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Paradigm
Joel David Hamkins: Philosophy of Mathematics and Truth
Aug 17, 2023
Renowned mathematician and philosopher Joel David Hamkins discusses concepts of truth and proof in mathematics, including the completeness and incompleteness theorems. He explores the beauty of abstract mathematics and the importance of following one's interests. The chapter also addresses online presence and ongoing projects, as well as the question of choosing a representative for AI superintelligence.
01:27:33
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Quick takeaways
- Abstract existence in mathematics poses challenges for understanding and asserting truth.
- Intuition varies across contexts and can lead to subjective biases when determining truth.
Deep dives
The concept of truth in mathematics and the nature of existence
The podcast episode explores the concept of truth in mathematics and how it differs from truth in other domains. It delves into the nature of existence in mathematics, which involves abstract objects compared to physical existence. The episode discusses the challenges of understanding abstract existence and making truth assertions about abstract concepts. It also touches on the problem of causal interaction with the abstract realm and debates around the role of causality in mathematics. Additionally, the episode explores the idea that abstract existence may be easier to comprehend than physical existence.
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Discover
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