Different Areas of Philosophy: Aesthetics, Ethics, and Mathematics - Essay Example

Defining truth is one of the most important jobs of epistemology and is even more important for defining what knowledge is. Defining truth is the same as listing the conditions under which something is true. Since early times, philosophers have talked about the two things as connected. Since knowledge and truth are so connected, and there are many ways of knowing things, there must be many ways for things to be true. If truth is objective, knowledge must also be based on objective truth, except a truth in one’s mind different from the way things actually exist. Even non-philosophers tend to think of truth as a set of objective facts existing outside of the mind. But what this means is actually the subject of a very extensive debate. A part of this debate is whether there are different kinds of truth that reflect different areas of philosophy: aesthetics, ethics, and mathematics. The different kinds of truths for these philosophical fields may occur because these different areas say fundamentally different things. It seems that truth is nothing more than something’s consistency with the system in which it is a part; the sentences “Murder is bad” and “This formula is right” are equally true in the case that the action of murder is inconsistent with a moral system or that a formula contradicts the rules of mathematics. With this definition of truth, that truth of anything is a matter of its coherence to the system, the truth of any sentence must be a matter of the sentence’s consistency to an entire moral, aesthetic, or mathematical system. This means we must see mathematics as a system in which there are no questions that cannot be answered. In this system, a mathematical theory can be true or false depending on whether its premises, or its conclusion, jive with the established truths already in the system. In the mathematical system, since it is a complete system, one can make true or false statements. Since mathematics makes up a complete system, one should anticipate any true sentence or statement about mathematics to fit somewhere in the complete system and not deny other aspects of the complete system. If truth is a sentence’s consistency with other parts of a system, one can define “consistency” to be simply the harmony between the different parts in the system. As a system of numbers, formulas, and equations, mathematics should be completely internally consistent so that it can contain truths at all. If the entire system of mathematics contained unresolved contradictions, the concept of it being a “complete” system would be lost. To illustrate, the quadratic equation in mathematics is a better expression of parabolas in graphs than, say, a Gaussian function. Substituting the quadratic equation with a Gaussian function would fundamentally change the rules of mathematic, and all of mathematics would need either to be removed or modified to reflect the change. How might one, if this definition of truth is correct, differentiate between mathematical truth and ethical, or even aesthetic, truth? A better way to answer this question might be to compare how mathematics, ethics, and aesthetics all are similar and how they are dissimilar. Of course, they are not equal in the sense of unique and universal notation. There are no single and universal systems for expressing and measuring ethical or aesthetic things in the sense that there are numbers and symbols people use with mathematical notation. Nevertheless, there are some comparisons to be made. One of the most important similarities to consider is that of systems. Systems of ethics are like mathematical systems in that they are complete systems. One can make true or false sentences and statements, like “Murder is bad” in a deontological framework similar mathematical sentences such as “4+7=11”. Such openness to sentences is characteristic of a complete system. While the person who is making the sentence must be mindful of the context, like the ethical theory one is making claims within, one can make or find sentences that are either consistent with or inconsistent with the system. An ethical statement’s truth is the same as a mathematical statement, even though there is a difference in the kind of truth one is expressing. When it comes to the aesthetic statement about art, like “This painting is good”, we are talking about something that is more abstract than a simple mathematical or ethical system, with its various normative theories. Talking about aesthetic truth presupposes answers to some very basic but troubling questions in philosophy. One of these questions deals with what exactly the aesthetic system is. Probably the best answer one can come up with is the so-called aesthetic “object”, which is still not conclusively defined by philosophers. Instead of attempting to say what the object is, just think of a magnificent artwork. This can be a painting, a statue, a musical composition, or anything traditionally classified as art. In addition, try to imagine those things that draw your senses to it and the things making it magnificent. Indeed, when it comes to any magnificent piece of art, what one finds is a logical utilization and combination of spatial (in paintings and statues) and temporal (in music) aspects coming together to generate emotional reactions. A piece of art is the aesthetic system. In that case, parts of the aesthetic system might be judged as bad or good in a very factual manner, just like parts of a mathematical or an ethical system might be given the labels of true or false. For most, art is to be judged as a complete system, with the whole being more important than any of the art’s parts. To illustrate, my friends that listen to rap music might say about the music, “This song is good”. In that case, he or she is talking about a rhythm or a memorable melody that serves as a linguistic stand-in for the whole song. Unlike my friends, my education in music has taught me more than to just associate the melody or the rhythm to the whole piece of music as a complete system. Principles we have applied to mathematical truths or ethical truths still affect art despite the increased relativity when it comes to artistic judgment. But the beginner looking at a magnificent painting does think of how the piece’s shapes harmonize with shading; rather, the beginner says the piece “is good”. Different kinds of truth model in many ways different kinds of knowing. Emotion, language, logic, and perception all are types of knowing facts (truths), and they are all connected to thoughts about of truth. For some, emotion is the standard of ethical behavior. But it is not pertinent or particularly helpful in finding out how people discover whether ethical sentences are true or not. The subject of aesthetics is similar. Since mathematics is, to some degree, a language, it is in part one way of knowing truths in mathematics. A branch of mathematics, logic is probably one of the best means to seeking truths in mathematics. But with aesthetic and ethical, the opposite is the opposite is the case. Logic lacks significance when one tries to express or come to know the ethical or aesthetic truth. Few thinkers base all of their moral philosophy on logic; those philosophers who do so are likely only doing so with the intention of removing ethics from other areas of philosophy. Mathematical truth is hardly related to perceptual ways of knowing and even less so tied to emotional ways of knowing. Perception, practically unrelated to knowing mathematics, which can be done without the help of the senses, is very important in aesthetics with music and visual arts. Language is a way of making a system, and the conceptual constructs in ethics and aesthetics real. If there were no way of knowing that involved language, ethical, and aesthetic truths would be altogether absent. Setting the conditions for truth is one of the central jobs of philosophers: important not only in its own right but also for defining what exactly knowledge is. Defining truth is the same as listing the conditions under which something is true. Since early times, philosophers have talked about the two concepts of knowledge and truth as inseparable. Whether it is ethical, aesthetic, or mathematical, truth is a matter of a system’s internal consistency. Read More