1. We about to get philosophical, yo. By Sara Parker
INQUIRY PROJECT
We about to get philosophical, yo.
By Sara Parker

2. How are math and philosophy linked?
The answer is really long. So let’s not.
We’re going to focus on one part: paradoxes.
Get ready to make your brains melt.

3. Philosophy v. mathematics
Bertrand Russell, philosopher, among other things
Martin Hairer, mathematician/Fields Medail recipient

4. Russell’s paradox
Do the set of all sets that do contain itself, contain itself?
There is a group of barbers who only shave those who don’t shave themselves. Do the barbers shave themselves? If the barbers shave themselves, then this is a contradiction because they can only shave those who don’t shave themselves.
Let R = {x | x ∉ x} then R ∈ R ↔ R ∉ R

5. TWO ENVELOPE PROBLEM
You are given two completely indistinguishable envelopes. They each contain money, but one contains twice as much as the other one. Once you choose an envelope, you’re allowed to switch and pick the other one. Should you switch?
Discuss!

6. re: two envelopes Any rationalization is completely pointless.

7. Is math really meant to be answered?

8. Absolute truths? Nah.

9. Other paradoxes Thompson’s Lamp: Sorites Paradox:
If you flick a lamp on and off an infinite number of times, is it on or off?
Sorites Paradox:
Can a single grain of sand make the difference between a heap and a non- heap?
Benardete’s Paradox:
Infinite gods, one man who wants to walk. However, these gods put up barriers (half of the way, quarter of the way, eighth of the way and so on until infinity) so the man will not be able to walk. However, if he doesn’t, then none of these barriers are raised. He is doomed to stay in one placed by unfulfilled intentions of an infinite number of bored deities.
Bedtime Paradox comic edits courtesy of Jacob Angelozzi

10. Sources:
Graham, Jacob N. Ancient Greek Philosophy. n.d. 24 October < Oppy, G.R. Philosophical Perspectives on Infinity. Cambridge University Press, Ted Ed - Jeff Dekofsky. YouTube. 16 January November < Wikipedia. Greek mathematics. 19 October October < —. List of paradoxes. 7 November November < —. Philosophy of Mathematics. 8 October October < —. Two envelope problem. 7 November December <