn’t not care. If that is the case, I am holding my opinion in the manner of a prejudice.

Mill argues it is bad for a rational being to hold an opinion in this manner, without reflecting first upon the possibility that the held opinion may be false.

Thirdly, Reflecting upon the possibility of falsity within an opinion is a way to providing reason for the opinion. For the example opinion I used earlier “I believe God exists.” A possible reason could be, “I believe this because I read it in the bible.” That is a reason. The reason makes the belief stronger. The reason allows you to show others where the truth of falsity lay; to strengthen opinion; to hold the opinion in an unprejudiced manner.

What if the opinion is irrational? First, People can have any opinion they want but they must do so by being open to reason. Second, any opinion contrary to your own is going to seem at least somewhat less temperate, it is going to make less sense to you. Therefore, irrationality is not enough to suppress an opinion. We must remember that irrational opinions, along with false opinion, may hold a grain of truth to them.

What is enough to suppress an opinion? First, When it will cause harm to others. Mill says harming people is bad, so we shouldn’t do it. Support? Beyond what is acceptable to morals? What we must ask ourselves is does this do more harm than good. Where is the line drawn? Should those who believe suppress others without this belief?

But I think I’d like to argue a case where the opposed opinion should be temporarily suppressed if it is relentless. Could this be so?

I think these two approaches are wrong.

In contrast to thes approaches. I propose the belief of God should be suppressed, in the case of violent protest.

Mill says, opinion should not be suppressed. This approach is kind of right, but wrong. Here is what I am going to do to fix those problems. these are the plausible arguments. I can understand why brilliant people would make them, but they are wrong.

I’ve just given you an argument for suppressing the belief of God. Now I am going to give an objection to this argument. What about when the belief of God promotes the harm of others, such as in the case of violent protest.

In the work On Liberty, T.S. Mill argues that opinion should never be suppressed, because ________________, but I suspect there is a case where opinion would need to be suppressed. In this argument I will attack this argument by arguing for objections and replying to further objections.

The strongest objection to this could be violent protest, and I’m going to defend it against that object and therefore his argument fails.

Opinion should not be suppressed. It is a basic assumption of this paper that Mill was right about this. But, this is a time when it should be.

Let us consider the belief in God as an opinion. An opinion is defined by a view that does not have to be based on fact. Belief in God suggests one’s viewpoint. There fore the belief in God is a valid opinion. The disbelief in God is opposite the opinion of the above viewpoint. This is known as the contrary opinion. The contrary opinion is opposing the held opinion, but in no way is either opinion held in higher regard. They are simply different ways of seeing.

Not all opinions are true. Mill argues that we should acknowledge all opinion regardless of certainty (truthfulness) or falsity. He reasons that by acknowledging all opinion is using my judgment to the best of my ability by opening my self up to be corrected. There may be some truth with in a false opinion. By not hearing all opinions I am suppressing not only all true opinions but false opinions that may hold a grain of truth to them. So not only will the truth be hidden but In doing so I have compromised my judgment. For these reasons no opinion should be suppressed.

What if the opinions is true, but has no good reason, accurate justification?

First we must reflect on the validity of the held opinion. Second, it is more important to know a reason than not. The reason does not need to be good, but there needs to be a reason. A reasonless opinion renders the opinion weak, defensive and offensive. It is as if I don’t know why my opinion is true, nor do I care. If that is the case, I am holding my opinion in the manner of a prejudice.

Mill argues it is bad for a rational being to hold an opinion in this manner, without reflecting first upon the possibility that the held opinion may be false. We need to know why we think the opinion is true, if we wish to convince others of its truthfulness. (otherwise?)

The reason may not be good but there must be a reason because if one is aware of why he believes an opinion they can then from there determine the validity of the opinion. It is important to know the reason. For example, “I believe God exists.” “I believe this because I read it in the bible.” That is a reason. The reason makes the belief stronger. The reason allows you to show others where the truth of falsity lay.

What if the opinion is irrational? People can have any opinion they want but they must do so by being open to reason. Any opinion contrary to your own is going to seem at least a little less temperate to you. Therefore, irrationality is not enough to suppress an opinion. Even It is possible for even an irrational opinion to hold a grain of truth.

What is enough to suppress an opinion? When it will cause harm to others. What we must ask ourselves is does this do more harm than good?