> A Conversation with Graham Priest About Abstraction Logic
but admit afterward that you talked to Claude prompted to sound like Graham Priest:
> A conversation about abstraction logic with Claude representing Graham Priest.
You also wrote an update stating:
> Update: The real Graham Priest says that it doesn't really sound like his voice. So enjoy with caution .
Don't you find it unethical to claim that you had "a conversation with Graham Priest about Abstraction Logic"? You didn't have a conversation with Priest. You had an interaction with Claude in Priest clothing. It doesn't even sound like Priest agrees with what you prompted Claude to say. Do you think it's permissible to let LLMs speak on behalf of people without their consent? Do you think that what an LLM says when prompted to speak as though it were some person should be accepted as what the person would actually say and believe?
Why should we find it interesting what any LLM has to say about your work, regardless of whose voice you dress it up as?
I don't see what is unethical about that.
> Why should we find it interesting what any LLM has to say about your work, regardless of whose voice you dress it up as?
Who is "we"? I don't even know who you are, AbstractPlay. The article exists because I personally find it interesting, and I actually learnt something through it. If somebody else finds it interesting, great. If you don't, too bad. Thanks for letting me know either way.
Very interesting, I think, that "A implies B" is the same as "A ≼ B", is apparently mathematical main stream, and not just popular in formal logic.
If you continue along these lines, you also not just need to ask, what is implication, but what are A and B? Well, they are things you can compare for their truth content, so let's call them truth values. Surely, "≼" should form a partial order, and if you want arbitrary conjunction and disjunction to exist, truth values with "≼" should form a complete lattice T. This means that "∧" and "∨" are now operations T×T → T. If you want implication ALSO to be such an operation "⇒", instead of just the comparison relation "≼", you can use the following condition (somebody already mentioned it in another comment here, via Galois connections), which just means that "A and B imply C" is the same as "A implies that (B implies C)", interpreting implication simultaneously as "⇒" and "≼":
A ∧ B ≼ C iff A ≼ B ⇒ C
That allows you to define B ⇒ C as the supremum of all A such that A ∧ B ≼ C, in every complete lattice. If the join-infinite distributive law [1] holds, above condition will hold with this definition, and you get a complete Heyting algebra this way.This is exactly how I turn abstraction algebra into abstraction logic [2].
[1] https://proofwiki.org/wiki/Axiom:Infinite_Join_Distributive_...
That sounds like a paradox.
Formal verification can prove that constraints are held. English cannot. mapping between them necessarily requires disambiguation. How would you construct such a disambiguation algorithm which must, by its nature, be deterministic?
[1] Autoformalization with Large Language Models — https://papers.nips.cc/paper_files/paper/2022/hash/d0c6bc641...
But maybe I just don't understand.
I am working on making it simpler to understand, and particularly, simpler to use.
PS: People keep browsing the older papers although they are really outdated. I've updated http://abstractionlogic.com to point to the newest information instead.
English was not developed to facilitate exact and formal reasoning. In natural language ambiguity is a feature, in formal languages it is unwanted. Just look at maths. The reasons for all the symbols is not only brevity but also precision. (I dont think the symbolism of mathematics is something to strive for though, we can use sensible names in our languages, but the structure will need to be formal and specialised to the domain.)
I think there could be meaningful work done to render the statements of the results automatically into (a restricted subset of) English for ease of human verification that the results proven are actually the results one wanted. I know there has been work in this direction. This might be viable. But I think the actual language of expressing results and proofs would have to be specialised for precision. And there I think type theory has the upper hand.
Only after you make the upfront claim, in bold letters, in words you chose: "A Conversation with Graham Priest About Abstraction Logic". You did not choose to title your blog post "A Conversation About Abstraction Logic With Claude Representing Graham Priest" which is the more honest title for your blog post, except that it's clear that Claude was not capable of representing Priest since "the real Graham Priest says that it doesn't really sound like his voice." You chose to title your blog post "A Conversation with Graham Priest About Abstraction Logic". Obviously this line gives the impression that you had an actual conversation with the actual Graham Priest. You must have recognized that the wording you chose is false and deceptive. Are you hoping that attaching Priest's name gives your work more gravitas or encourages more sales of your book?
> I don't see what is unethical about that.
You see nothing unethical about prompting an LLM to take on someone's persona and then presenting the resulting conversation in a blog post with a title which gives the initial impression that you had an actual conversation with the actual person?
Be clear about where you stand on this at least so that any university or elsewhere that might have any interest in offering a job for you to continue your work in abstraction logic might know where you stand on misrepresenting professional academics.
> Who is "we"?
The general public to which you are presenting your work and advertising your book.
> I don't even know who you are, AbstractPlay.
I'm a member of the general public to which you are presenting your work and advertising your book.
> The article exists because I personally find it interesting, and I actually learnt something through it. If somebody else finds it interesting, great. If you don't, too bad.
Okay, but you're presenting this pseudo-conversation on the website through which you are presenting your work and advertising your book to the general public. Presenting it there gives the impression that this pseudo-conversation is meant to support your work, not that it's some tangential, self-satisfying curiosity appropriate for a personal blog.
It would be far more interesting if you posted actual conversations you actually have with actual academics actually commenting on your work instead of this fantasy world of LLM regurgitation that you expect us to believe is ultimately intended to only be interesting and enlightening to you.