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In Terence Tao's book "Compactness and Contradiction", at the very start on page 1, he introduces material implication "If A Then B" (or "A implies B") as "B is

In Terence Tao's book "Compactness and Contradiction", at the very start on page 1, he introduces material implication "If A Then B" (or "A implies B") as "B is at least as true as A", and then lists the various easy conclusions one can draw from this. 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_Law https://proofwiki.org/wiki/Axiom:Infinite_Join_Distributive_... [2] http://abstractionlogic.com http://abstractionlogic.com

AbstractPlay 1y ago
On your website, you seem to claim in bold letters that you've talked to Graham Priest about your work: > 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?
- practal 1y ago
  All the information you need to know about that article is right at the top of it [1]. I am very clear that this is a conversation with a Claude impersonation of Graham Priest, not Graham Priest himself. 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. [1] https://practal.com/press/cwgpaal/1 https://practal.com/press/cwgpaal/1
  - AbstractPlay 1y ago
    > I am very clear that this is a conversation with a Claude impersonation of Graham Priest, not Graham Priest himself. 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.

AbstractPlay 1y ago

On your website, you seem to claim in bold letters that you've talked to Graham Priest about your work: > 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?

practal 1y ago
All the information you need to know about that article is right at the top of it [1]. I am very clear that this is a conversation with a Claude impersonation of Graham Priest, not Graham Priest himself. 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. [1] https://practal.com/press/cwgpaal/1 https://practal.com/press/cwgpaal/1
- AbstractPlay 1y ago
  > I am very clear that this is a conversation with a Claude impersonation of Graham Priest, not Graham Priest himself. 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.