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ToK essay .5/1

Blogs > kdog3683
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kdog3683
Profile Blog Joined January 2007
United States916 Posts
Last Edited: 2008-01-11 10:24:12
January 09 2008 02:14 GMT
#1
Prompt: Mathematicians have the concept of rigorous proof, which leads to knowing something with complete certainty. Consider the extent to which complete certainty might be achievable in mathematics AND at least 1 other area of knowledge.

The issue raised in this prompt of 'complete certainty' strikes at the very core of justified true belief and essentially, knowledge itself. It implies that we know something beyond doubt, that it is essentially a priori. However, there is a hypothetical flaw in knowing completely. The question of our consciousness denies it because we can never know if we are truly conscious. If we are not conscious, than what we are thinking is merely a figment of our imagination. If our thinking is from our subconscious, that means the certainty derived from that thinking is also derived from our subconscious, so thus, that certainty can not be real because it is merely generated by our subconscious. Nevertheless, I feel lucid despite drowsiness, my neck itches, for the sake of this essay, this problem of never attaining "true complete certainty" can be ignored because you cannot prove the opposite of being false.

However, what we can do is to split complete certainty into categories, global certainty, and individual.
Thus, herein, lies the motive for a difference between individual certainty and global. A colorblind man may be convinced grass is blue. Isolated, his only means are to rely on his sensory and if his sensory says grass is blue, then for that individual, it is 100% completely certain to be blue. The same applies for a child. Conditioned everyday to believe god exists, seeing his caretakers as believing in this god, than he too will be completely certain god exists.

However, let us now take these two subjects, the colorblind man and the godfearing child; let us take their individual complete certainty and transpose them from isolation into population. The global certainty now contends with their own certainty.

"Mathematicians have the concept of rigorous proof, which leads to knowing somthing with complete certainty." In response to the prompt, it would seem the extent to which CC can be achieved is very high. However, it is only a pseudo-CC, a false imitation of the real.

Consider the analogy of mixing different colors. After mixing yellow and blue repeatedly, a distinct new color is created. Nobody knows what this color is; all they know is that every time blue and yellow are mixed together, this color manifests. And so, they name it 'green' and is titled as its very own color. Essentially, this is the process of creating math. We create words which symbolize certain procedures or things. For example, a man could say I have an apple, apple and apple. Another man would simplify, and say "You have 3 apples." Having created a system to represent this pluralness, it can now be operationalized it. Logically, if i have apple, apple and i give you apple, I only have an apple left. The man with the system of counting would say "Since I have 2 apples and gave you 1, I only have 1 apple left." A name can now be created for this component of the system; Addition and subtraction. This can then be further operationalized to multiplication and divison, exponentials and etc. Essentially, the world of mathematics is built up on itself. If even one rung of the mathematical ladder is constructed incorrectly, then the entire system crumbles. Thus, that is how mathematics is able to have CC. If it can be proved that the "rung" in question does not cause the ladder to crumble, then it like "green", is titled as a new element and can be added to the library of information to cross reference potential 'rungs' (theories).


A very famous problem in math is Fermat's Last Theorem. ...True, within the system of vigorous proof, Andrew Wiles was able to conoct a veritable proof. However, can it be completely certain/ Could there not be a variable in the procedure which is based outside his framework? Following this logic, since gravity applies in our world, every inch of our world, it must applie every where. Thus, gravity applies on the moon? Can we know for certain that gravity applies on the moon without ever having tested it? Herein lies the problem of complete certainty in mathematics. Vigorous proof is the method to bypass an infinteless gathering of empirical data. 5^3 + 4^3..no, 5^4... etc. Vigorous proof is the only method available and it is always correct. THe problem of the matter is that this correctness does not create CC.

However, there is the counterclaim that it is very hard to know math with CC. Take for exampl sqrt 2. The answer is 2. That is CC. However, that is not the only answer. There is also -2. The concept of infinity


Whereas Mathematics is able to have a pseudo-CC, the author believes the extent to which this CC is applicable to history is nonexistent.

the useful component of mathematics is it that is a perfect language. Each symbol has one meaning, and if it has more than 1 meaning, those meanings are justified through the logic of the system. For example, referring back to the color analogy, if blue + yellow is green and yellow and Red is orange, than orange - red + blue is also green. Removing the asthetic beauty of mathematics which is not relevant to it's role as a language, there is no emotion, nothing to bias the reader. A writer of math has no method to show bias because his writing is deemed incorrect if it violates the system. The concept of perception does not exist because perception is based on emotion, and enviorment, two aspects which are not present in math. there are those who are "magician" and can see colors associated with certain numbers, which allow him to say 3 is ugly and 7 is beautiful, but when asked to add 3 and 7, no matter whether the 3 is ugly or beautiful, the answer will always be the same. 10.

