### Central to the examination of Mathematics is the debate of **PLATONISM **versus **FORMALISM.**

**Platonism**: Is a concept of math, and Truths in General, put forth by Socrates/Plato in *The Republic* as well as his other works. It’s the idea that TRUTHS with a capital ‘T’ are mere shadows compared to the FORMS–God based TRUTHS. Plato believed that math was a perfect example of this.

Take for example a circle. There is no mathematical perfect circle that exists in the real world. However we can conceive of a mathematically perfect circle and we use such a circle to perform calculations in geometry.

**In short, it’s the idea that mathematical truths exist A’Priori…prior and independent of our existence. They’re “OUT THERE” **

**Contrast this with FORMALISM;**

Formalism is the belief that we construct mathematical “truths.” Math is nothing more than elegant descriptions of the way things work, or rather the way things SEEM to work–TO US.

Some Questions we’ll be examining during our investigation of Math as an Area of Knowledge:

Do #s exist? Have they existed since the big bang? Before? If so, where do they exist?

**A Knowledge Question related to the above is as follows: **

**“In order for something to exist, it must be possible to observe it.” Do you agree or disagree with this statement? Make sure to integrate ways of knowing such as: Faith, Intuition, Emotion, Sense Perception, and language.**

The following was a question on the May 2014 exam:

### Journal:

### “When the only tool you have is a hammer, all problems begin to resemble nails” (Abraham Maslow). How might this apply to ways of knowing, as tools, in the pursuit of knowledge?

Most students would not have applied the AOK of MATH to this question, which is exactly why I want you to. Consider it within the context of explaining existence or unseen phenomena. And of course, discuss WOKS in the process as well! (journal)

### A very interesting perspective based on mathematics, “Is the Universe a Simulation?” It’s not as crazy as you think if you put your faith and trust in the AOK of Math!!!! Read the times article below:

http://www.nytimes.com/2014/02/16/opinion/sunday/is-the-universe-a-simulation.html?src=me&ref=general&_r=1

### This piece from the New Yorker titled *The Philosopher of Doomsday* is incredibly interesting and goes into more detail on Bostrom’s Work at Oxford and the *Future of Humanity Institute*:

http://www.newyorker.com/magazine/2015/11/23/doomsday-invention-artificial-intelligence-nick-bostrom

### And then we’ll watch Nick Bostrom himself go over the argument:

https://www.youtube.com/watch?v=nnl6nY8YKHs

### Journal:

### “Why is there something rather than nothing?” Read the linked PDF from Jim Holt’s *Why does the World Exist? *A work in which he examines that very question in incredible detail.

### Why does the World Exist: On Math as Platonic

For this journal, simply react to the above reading. What does it make you consider about math and existence in general. Do you think humanity will ever be able to know why there is something rather than nothing?

### The Math Presentation!!!

We’ve been examining Mathematics as a Area of knowing. Two major issues have come up:

1. Is Math discovered (platonic) or descriptive? A good resource for the, “why does the world exist” excerpt for Journal #4 !

2. Does belief in mathematics necessitate FAITH as a way or knowing? Faith and Reason? or Simply Reason?

You need to utilize a **REAL WORLD SITUATION** to come up with a **KNOWLEDGE QUESTION **that you want to investigate for your “mini” presentation.

This guide to creating amazing TOK PRESENTATIONS created by a TOK examiner is truly invaluable:

For Math, here are a few that come to mind:

**RWS: Scientists discover evidence for inflationary theory**

**KQ: Can Science Explain Existence? **

**RWS: Quantum Mechanics differs from Relativity**

**KQ: Will there ever be a “final theory” Discovered? Or is math simply describing deeper layers of existence? **

**RWS: Quantum Mechanics/Relativity/Big Bang/Expansionary Theory…all intense; far out etc. **

**KQ: To what extent does Faith as a WAY of Knowing factor into belief in quantum physics?**

Or better yet, come up with your own ! !

Here is another amazing guide to the TOK Presentation!!

http://www.timwoods.org/2013/09/13/how-to-structure-a-theory-of-knowledge-presentation/