James Robert Brown: Thought Experiments Reveal Mathematical Reality

James Robert Brown (University of Toronto) argues for mathematical Platonism and examines the Continuum Hypothesis He examines moral realism, the nature of mathematical objects, and debates free will versus physics while probing Platonism and alternative foundations.- 00:00:00 - Introduction- 00:01:17 - The connection between mathematics and ethics- 00:03:05 - Mathematical concepts that are interpreted solely physically (thick and thin concepts)- 00:16:33 - The continuum hypothesis- 00:19:23 - A counter proof to the continuum hypothesis- 00:24:45 - What's possible can have probability of zero (measure zero, technically)- 00:33:50 - Platonism and "thick" mathematical concepts- 00:34:39 - Moral realism / objectivity, without God- 00:36:59 - Does 2+2=5?- 00:40:43 - Moral intuitions as serving a marker for what's "correct"?- 00:46:42 - What's makes some theory correct beside its ability to predict / explain?- 00:47:54 - Does libertarian Free Will exist, and how is it coexistent with physics?- 00:53:13 - VIEWER TEST: Platonism test for the audience- 00:54:53 - Did Shakespeare invent Hamlet, or discover it?- 00:56:09 - What created the Platonic world?- 00:57:42 - Eternal vs Sempiternal- 00:59:12 - Thought experiments as a tool of probing physics, without experiment- 01:00:39 - Galileo's thought experiment demonstrating objects fall at the same rate despite different masses / heaviness- 01:03:39 - Thought experiment demonstrating relative motion (invariance of physical laws given uniform motion)- 01:05:01 - The Tower thought experiment demonstrating the opposite of the above- 01:09:43 - VIEWER TEST: Are you a Newtonian absolutist, or a Leibnizian relationalist?- 01:12:45 - Why did Prof Brown go into the philosophy of math, instead of directly into mathematics (or physics)?- 01:13:20 - Have any philosophical problems ever been solved?- 01:14:47 - Is God good? Or is goodness independent of God?- 01:15:41 - Descartes vs Leibniz on God's power (God can do anything -- except what's logically impossible)- 01:18:43 - The parochial view of physicists / mathematicians to dismiss what they can't define- 01:22:31 - Thought experiment from Newton regarding the necessity of space- 01:24:45 - Einstein's variation on the above thought experiment- 01:28:17 - How to classify thought experiments- 01:31:35 - Prof. Brown's thoughts on Wolfram's TOE and Eric Weinstein's TOE- 01:32:40 - Nicholas Gisin's thoughts on real numbers, and free will- 01:33:02 - What other foundations are there to physics, other than classical logic?- 01:39:05 - What does Mathematical Realism look like when it's NOT Platonic?- 01:45:31 - The physical laws themselves as abstract entities, which have causal power- 01:55:55 - Lee Smolin's Principle of Precedence as a bridge between Platonism and non-Platonism- 01:59:01 - Deriving an "ought" from an "is"- 02:03:29 - What does James not like about Sam Harris?- 02:06:45 - Is Math discovered or invented?- 02:10:18 - Does Platonism entail some idea of a God?- 02:14:49 - Theism vs Deism- 02:16:34 - On the Sokal Affair and the trouble with Postmodernism- 02:22:01 - Limits of free speech?- 02:27:41 - The problem of commercializing research- 02:33:09 - On Jordan Peterson's "Darwinian" definition of truthSPONSORS:- Patreon: https://patreon.com/curtjaimungal- PayPal: https://bit.ly/2EOR0M4- Twitter: https://twitter.com/TOEwithCurt- iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802- Pandora: https://pdora.co/33b9lfP- Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e- Google Podcasts: https://play.google.com/music/listen?u=0#/ps/Id3k7k7mfzahfx2fjqmw3vufb44RESOURCES:- Graphics are included in the YouTube version to make it easier to comprehend: https://www.youtube.com/watch?v=NV7BQZy1A6o- http://betterleftunsaidfilm.com Theories of Everything with Curt Jaimungal features long-form, technically detailed interviews with leading researchers in physics, mathematics, consciousness, and philosophy, exploring topics at the level of active research. For academics, graduate students, and anyone seeking depth beyond popular science. FOLLOW: Substack | Spotify | YouTube | Twitter Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices