• alcontali
    829
    Do you know what PD is? Do you have an opinion on its truth or falsity, and knowledge of how it relates to other candidate axioms floating about?fishfry

    I have already said that this is exactly what does not matter. PD does not need to be true or false. PD rather needs to be independent from ZFC and not exactly the same as CH; which it obviously is not. If Woodin manages to prove CH from PD, while staying clear of ZFC, he will have managed to finish the job. I have just quoted Woodin saying that he has not (yet) managed to do that.
  • fishfry
    848
    As I said, Woodin's strategy to prove CH from PD -- while staying clear of ZFC in any form or shape -- sounds really interesting, but he has also clearly said that he still hasn't managed to do it. I am just repeating Woodin's own words.alcontali

    You're repeating them out of context without understanding. I'm always up for a chat about set theory but this ain't it.

    Without looking it up, what is a projective set, and what is projective determinacy? What are some arguments as to why it might be true? False? What other well-known axioms does it conflict with? This stuff is basic basic in advanced set theory.

    If Woodin said that he's "not finished," he means he's not finished with his decades-long research project. He's got plenty of published proofs, he's one of the top set theorists in the world. Your comment that there's nothing on Wikipedia because he doesn't have a finished proof is, I apologize for my directness, laughable. I don't know what else to say. You're deeply misconstruing this entire topic. You don't know what you don't know.

    you can see that the only workable proof strategy is exactly about avoiding set-theoretic knowledge.alcontali

    That's your strategy. Avoiding knowledge. If I came here and conversed with demonstrable ignorance about your own area of technical competence, you'd recognize it. If you mentioned finite fields and I said, "Oh yeah like a wheat field bounded by corn fields?" you'd laugh at me, you wouldn't placate me. First, of course, you'd try to explain what a finite field is in abstract algebra. And if I said, "Ignorance of abstract algebra is the only workable proof strategy," then you'd laugh.
  • alcontali
    829
    I'm always up for a chat about set theory but this ain't it.fishfry

    I am not a researcher in set theory. It is obvious that there are numerous people trying to advance the field, but I am not one of them.

    If Woodin said that he's "not finished," he means he's not finished with his decades-long research project.fishfry

    The Continuum Hypothesis (CH) has been an outstanding issue for over a century now. Woodin is trying out an interesting direction to prove it. That's about it, I guess.

    He's got plenty of published proofs, he's one of the top set theorists in the world.fishfry

    Of course, Woodin has published commendable work and numerous proofs, but not one for CH. Well, not yet ...

    our comment that there's nothing on Wikipedia because he doesn't have a finished proof is, I apologize for my directness, laughable.fishfry

    Well, that's the way it works ...

    That's your strategy. Avoiding knowledge.fishfry

    There is no point in me trying to learn the nitty-gritty details in cutting-edge set-theoretical research, because it is not my job to try to advance the field. ZFC is endless. There is obviously no limit to the number of theorems that can be developed in it.

    But then again, the article you mentioned yourself, argues that cutting-edge ZFC research is not going to help with solving CH:

    It is the same with the continuum hypothesis: we know that it is impossible to solve using the tools we have in set theory at the moment. And up until recently nobody knew what the analogue of a ruler with two marks on it would be in this case. Since the current tools of set theory are so incredibly powerful that they cover all of existing mathematics, it is almost a philosophical question: what would it be like to go beyond set-theoretic methods and suggest something new? Still, this is exactly what is needed to solve the continuum hypothesis.

    I find CH to be interesting, but it is certainly not something I encounter in a professional context. So, why spend time on that and not on something else?
  • Pattern-chaser
    1.8k
    Anything more on offer more central to the OP, the philosophy of Software Engineering? :chin:
  • S
    11.8k
    The philosophy of software engineering? Oh boy, that sounds exciting. Where do I sign up?
  • alcontali
    829
    Anything more on offer more central to the OP, the philosophy of Software Engineering? :chin:Pattern-chaser

    The philosophy of software engineering? Oh boy, that sounds exciting. Where do I sign up?S

    I have had similar heated discussions, mutatis mutandis, with programmers who get up in arms because I refuse to learn AngularJS and/or ReactJS, because I prefer to stay on JQuery, hoping that the current fads will be replaced by new fads before I will have been forced to waste time on them. Same story for MongoDB. The NoSQL hype seems to have subsided. I have superbly managed to avoid it. Congratulations to myself.

    I did do a stint in Docker, and I actually regret it now, because you don't really need Docker to do program closures, because you can do all of that with much simpler tools. Furthermore, Docker is just being abused as a glorified installer anyway.

    So, I hereby retract every positive thing that I ever may have said in the past about Docker. So, what else have I successfully managed to avoid? A lot of stuff, actually. Too much to mention ... I am so proud that I do NOT know these things. I just don't. Am I great, or what? ;-)
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