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Topos Institute - Ontological Commitments for Boundaries

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In April, I attended the Mathematical Boundaries Workshop with many fellow Topos researchers. I had two big takeaways: Here’s a little story from the workshop that captures a bit of those two takeaways. On Friday morning Nathaniel Virgo gave a talk on the good regulator theorem. That afternoon, a small group of us wrote down all of the key words and mathematical symbols that he used. Our goal was to go through the talk slowly. We wanted to understand what were the key ideas in his talk. In other words, what is it that Nathaniel cares about? What are the bones of the house and what was Nathaniel’s choice of paint color? Here is our list: Everything written here — critically, even symbols like ℎ : 𝐸 × 𝐴 → 𝐸 × 𝐴 h:E×A→E×A — is intuition. It is not formal. This is hopefully a little surprising. Certainly, when Nathaniel spoke, he was thinking about 𝐸 E and 𝐴 A as sets, × × as cartesian product, and ℎ h as a set map. But as a group, we hadn’t committed to such an ontology. In con

Ontological Commitments for Boundaries – Topos Institute In April, I attended the Mathematical Boundaries Workshop with many fellow Topos researchers. I had two big takeaways: “Doing math about things I care about” is a lot like Gendlin’s focusing . David Jaz’s double categorical systems theory is a natural abstraction for talking about Boundaries. Here’s a little story from the workshop that captures a bit of those two takeaways. On Friday morning Nathaniel Virgo gave a talk on the good regulator theorem. That afternoon, a small group of us wrote down all of the key words and mathematical sym

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