High Signal Podcasts Evidence ledger
Method
Browse
How the evidence works

Public evidence record

Joel David Hamkins

Published podcast speaker

Claims
24
Episodes
1
Shows
1
Named items
0

Claim ledger

What Joel said.

2 transcript-backed records

01 / prediction

I argue that it’s really the philosophy of structuralism that leads them to omit the ur-elements because it turns out that if you adopt ZFC axioms with ur-elements, ZFCU it’s called, or ZFA, then any structure that exists, any mathematical structure that exists in that set theoretic universe with the atoms is isomorphic to a structure that doesn’t use the atoms at all.

“I argue that it’s really the philosophy of structuralism that leads them to omit the ur-elements because it turns out that if you adopt ZFC axioms with ur-elements, ZFCU it’s called, or ZFA, then any structure that exists, any mathematical structure that exists in that set theoretic universe with the atoms is isomorphic to a structure that doesn’t use the atoms at all.”
Publisher
Lex Fridman Podcast

02 / prediction

The main lesson of computability theory, in my view, is that it’s never the case that you can have a thorough understanding of the behavior of a program by looking at the program, and that the content of what you learn from a program, I mean, in the most general case, is always obtained just by running it and looking at the behavior.

“The main lesson of computability theory, in my view, is that it’s never the case that you can have a thorough understanding of the behavior of a program by looking at the program, and that the content of what you learn from a program, I mean, in the most general case, is always obtained just by running it and looking at the behavior.”
Publisher
Lex Fridman Podcast
Search evidence