Talk:Strategy-stealing argument

Gender
Hi, why both players are females ? i think the neutral gender in english in the male gender .. &mdash;the preceding unsigned comment is by 200.78.53.94 (talk &bull; contribs) 05:40, 13 February 2005


 * See Gender-specific pronoun -- Dominus 15:20, 18 July 2005 (UTC)

It used to be, but not really any more. &mdash;Simetrical (talk) 02:18, 26 December 2005 (UTC)

Tic-Tac-Toe
I don't see how strategy-stealing applies here. Player 1 can never pretend to be player 2 -- whenever it's player 2's turn to play there are an even number of vacant squares, but when it's player 1's turn to play there are an odd number of vacant squares. —Preceding unsigned comment added by 72.93.194.10 (talk) 22:07, 24 May 2008 (UTC)


 * You're right, the argument needs a little elaboration. Suppose there is a winning second-player strategy.  The first player can place an X at random and thereafter pretend to be the second player.  Having an extra mark on the board cannot hurt him.  If the strategy calls for him to play where the extra X is, he can simply play somewhere else at random.  This cannot make his position worse than it was, so the winning strategy is still a winning strategy. -- Dominus (talk) 10:03, 25 May 2008 (UTC)


 * I have made the argument more rigorous and hopefully more clear by explaining that first player may "ignore" the extra X so as to treat his position exactly as the second player's, and thus use the supposed winning second-player strategy. Denziloe (talk) 21:45, 27 August 2014 (UTC)

Go
Shouldn't Go be considered in this? If it is true, then in Go you can steal the strategy as well. It is a symmetrical game and there is no penalty for having an extra move (you can pass, and you can lose maybe one territory for putting down a stone in your own territory; you may even lose a lot of territory if you put a stone in one of 2 eyes when the territory is surrounded completely by the other side... not sure if all this is necessarily a penalty). &mdash;the preceding unsigned comment is by 128.6.175.45 (talk &bull; contribs) 21:07, 19 October 2005 (UTC)


 * I think the problem with that is that if there's a winning second-player strategy and the first player passes, then the second player would also pass, and it could continue like that forever, making the game undecidable. It would be known that whoever made the second move would automatically win, and therefore it would never be advantageous to play first.  If there's some draw rule in Go based on consecutive passes, or some limit on consecutive passes, this might not be an issue. As for whether making an actual move (not passing) is ever a penalty, I am neither a game-theorist nor a Go player (beyond a cursory knowledge of most of the rules), so I'm afraid I don't know.  Game theory is a mathematical discipline, of course, so even if no one's thought of any disadvantageous moves yet, they can't be assumed not to exist until their existence is proven impossible. &mdash;Simetrical (talk) 02:18, 26 December 2005 (UTC)


 * Actually, if there are two passes in a row, it ends the game and the determination of dead or not dead pieces begins. The board would have to be at least "half full" before people would actually pass. with just two moves, it is hardly conclusive and there is so much space that it wouldn't be a disadvantage to have an "extra move." Interestingly, it can be a disadvantage to move later in the game, perhaps the endgame. Similar to the zugzwang in chess, Go has kamikaze/suicide attacks. If the player has other options of course they can move those before. But we also have to consider perfect strategy. Although the strategy stealing argument doesn't lead one to perfect strategy besides perhaps strategy stealing (though I think you would always be a move behind), we have to assume perfect strategy in the process of the game, and we have no idea what it would be. 70.111.224.85 13:36, 5 January 2006 (UTC)

Fatal flaw?
I diagree that the strategy stealing argument means first player can always force a win. Let's say that second player knows the best strategy, first player doesn't. Thus first player moves "randomly" to steal the second players strategy. Second player begins his "best strategy," BUT first player "steals" it. Although the first player has stolen the best strategy, second player has an advantage: initiative. So if this continues out, the second player will win. One might go on to say that second player could steal the first player's strategy stealing strategy, and both players continue to place random pieces down until the game is over by chance! If a game is such that the second player always wins, then that means that it is the first move that is bad. Which means that whereever your first move is, it is a disadvantage because the second player can react to that with the appropriate "best strategy," leaving the first player unable to steal the strategy because he/she is always behind by at least one move. &mdash;the preceding unsigned comment is by 128.6.175.45 (talk &bull; contribs) 14:47, 21 October 2005 (UTC)


 * "Let's say that second player knows the best strategy, first player doesn't" is an invalid premise. Possibly you should take a look at winning strategy&mdash;a strategy is only a winning strategy if it wins no matter what the other player does.  It must work even if your opponent knows the strategy as well as you do.  If both of us know and use a second-player winning strategy, then the one who plays second must win.  If it can be proven that in a given game any strategy valid for the second player is equally valid for the first player, which is what the strategy-stealing argument is, then there can be no second-player winning strategy&mdash;if there were, we'd both have a winning strategy, which is nonsensical. &mdash;Simetrical (talk) 02:18, 26 December 2005 (UTC)


