To What Extent Is Truth Different in Mathematics, the Arts and Ethics?

To what extent is truth different in mathematics, the arts and ethics? We have always had problems with clearly defining what truth is. It resulted into relativism, which says that there is no absolute truth. However, it can be easily shown that this theory is wrong, because in contradicts itself. Does it mean that absolute truth must exist? From my point of view, this is satisfactory proof to believe so. Where should we search for absolute truth? The first area of knowledge that seem to provide us absolute truth is mathematics, because truth is not determined by a time or place, but generally valid. Mathematics tries to describe hidden patterns and structures in our world and creates new imaginary system for that purpose. Of course, it is based only on our observations, we select the best-fitting choice. Axioms are used to describe each part of this system. They always look evident and therefore are assumed to be true without controversy. We have no reason to not to believe them, because they determine that system which we wanted to create and it satisfies not only current situation, but also the long period of time before. I would say that they are absolute truth in our relatively true system.

If we accept that these axioms are absolute truth, we are able to deduce many important structures by reasoning, which will give us better understanding of our system. We take axioms as premises and hence, also the conclusion must be absolute truth. Absolute truth in terms of the system, that describes our world best for the years. Now, when you have these conclusions, you do not need to work with axioms, but use them as premises. Or even combine the axiom with one of the conclusions, take them as premises and you can be still sure, that the conclusion will be absolute truth. This can be really useful tool, because you do not need to come back to the ground, but build on your knowledge. For me, it is really easier to take some lemmas as fact and do not worry about their validity. This access gives you advantage, because you do not need to understand all to unnecessary extent. It enables children to learn mathematics and only later they will realize that we have serious problems with proving things, which may seem clear for the child. But they will discover what is really behind those “easy” things. It is appreciated that you do not believe everything you read and try to reason common things that come as facts out, but you should keep healthy amount of skepticism. Arts is area of knowledge, where people put their emotions and feelings.

Can it provide us absolute truth? It would need to be independent from the time and place. But time and place determine our emotions and feelings. It is impossible to create a painting that would depict absolute truth. Imagine the rainforest painted by different people. One man is lost, trying to find the way back for two days and exhausted of all insects feeding on his blood. He paints his surrounding to show others those conditions. The second one just arrived there, he well-prepared and fascinated by a wonderful nature. He wants to catch untouched plants and animals moving around. Their perception is determined by their current state, so even though they have to paint the same thing, the result is different. This means that none of these paintings gives us absolute truth, they are both somehow biased. But photo seems to provide us absolute truth and it is part of an arts, too. Does it mean that we found absolute truth? I do not think so. The first thing is we have to believe all of the apparatuses inside the camera. But okay, we have camera, that captures exactly what it sees. However again, if you would let two photographers to take a photo of one object, each will focus on a different details.

And also static picture cannot give us true image of our dynamic world. We can look at arts from the other perspective, from people’s seeing this arts view. They somehow percept it and create they opinion. If this opinion would be shared thorough all people, it will become an absolute truth. But as each of us is very specific, I do not think there will ever be a work liked by all of us. And I also think that the same applies for disliking. At least the creator does not dislike it, or it is not part of an arts, but only attempt to gain audience and outrage others. There is also a lot of science in arts. For example the golden ratio is known as aesthetically pleasing. It also occurs in the nature very often. We try to put things to our creations, which are natural for us. This means that we have an absolute truth in relatively true arts. But relative truth in arts may be absolute in other areas of knowledge. For example, it was believed that crystals can have only 2-fold, 3-fold, 4-fold, and 6-fold rotational symmetry. However, Aluminium-Manganese alloys had shown 5-fold rotational symmetry on diffractogram.

In that time, Roger Penrose was experimenting with aperiodic tilings and created the one with 5-fold symmetry. Later, these explorations were linked by Alan L. Mackay, who had shown that Fourier transform of this tiling is exactly what we see on diffractogram. It resulted into considering new structure, which is ordered, but not periodic called quasicrystals. Defining what is truth in ethics is very hard, because every culture has its own rules and beliefs, so we have problems to find absolute truth. But I believe that some of these truths in ethics have heavily influenced the human nature. For example nature rights, which was established thorough the world. They are like axioms in mathematics, but we do not consider imaginary system, but whole society. One of them is “Everyone has the right to life”. You may just imagine consequences if this would be disobeyed by us. The society would not be able to work anymore. There is also relative truth, because ethics varies from culture to culture.

We can see huge difference between developed countries and people living alone in forgotten parts of the world. They may do something that would be inadmissible in our conditions and they would be accused, but there is really no other option, when they want to survive. For example, Inuit parents had put their child into the freezing winter and he was reliant to himself. Of course, he had no chance to survive and all of us would immediately condemn his parents. But we must also look at this situation from their point of view. In that moment, they had three other children and it was winter, so it was very hard to secure food and other resources needed to live. They had problems with three children and fourth one would probably mean that they will all die. Therefore it was the only logical step to ensure that they will be able to survive this winter. Unfortunately, victim was one human life. We see that we find different types of truth in these areas of knowledge. They have some shared properties, but understanding of the truth is different. It matters on how we define absolute truth – here comes the conflict between relativism and universality. I like the universality truth more, because I think that it is more open to the research.

Sources

http://fly-bypr.blogspot.com/2010/09/one-of-most-interestingunits-on-public.html http://en.wikipedia.org/wiki/Penrose_tiling