Complete 5 pages APA formatted article: Different Areas of Philosophy: Aesthetics, Ethics, and Mathematics. 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 the mathematics would need either to be removed or modified to reflect the change.