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 one other area of knowledge. In Theory of Knowledge, the course divides into two core subjects which are the Ways of Knowing and Areas of Knowing. Based on the title, there is an extent to which the areas and ways of knowledge may elucidate the question.
The title discusses the concept of mathematical rigorous proof which involves the process of uncertainties and contradictions, if none are available then the proof exists on complete certainty. The question, in this case, is, are proofs completely certain and reliable to act as a general statement? Aren’t proofs based on a structure of logic and rely on a certain depth of axiom? All proofs in mathematics have a range of fundamental laws which are based on known axioms.
Expressions which are false and considered to be true, then used as the main subject of logic such as mathematics, are the reasons that prevent proofs from being absolutely certain. A number of mathematicians claim that axioms are self-evident and that the truth behind them can be recognized, understood and reflected upon. In the end there is a definite possibility of that axioms being wrong, contradicting the issue of absolute truth in that proof. Logic is frequently used by mathematicians; historians etc. to support and justify their subjects in arguments.
But what is logic? For humans, it’s an everyday use in our lives. For instance, suppose you were to travel for a business conference on Sunday and Today is Wednesday, and you had to get your clothes from the dry cleaner which you know will take an hour. So you ask yourself, when is the best time to get it? First, you know that you’ll be away for the weekend with your family, so that leaves out Friday and Saturday. You also distinguish that you have a date with a friend on Thursday because on the weekends you’ll be with your family.
So you conclude that the only day to go to the dry cleaner is today. You make your decision based on that logic. This is an example of your logical thinking. You state a problem, you find solutions, and at the end you come to a conclusion which all of your reasons have produced evidence to support it. Logicians divide up the subject into two parts: deductive and inductive logic from. Mathematics is a system based on deductive logic to which the core of it is axioms and where proof is obtained that. I believe in this case, Math uses the concept of logic in our present life based on proofs.
For example, if you have an equation that ends up with 1+1=x, of course you would say that that the answer is 2. But is your answer based on belief or logic from proofs. Just imagine the first person who came across to Math, weren’t theories and proofs mainly based on belief then reasoning? Have you ever asked a Math teacher, on the basis of TOK, what he/she is teaching you is based on what he believes is true, or rather what he knows is true? Has he/she been taught by authority such as us to accept the values of math and apply it as if it is applicable to every situation?
Does he/she have complete certainty of what he is teaching correct or is he/she is teaching it because he knows the subject blindfolded? As Charles Darwin said “A mathematician is a blind man in a dark room looking for a black cat which isn’t there. ” Certainty is based on a person’s strength of belief and ability to show reasoning with his/her word. As you can see in TOK, the requirements of a good TOK essay is that you can support your belief by proof and belief by opinions and backed up with facts to show your understanding and certainty of the topic.
Similarly related, is the concept of certainty about the existence of God. Is it mainly based on belief or proof, or theory, or even logic? Or is it a mutual feeling between all of them? Using the concept of axioms, if all of the theories were assumed to be true, and taught to others, and found out that at least one was false, wouldn’t it make all of assumptions of the world and the creation wrong( if each assumption was linked together)?
Ask yourself, how certain are you that all your knowledge is just based on proof, and not proof by reasoning, or vice versa? Based on past experience, I ask myself sometimes, how do I prove to myself that God really exists? Then I started to realize that from The Holy Quran, it has shown great reasoning and given me faith to believe that this universe had to be created by a powerful creature other than anything else in the earth that we know of. But have we seen God to complete that absolute truth?
Here is the answer to certainty. There is nothing that can be given and understood in complete form: there must always be an obstacle stopping us from knowing the complete truth. Does uncertainty apply to the human sciences? Well, if you look at it from a certain angle, you can see that, for example, psychology is based on observations and individual opinion for a certain period of time. Therefore, if a subject was to be analyzed by observers and examiners, wouldn’t each have a different view in their assessment?
Predicting the subject’s actions would be hard, since any written observation cannot be necessarily true. For example, if I make TAC Pete upset I would predict that he would go to his laptop and cool down; but that might not be the case. He could go and bother everyone and make their lives miserable. The point, for that a human, no matter how long you know him/her and how long he/she does a routine, you cannot be certain of his actions. After all, in the psychology there are factors that affect the results observations which are 1.
Seeing what can’t be seen 2. Being seen by the seen 3. Seeing what you want see. Scientists tend to concentrate on objects that can’t be seen, and tend to have different views of the matter. Secondly, the subject might know that he/she is being watch end and might tend to act differently towards the observer and might result into false observations. Thirdly, scientists may decide some of their observations based on what they want to see, which is of course biased.
So if all these factors affect the certainty of an observation, how can you be certain of the subject and its observations which are assumed to be true? That is why when you go to a doctor in any department (medicine, psychology, and etc. ), their answer most of the times is “I believe or I think or I assume that. ” That is because most of the time they don’t have a certain answer because of the fact that all of the research is based on predictions and uncertainty. Thus, the concept of achieving a complete level of certainty to reach the absolute truth is theoretically possible.
Even though in reality this may be never achieved, we must always keep in mind that the theoretical absolute truth is relatively different from the actual truth, as it is set up to satisfy the conditions of the universe that we cannot perceive. The main reason why we humans take absolute in a theoretical situation is because we cannot be certain of anything. Our senses fool us into making us think that it simply doesn’t matter. We don’t have the power to know the difference between the actual and theoretical truth, and there is no way to find the actual absolute truth, so we ignore it.
In life there are obstacles that a human mind may not pass through to search for absolute truth. There is a way to find the truth behind these barriers, but only to the extent of our mind’s limits.
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