A Short History of Mathematical Truth - Epistemology Video 16

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This is video 16 in an introductory course on epistemology, the philosophy of knowledge. One important kind of (putative) a priori knowledge is mathematical knowledge. However, our understanding of the nature of mathematical truth changed drastically around the late 19th and early 20th century. Therefore, it is interesting to tell a short history of the mathematical truth and delve into the nature of axioms, and the relation between mathematical systems and the world.
Victor Gijsbers teaches philosophy at Leiden University in the Netherlands. You can follow him on mastodon: @victorgijsbers@mastodon.gamedev.place.
This video is part of a lecture series originally recorded for my students during the 2023/2024 spring semester. The entire playlist is here: • Course in Epistemology

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Опубликовано:

14 мар 2024

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Комментарии : 18

@louisparry-mills9132 27 дней назад

Incredible Video, you're a fantastic communicator !

@YohnzyRR 4 месяца назад

Excellent video!

@CjqNslXUcM 3 месяца назад

Now I finally understand the significance of the "unreasonable effectiveness of mathematics in the natural sciences". Thanks!

@VictorGijsbers 3 месяца назад

Glad to help! :-)

@JamesColeman1 4 месяца назад

Nice work

@das.gegenmittel 4 месяца назад

Great Video! Could you include example sources? That would be amazing. 🙏

@necaro 28 дней назад

Thank you so much for such a clear and insightful lecture!! What is the contribution of Kurt Gödel to this discussion? (Subscribed! 🙂)

@nathanwycoff4627 4 месяца назад

How do we spell the name of the philosopher he mentions at 8:44? "Yune"? The one who studies math as an empirical science.

@VictorGijsbers 4 месяца назад

David Hume. :-)

@nathanwycoff4627 4 месяца назад

@@VictorGijsbersHahahaha! For some reason without the aspirated "H" I couldn't recognize it. Is this just in his Treatise or is there another work that's more focused on math?

@VictorGijsbers 4 месяца назад

@@nathanwycoff4627 In the Treatise there's a part on space and time, quite early on, where he talks about how there can't be infinitely small quantities because we can't imagine infinitely small things, so they can't exist in reality. I don't know that there's a longer treatment elsewhere, though of course others have tried to defend an empiricist mathematics more systematically!

@nathanwycoff4627 4 месяца назад

@@VictorGijsbersThanks for all your help so far. Can I bother you with one last request for a good entry point to that literature on the empirical perspective of math? I see Eugene Wigner and Richard Hamming mentioned on the "Quasi-empiricism in mathematics" Wiki page but not sure if that's the place to start.

@VictorGijsbers 4 месяца назад

@@nathanwycoff4627 I'm not really into it myself, I'm afraid your googling (perhaps try Google scholar if you haven't already) is probably as good as mine!

@darrellee8194 2 месяца назад

A prestablish harmony has been implanted in our minds organically by evolution. A Priori knowledge exists because of 13.8 year of our development in the universe. So of course there is a harmony. In a sense Plato's theory of recollection isn't that far off. I mean, I'm technically as old as the universe, and so are you. 10:55 Math is empirical, even when it's just about our ideas. Our ideas are in and of the world.

@hyperreality753 4 месяца назад

Perhaps a solution to the problem is an evolutionary understand of math's. Why does any property of lifeforms exist, including the property in our minds called math's? Well, maybe because they are the product of replicators, things that copy themselves, which change due to things like mutations or recombination which better enable these things to copy themselves. Perhaps math's intuitive sense of being a priori, even in relation to the world, is due to this mechanism. Maybe being very good at predicting the world around you mathematically, whether it's writing models and equations or catching a ball in space is very beneficial to your reproduction. The information about the physical world we inhabit is written to genes and then deployed as our bodies. Not quite a preestablished harmony, but maybe an ever iterative one that gets us closer and closer to accuracy, truth, so long as it benefits our replication. Who knows, anyways thanks so much for your content sir. You're an invaluable educational resource.