Cortney Wikle, Holly Baker, Ethan Kitzmiller, Matthew Scott, Andrea Holyoak, J. Justin Draper, Emily Fitchette, Karianne Nelson, Kelsey McIntire, Olivia Payne

Nominalism

  • We believe that rather than math existing before the establishment of the universe, the universe existed first and then we invented math to fit the universe. All math is simply our way of modeling the things that really do exist.
  • Fictionalism is the idea that math is like a story. It was made up by people and is accepted by the population. Math is not true in a literal sense, but within the story of math it is certainly true. The statement “4 is even” is similar to the saying Santa Claus lives in the North Pole. It is not literally true, but it is true within the context of the story.
  • As nominalists we believe that abstract objects do not exist. For example, numbers are abstract ideas that are simply a way of naming some quality. Four doesn’t exist by itself, but rather can be used to describe some quality.
  • We still think that math is useful, but it’s just not about truths. It is useful to help us describe the universe. We’ve made math work, so thus we’ve made it useful. So we still believe that the study of math should be pursued.

Arguments

  • We changed the model of our solar system as we discover that our model is incorrect.
  • As we make new discoveries about the universe and the solar system, we realize that we were wrong. To correct our mistakes, we update our models to make them fit what we then know. Similarly with math and other ideas, they are adapting and evolving as we discover new and more correct models.
  • Occam’s Razor- theory that whatever is the simplest explanation is the truest explanation. So numbers take away the simplest.
  • Logical reasoning is simpler than numerical reasoning. Math complicates the ideas. Taking away the symbols and numbers by inserting words and logic creates an easier to comprehend idea without the clouding of the specific numbers and formulas. The meaning behind the symbols does not get lost.
  • Mathematical objects don’t interact
  • Mathematical objects exist in an abstract realm we, obviously cannot enter. Therefore, we cannot interact with them and so our senses are not affected by them. Thus, we cannot come to know that they exist.
  • Math is simply language created by humans to define and describe the physical world.

Example: Time

  • Time is purely relative. It is based off of either the rotation of celestial bodies or the monitoring of atomic decay. Both are not necessarily fixed. We originally took time to mean a subdivision of the heavenly rotations and fixed a day to be sunrise to sunrise (or sunsets) and an hour 1/24 of the day. This was our association, not a universal truth. Then, our days are off (~365 ¼… per year) our clocks have to be constantly readjusted and time zones and so on. It is all relative and fit to the models we create and adopt.
  • They don’t stand alone. You can’t say just “three” it’s “three of something”
  • There are not exactly similar objects