Geometry as Logic | Steve Patterson
Mathematics is an extension of logic. Every domain in mathematics can be reduced to logic.| Steve Patterson
Mathematics is an extension of logic. Every domain in mathematics can be reduced to logic.| Steve Patterson
I was recently impressed by a series of tweets from Joscha Bach. I’ve never heard somebody use this language before. That’s a wonderful and provocative notion that accords with my own quixotic ideas. Perhaps we don’t need to reform mathematics, but replace it altogether. That sounds like fun. What’s wrong with math? If you ask a computer scientist, they …| Steve Patterson
Immaterial things are hard to understand, and taking their existence seriously has been unfashionable for centuries. Modern materialists have gotten comfortable simply defining them or laughing them out of existence. But since my philosophical conversion to Platonism, I now think that immaterial stuff way more important than material stuff—and there’s even a meaningful sense in which …| Steve Patterson
Countless thinkers for the past two thousand years have appealed to Euclidean geometry as an example of rock-solid reasoning. The proofs in Euclid’s Elements are beautiful deductive structures. One proof builds on the next, and by accepting the starting axioms, you are compelled to agree with the final conclusions. The geometric objects within Euclid have properties which …| Steve Patterson
It’s been nine months since GPT4 was released. I’m still trying to make sense of things. There’s a dearth of level-headed analysis out there. Most people’s analysis seems to be framed by science fiction novels, or they are still using frameworks inherited from the pre-GPT world, which did not anticipate the success of LLMs. Even […]| Steve Patterson
There’s an ongoing quest to reduce everything to mathematics. It’s part of the reason we’re in a dark age. Seems like a good time to ask the question: is everything quantifiable? Were the Pythagoreans correct in saying that “All is number”? Consider three statements: 1 Alice is taller than Bob. This claim is easy to quantify. […]| Steve Patterson
