Summary of Mathematical Explanations, by Joseph Y. Halpern
Mathematical Explanations
by Joseph Y. Halpern
First submitted to arxiv on: 31 Dec 2023
Categories
- Main: Artificial Intelligence (cs.AI)
- Secondary: None
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper proposes a framework for defining what constitutes a good explanation of a mathematical statement. The authors argue that mathematical facts cannot be part of an explanation under traditional notions, as all mathematical truths must be true in all causal models and hence known by an agent. To address this issue, the researchers introduce the concept of “impossible possible worlds,” which enables them to redefine what counts as a good explanation. This work has implications for our understanding of mathematical knowledge and how it is represented. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand what makes one explanation better than another when we’re talking about math. Math facts have to be true in all kinds of situations, so they can’t really be part of an explanation. To fix this problem, the scientists come up with a new idea called “impossible possible worlds.” It’s like a special tool that lets us rethink what makes a good explanation. This is important because it helps us understand how we learn and know math. |