History on the otherhand, is written in an imperfect language. Unlike mathematics, it is not built up one step at a time. the reason for its imperfection is that
Taken to the fullest extreme, history is fiction. No different from a children's book. many critics have labeled
"the da vinci code" as unnerving in its blend between fact and fiction.

My 7 + 3 will always = 10 just as your 7 + 3 will always equal 10 because we are both operating under the same system. However, your memory of 1993 will be different than my memory of it. What you remember and see may totally differ from what I see. History is essentially the written tale of what was remembered, how it was remembered, and why it was remembered. But to generalize even further, history is every part of life that is not this exact second of conciousness. For each individual, from the point of his birth to his death, is his history. However, is it fair to say his version of his history has the most legitimacy? Everyone is subject to holding bias whether they are concious of it or not. a autobiography may choose to omit information which the writer does not want others to know whereas a impersonel author will choose to include every aspect. the same holds true to all writings of history. an easily viewed example would be the Rape of Nanking. In chinese textbooks, it is vilified to the extreme; the japanese soldiers portrayed as monsters who defiled the very soil they invaded. To this day, the middle aged era still holds a grudge against Japan for having never apologized.

Additionally, what the USA labeled the "Tian an men Square Massacre" is extremely angering for myself. In 9th grade history, we analysed the connotation of the article and it was extremely negatitive. Words such as "innocent college students, non-vionlent protest" struck symapthy towards those who . personally, it is angering because the U.S article, in English is not meant for or accessible to the chinese, but rather its own populace. My uncle and aunt say that it was necesary. That when college students are tricked by those who wish to have a coup de tat, that when wielding weapons must be taken at force.

Once again, this problem of subjectivity arises. Can we ever have a 'correct' answer? On multiple-choice history tests, it would seem there is a 'correct answer.' however, that answer is merely a label and not a true, indepth answer. In mathematics there are multiple answers as to the reaasoning why 7+3 equals 10, that are all completely verifible. In History, the reasoning behind the answers becomes unclear because depending on the language, either side could be considered.

there is often the stereotypical view that our age-old history books hold the truth necessary to understand the world. True as it may be, this 'under standing of the world' we are given is based on its author, who is no different from any other human in his need to survival, who is influenced by his life, influenced by every single aspect around him from the color of the weather to his editor pressing him for a selling book. A wonderful example of the corruption of history is that everybody's answer is correct even though everybody knows their answer may not be correct, they use it. ( I use everybody in a very vague sense, but mainly applying to the status of rulers) Take a map of the USA. Concidentally enough, it's located in the middle. China's soemwhere off in the distance. many miles east of new york. take a map of china, we have the exact reciprocal. the paradox is both maps have the exact same content, and are both perfectly accepted, yet have differnet looks. this can be attributed to many factors - hubristic pride, pride for country, but additionally to the nature of human beings, the need to make order out of chaos. To start with what is known, and work outward, to start with the home region, and expand. Thus, the home state, is the reference point to the rest of the world. Because the home state is the CC.

not finished, 1 hr 15 + chat time = 45 min. 6:15, break !resume after dinner.

*
Multiply your efforts.
nA.Inky
Profile Blog Joined October 2004
United States794 Posts
January 09 2008 03:06 GMT
#2
This seems kind of verbose so far. I think you could more directly answer the question. I like your idea of comparing history to math, but I would be more direct about the differences.

I like where you are going with human "subjectivity." You could be building a critique of Enlightenment thinking here.

My humble 2 cents.
Email (use instead of PM): InkMeister at aol dot com AIM: InkMeister
Jibba
Profile Blog Joined October 2007
United States22883 Posts
Last Edited: 2008-01-09 03:33:55
January 09 2008 03:26 GMT
#3
I think good historians do a pretty decent job of taking into account human credibility when they "record" history. This isn't the case when history is written by the victors, but in more recent times (primarily the 20th century) it has really been developed.

But you're right, there is no pure, perfect history. It's a story pieced together through as many different points of view as possible. An excellent example would be Microsoft's photo merging software they were developing a few years ago, that took many different photographs of the same thing (Sistine Chapel I believe) and tried to recreate it based on everyone's different angles. That's essentially what history is.



Everyone's probably seen it before but it's just so neat. o.o
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