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Any discussion of finitism warrants a citation of Bendegem's paper: A Defense of Strict Finitism, https://www.researchgate.net/publication/288354797_A_Defense

Any discussion of finitism warrants a citation of Bendegem's paper: A Defense of Strict Finitism, https://www.researchgate.net/publication/288354797_A_Defense_of_Strict_Finitism https://www.researchgate.net/publication/288354797_A_Defense...

yamrzou 4y ago
Thanks for sharing. I'm going to add here some links that I've been curating regarding the "existence" of infinity: The physics of infinity - https://www.nature.com/articles/s41567-018-0238-1.epdf?shared_access_token=nhIyZJldj4QzWZs7LvZIttRgN0jAjWel9jnR3ZoTv0PMOaEWTfe0Iq_Ol3Eo9bd6Lh9xyPK-ya44kxWDxYi4IQo2Zqj-Ymd6yZVANNbW9FXmT1HwoVMnEtM00qpXT48gLDqpQXX3mvS3gRH22aRhLs-Cf_4dd6NkVcLZZP3rPbg%3D https://www.nature.com/articles/s41567-018-0238-1.epdf?share... - Discussion: https://news.ycombinator.com/item?id=17599087 https://news.ycombinator.com/item?id=17599087 Is infinity Real? - https://www.quantamagazine.org/the-infinity-puzzle-20160616 https://www.quantamagazine.org/the-infinity-puzzle-20160616 - Solution: https://www.quantamagazine.org/the-infinity-puzzle-solution-20160630 https://www.quantamagazine.org/the-infinity-puzzle-solution-... Do infinities exist in nature? - https://plus.maths.org/content/do-infinities-exist-nature-0 https://plus.maths.org/content/do-infinities-exist-nature-0 Does infinity exist? - http://plus.maths.org/content/does-infinity-exist http://plus.maths.org/content/does-infinity-exist - Discussion: https://news.ycombinator.com/item?id=4526049 https://news.ycombinator.com/item?id=4526049 How to count past infinity - https://youtu.be/SrU9YDoXE88 https://youtu.be/SrU9YDoXE88 How real are real numbers? - https://arxiv.org/abs/math/0411418 https://arxiv.org/abs/math/0411418 - Discussion: https://news.ycombinator.com/item?id=14080024 https://news.ycombinator.com/item?id=14080024 / https://news.ycombinator.com/item?id=24029791 https://news.ycombinator.com/item?id=24029791 Are Real Numbers Real? - https://ptolemy.berkeley.edu/~eal/pnerd/blog/are-real-numbers-real.html https://ptolemy.berkeley.edu/~eal/pnerd/blog/are-real-number... - Discussion: https://news.ycombinator.com/item?id=33316803 https://news.ycombinator.com/item?id=33316803
- naasking 4y ago
  Nice list! I'll add one more I enjoyed: Struggles with the Continuum, by John Baez, https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421
vintermann 4y ago
Thank you, that seems really interesting, and it touches tantalizingly onto some ideas I've wondered if anyone has formalized. There's the old joke that 1. Not all numbers are interesting 2. If not all numbers are interesting, then there's a smallest number that's not interesting 3. But that's interesting in itself! Ha! Contradiction! But it seems to me all you need to resolve that contradiction is to be a bit tough and say that no, it being the smallest boring number isn't interesting. Who cares. What I would like to know is if there is a formalization of "we don't care about that". Obviously we use the idea sometimes (Karnaugh maps come to mind).

yamrzou 4y ago

Thanks for sharing. I'm going to add here some links that I've been curating regarding the "existence" of infinity: The physics of infinity - https://www.nature.com/articles/s41567-018-0238-1.epdf?shared_access_token=nhIyZJldj4QzWZs7LvZIttRgN0jAjWel9jnR3ZoTv0PMOaEWTfe0Iq_Ol3Eo9bd6Lh9xyPK-ya44kxWDxYi4IQo2Zqj-Ymd6yZVANNbW9FXmT1HwoVMnEtM00qpXT48gLDqpQXX3mvS3gRH22aRhLs-Cf_4dd6NkVcLZZP3rPbg%3D https://www.nature.com/articles/s41567-018-0238-1.epdf?share... - Discussion: https://news.ycombinator.com/item?id=17599087 https://news.ycombinator.com/item?id=17599087 Is infinity Real? - https://www.quantamagazine.org/the-infinity-puzzle-20160616 https://www.quantamagazine.org/the-infinity-puzzle-20160616 - Solution: https://www.quantamagazine.org/the-infinity-puzzle-solution-20160630 https://www.quantamagazine.org/the-infinity-puzzle-solution-... Do infinities exist in nature? - https://plus.maths.org/content/do-infinities-exist-nature-0 https://plus.maths.org/content/do-infinities-exist-nature-0 Does infinity exist? - http://plus.maths.org/content/does-infinity-exist http://plus.maths.org/content/does-infinity-exist - Discussion: https://news.ycombinator.com/item?id=4526049 https://news.ycombinator.com/item?id=4526049 How to count past infinity - https://youtu.be/SrU9YDoXE88 https://youtu.be/SrU9YDoXE88 How real are real numbers? - https://arxiv.org/abs/math/0411418 https://arxiv.org/abs/math/0411418 - Discussion: https://news.ycombinator.com/item?id=14080024 https://news.ycombinator.com/item?id=14080024 / https://news.ycombinator.com/item?id=24029791 https://news.ycombinator.com/item?id=24029791 Are Real Numbers Real? - https://ptolemy.berkeley.edu/~eal/pnerd/blog/are-real-numbers-real.html https://ptolemy.berkeley.edu/~eal/pnerd/blog/are-real-number... - Discussion: https://news.ycombinator.com/item?id=33316803 https://news.ycombinator.com/item?id=33316803

naasking 4y ago
Nice list! I'll add one more I enjoyed: Struggles with the Continuum, by John Baez, https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421

vintermann 4y ago

Thank you, that seems really interesting, and it touches tantalizingly onto some ideas I've wondered if anyone has formalized. There's the old joke that 1. Not all numbers are interesting 2. If not all numbers are interesting, then there's a smallest number that's not interesting 3. But that's interesting in itself! Ha! Contradiction! But it seems to me all you need to resolve that contradiction is to be a bit tough and say that no, it being the smallest boring number isn't interesting. Who cares. What I would like to know is if there is a formalization of "we don't care about that". Obviously we use the idea sometimes (Karnaugh maps come to mind).