Introduction
While sometimes it is necessary to look at dense philosophical arguments, other times it can be helpful to look at more mundane questions. In this particular case, we will be examining something that was, in high school, anathema to many of us: geometry. Specifically, we are going to look at triangles and examine what, if anything, they can tell us about the existence of God.
What are triangles, really?
Think about a triangle. Any kind. Now that you have it in your head, think about a drawing of a triangle. Think about a triangle-shaped statue. What is the difference between the drawing and the statue vs. the triangle in your head?
Adding another layer, what would happen to the triangle on the page if you erased the drawing? Would it cease to exist? Further, what would happen if every triangle shape, everywhere, were destroyed? Would triangles still exist, even though there are no physical representations of them?
Getting Abstract
The answer to this last question is: no. The reason triangles don’t need a physical representation to exist is because they are what philosophers call abstract objects. Abstract objects are those objects that exist in a non-physical way. The same thing could be said for anything in the realm of math.
Abstract objects exist even if all of their physical representations disappear and/or if nobody believes in them anymore. Even if everyone everywhere decided that the number two, or triangles, didn’t exist, those abstract objects would still be there.
Where Do Abstract Things Come From?
This question has been a source for philosophical debate for centuries, but particularly in the past 100 years. However, consider that abstract objects, by definition, exist in a way that is non-physical. Likewise, this abstract objects must have existed at the exact same moment the universe began. (At the moment of beginning, there was a number of particles un the universe)
This abstract “realm” must be different than the physical universe. If this is true, where do abstract objects come from?
In short, we are left with only two real options: Either, abstract objects exists because they do and we will never or can’t discover the reason (sometimes called a brute fact) or they exist and are sustained by a timeless, immaterial, powerful being like God.
If triangles really exist, the best explanation for them is something like God.
Additional Material