We about to get philosophical, yo. By Sara Parker

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Presentation transcript:

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

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.

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

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

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!

re: two envelopes Any rationalization is completely pointless. https://en.wikipedia.org/wiki/Two_envelopes_problem

Is math really meant to be answered? https://intelligence.org/2013/11/04/from-philosophy-to-math-to-engineering/

Absolute truths? Nah.

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

Sources: Graham, Jacob N. Ancient Greek Philosophy. n.d. 24 October 2016. <http://www.iep.utm.edu/greekphi/#H3>. Oppy, G.R. Philosophical Perspectives on Infinity. Cambridge University Press, 2006. Ted Ed - Jeff Dekofsky. YouTube. 16 January 2014. 22 November 2016. <https://www.youtube.com/watch?v=Uj3_KqkI9Zo>. Wikipedia. Greek mathematics. 19 October 2016. 24 October 2016. <https://en.wikipedia.org/wiki/Greek_mathematics>. —. List of paradoxes. 7 November 2016. 22 November 2016. <https://en.wikipedia.org/wiki/List_of_paradoxes>. —. Philosophy of Mathematics. 8 October 2016. 24 October 2016. <https://en.wikipedia.org/wiki/Philosophy_of_mathematics>. —. Two envelope problem. 7 November 2016. 6 December 2016. <https://en.wikipedia.org/wiki/Two_envelopes_problem>.