Ontology vs. Epistemology

Topics: Euclidean geometry, Non-Euclidean geometry, Mathematics Pages: 7 (2610 words) Published: November 27, 2011
Ontology deals with questions concerning what entities exist or can be said to exist. What do we know? What are we certain of? What can we prove? What is the nature of existence? Epistemology is the study of knowledge. How do we know what we know? How can we establish truth and certainty? Are their limits to what we can know based on how we come to know it? These epistemological questions when combined with ontological questions have philosophers pondering what exists and how we know it exists.

In A Certain Ambiguity, by Gaurav Suri and Hartosh Singh Bal, there was a constant question of proof. How do you go about proving something? Well the book suggests that it is only possible to prove something if you have a set of accepted axioms. An example that was often used to illustrate this was Euclidean geometry. When you have the five axioms defined and the postulates formed from the axioms you have basic geometry that you learned in high school (Euclidean). However you learn later on in the book, that if you ignore the 5th axiom than you have a whole new kind of geometry, called non-Euclidean geometry. What everyone thought they knew about geometry and axioms was completely changed by altering the original axiom. That is deep. The fact that one alteration could have that much of an effect on what mathematicians “knew” is mind blowing. Most people trust math and believe that it is flawless but if you think about it, isn’t math just created by humans. Since we, as humans, are incapable of knowing everything it would be illogical to say that we know everything about math or that what we know is one hundred percent true now and forever. Yet people continue to trust it; similar to what was discussed in my first essay about people and their belief in religion. People that believe in God “know” He exists with every ounce of their being simply based on the idea (axiom) that all this complexity we are surrounded by had to be created by someone or something. They choose to make their axiom that God exists, which makes one type of reality (Euclidean). Then there are people who chose to make the same axiom not true and they form a new reality, which results in God not existing (non-Euclidean). Two different realities can form from two different applications of one axiom.

We are able to solve mathematical problems such as proving there is no largest prime number. We can be certain in the fact that there will always be a larger prime number because we have created proofs that convince us it is true. Behind every “proof” is a set of axioms that are accepted as true whether you realize what they are or not. As proven by the discovery of non-Euclidian geometry we don’t really “know” every mathematically possibility; our minds are not capable of grasping every idea and concept about a world we can’t even prove exists.

On page 25 Adin discusses his view on the importance of certainty. “Mathematics requires proof, and proof confirms truth. I’ve always been interested in how one can be sure of something, and mathematics seems to provide the way to certain truth.” I do not agree that mathematics can provide certain truth, especially if proof can be subject to interpretation—which I will be discussing in more detail. It can pacify us and our curiosity temporarily but I would be hesitant to name anything to be “certain” in this world. Our knowledge is so limited. We are learning new “truths” and have disproven previously accepted “truths.” Even though, nothing is certain we still accept things that make sense because we have defined it as “common” knowledge. The expression two plus two equals four is certain only because the value of each of these numbers are defined. Everyone over two years old “knows” what the value the number two represents and when you count two numbers above that you reached the value of the number four and the problem is solved.

In my first essay, I explained how if all of a sudden a person was moved from a third...
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