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WikiProject Mathematics (Rated Stub-class, Low-priority)
WikiProject Mathematics
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Mathematics rating:
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 Field: Foundations, logic, and set theory


User:Trovatore claims that I misunderstand the nature of "considered in the abstract" following the term "large cardinal axioms". Needless to say, this is not only an instance of bad writing and pedantry (tendencies that often find free reign in science and mathematics related articles under the pretenses of expertise), but it is also illogical in that we are implicitly led to believe that "large cardinal axioms" are usually not considered in "the abstract" in the first place, which is laughable and absurd. The issue is not only accuracy, but clear, straightforward English that needs to be maintained for a decent article to be developed. Trovatore, if Woodin himself used his own (unique) definition of large cardinal axioms, then that is obviously something that would have to be added to the article—rather than stuffed behind the obfuscating phrase "considered in the abstract", which means diddly-squat. After reading this abstract I am further left to conclude that the lead is poorly written. Well, stuff that in your logic and smoke it... considered in the abstract.—αrgumziΩϝ 18:55, 7 June 2010 (UTC)

I am willing to allow that the particular language may not be the best possible. It was intended to give a rough idea of the broad outlines of the subject without getting into detail.
However there is nothing "laughable and absurd" here. Large-cardinal axioms are typically considered one-by-one. There are lots of observable commonalities and regularities among them, but there is no accepted abstraction from them that says "this is what a large-cardinal axiom is, exactly". Woodin offers an attempt at such a definition as part of this work. --Trovatore (talk) 19:15, 7 June 2010 (UTC)
Trovatore, you haven't expressed agreement with me; if I've parsed your words correctly, you have said that you "may" concede that I'm right. All the details you mention are irrelevant and do not damage my argument, because large cardinal axioms is piped to its article, like any sane editor would have it, where it can be discussed at length. So which is it? Please indicate agreement (if you do) by removing the vacuous latrinalia so that this laughable and absurd logomachy can come to a fitting conclusion.

Moreover, I would also like to allay your concerns by saying that the article will be fleshed out in detail at a later point (why wouldn't it?), for it certainly doesn't clarify what Ω-logic is. Indeed, my point is that "considered in the abstract" doesn't come close in helping anyone to understand either Ω-logic or large cardinal axioms, so it's best left out before it gives someone like myself an aneurysm.—αrgumziΩϝ 20:24, 7 June 2010 (UTC)

You can be right about some things but not about others. I do not claim the lead is currently very well-worded. I do claim that removing the "considered in the abstract" phrase, without replacing it with something, is not an improvement.
By the way, would you please clarify your set theory background? This is an "unavoidably technical" article; unless you know quite a bit of set theory, it's not likely to make much sense to you, and there's only so much that can be done about that. --Trovatore (talk) 20:42, 7 June 2010 (UTC)
No. Whether amateur or credentialed, anyone can edit Wikipedia; although it is clear that you make use of that in your edits here. (Yeah, I saw your profile page.) And claiming that my background has anything to do with a "misunderstanding" of the vacuous, indefensible phrase "considered in the abstract" is nothing short of appeal to authority at best—a logical fallacy, if you're aware. Since you cannot provide a reason for the phrase, PhD'ed or not, I'll proceed to remove it. Cheers.—αrgumziΩϝ 21:44, 7 June 2010 (UTC)
Anyone may edit it, but it helps if you understand what you're talking about. --Trovatore (talk) 22:02, 7 June 2010 (UTC)
The "broadly understood" formulation is just wrong. It's not that Woodin was loosening the requirements for what it meant to be a large-cardinal axiom. The point is that he was studying the notion of large-cardinal axiom in the abstract, as opposed to specific concrete large-cardinal axioms. --Trovatore (talk) 22:05, 7 June 2010 (UTC)
Source? Reference? In-line citation? Where is the exact precedence for all of this? Please, improve the article before thinking that you have a right not to explain things in the article to all people who wouldn't know about Woodin's work in the first place. As it stands, your argued-for wording is inept and confusing for anyone who knows how to read proper English. This is not a matter of expertise in set theory; this is a matter of clear writing for those who don't have expertise—the audience of Wikipedia. At this point, all you've done is argue semantics that really don't convey what you think they convey. It is not I who has misunderstood. But I do apologize: it seems I didn't make myself clear to someone who seems to believe that their words have only one distinct meaning when there isn't one at all. Trust me, I understand the distinction you're trying to make, but the wording you're using doesn't work one iota. My new suggestion: why not express it as you've done here? It may not be brief, but it will get the job done. Cheers.—αrgumziΩϝ 00:13, 8 June 2010 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── I have made another attempt to uphold the facts of Ω-logic and clear, straightforward English. Trovatore, please let me know whether you agree or disagree. Thanks.—αrgumziΩϝ 04:59, 9 June 2010 (UTC)

No, this is still not the point. The point is that a commonality has been abstracted from previously recognized large-cardinal axioms. It's like you see a robin, you see an eagle, you see a dove, you abstract the notion of "bird", and somehow you give that abstraction a precise definition. Prior to Woodin, there was no such thing for large cardinals. It's not clear there is now, either, because Woodin's definition is not clearly accepted by set theorists in general (for that matter, I'm not all that sure it's accepted by Woodin) but this was the intent of the work. --Trovatore (talk) 09:27, 9 June 2010 (UTC)
Yes, I understand the notion of abstraction; the issue is conveying it clearly in the article so that others will grasp the point. Furthermore, I am now questioning the extent to which one can say that this is the case, and would like to investigate Woodin's work in detail to see if this can be attributed to his work (but I don't seriously doubt it). If you decide to change the wording again, then I won't change it back. However, given that this is a stub and could use some liberal endowments, I won't make so much fuss about clarity; it is simply my hope that others will see all this and begin contributing to an article that needs it. Cheers.—αrgumziΩϝ 15:56, 9 June 2010 (UTC)