 * What I said meant that the second player had a winning strategy, while the first tried using the strategy stealing argument as their winning strategy. Now we have to wonder if the second player would later steal the strategy stealing strategy so that they both end up with the same thing. Resulting as I mentioned earlier a perhaps random game, where the players randomly move on the board until the game is done. This game would most likely be won by the first player just because of first move advantage. This is ridiculous of course and leads us to the current strategies in place for all games today. (I'm assuming there is no such game in which if you randomly move, you will win every time.)
 * Another question that games have to critiqued is fairness. If a game isn't fair, there is no point in even applying the strategy stealing argument, as it could be impossible for a person to win anyway. Since none of the games mentioned are fair (they are proven to be a forced win for first player), they cannot apply. Connect6 is a contender for fairness, but in my experience playing it, a defensive strategy is almost infallible. If both players use this strategy, there is likely to be a draw. More gameplay has to be done to prove/disprove this. 70.111.224.85 14:08, 5 January 2006 (UTC)

Shannon Switching Game
I'm sure the strategy-stealing argument doesn't apply to the Shannon Switching Game, because although there can be no draws and an extra move is never a disadvantage, the game isn't symmetric. "Short" is trying to join A to B and "Cut" is trying to make this an impossible task by disconnecting A from B, therefore they have different winning strategies. Also, the Shannon Switching Game can be played on any graph, and it is trivial to show that some graphs give an automatic win to Cut and some give an automatic win to Short. Is there, in fact, a particular graph or set of graphs for the Shannon Switching Game for which the strategy-stealing argument DOES apply, or am I just misunderstanding the rules of the game? 91.84.76.81 (talk) 19:33, 6 May 2008 (UTC)


 * The Shannon Switching Game is symmetric. Mathematically, it it equivalent to the Gale Game (aka Bridj-it). Yes, the two games look quite different upon first sight, but aren't. When player A conquers an empty cell in the Gale Game with a connection, it's the equivalent of a short. If the other player conquers a cell, it's a cut. A cell in the Gale Game is the equivalent of an edge in the Shannon Switching Game. In the Gale Game, both players try to win by connection two sides of the playfield. In the Shannon Game, one player tries to build a path between the two endpoints via "shorted" edges, while the other tries to build a "sideward" path, which can be traversed without crossing any edges (colored/shorted or uncolored/resistive).
 * An implementation of the Gale Game can he found here (there's also further information the Shannon's solution for the computer player, which makes the equivalence even clearer). --Klaws (talk) 13:24, 14 September 2011 (UTC)

Constructivity
I deleted:
 * The strategy-stealing argument is non-constructive. It proves that a strategy exists, but provides no help in discovering what that strategy is. In other words it is an existential proof of a win or draw for the first player.

There's a lot of confusion on this point, but the SSA shows the absence of a strategy for second player. A constructive proof of such a negated proposition means that one can construct an absurdity from any purported winning 2nd player strategy, which looks like proof by contradiction but is not. If the SSA is used as part of an argument that there is a first-player win, that argument is in all likelihood non-constructive, but constructive arguments may indeed form part of non-constructive proofs.

There's enough confusion about this that it maybe deserves inclusion in the article. &mdash; Charles Stewart (talk) 14:01, 18 March 2009 (UTC)

Chess
The chess section states, "In chess, it is common knowledge that having the first move is a small but significant advantage for White"

An advantage cannot be both small and significant. The words have opposite meanings. Perhaps the writer meant something like "small advantage that can be significantly exploited by a skilled player". I know next to nothing about chess strategy so I'm not going to try and correct this. But somebody should! 99.23.132.69 (talk) 22:49, 5 September 2009 (UTC)


 * I disagree that an advantage cannot be both small and significant. —Dominus (talk) 02:40, 6 September 2009 (UTC)

unnecessarily complicated.
The exposition was impossible to understand, even though I know the concept very clearly! Sorry, I don't have any suggestions: it just needs to be clearer, perhaps by starting from an example (really introduce chomp) or perhaps mention states (go directly to any third state on the first move, though this is only a subset of games where there is a strategy stealing possibility). Sorry I don't have more explicit advice, I just know that how it reads now is really unclear!

Possibly infinite games
It probabl;y needs to say better the conditions too as Determinacy shows how even with a well determined outcome the result isn't assured. Dmcq (talk) 16:04, 26 November 2009 (UTC)

Constructivity & NPOV
As presented in this article, the strategy-stealing argument does not provide a strategy for the first player, so therefore cannot be a constructive proof of a strategy for the first player under any assumptions; this is a simple matter of definition. It may be that the SSA (as presented) is the only major component required for such a proof (e.g. in finite games), but that would not be definitional and should instead be backed up by a reliable source. The currently cited source is reliable (Bishop is, to my knowledge, an expert on the subject of constructive mathematics) and states that the SSA is non-constructive, albeit in a different form. Probably what we need is a source that more closely matches what the article is talking about. But until a better source is found, the article should present what's in our source as fact without non-NPOV fact-as-opinion phrases like "has been called". Another strategy for improving the article in the meantime (instead of just reintroducing the problem) would be to reword the article to specify the conditions and definitions under which the quoted source by Bishop applies. Mathematical statements which are contingent upon side conditions are not the same as opinions. Belovedeagle (talk) 11:21, 2 April 2022 (UTC)
 * Strategy stealing does not provide a strategy: correct. However, this is mathematics, and "constructive" in mathematics has a technical meaning, Constructivism (philosophy of mathematics), which (for finite games) this lack of a strategy does not encompass. We should not confuse readers by using this word in some sense other than its technical sense, or in attempting to use this technical word incorrectly. There is nothing NPOV about saying it has been called non-constructive, pointing to people who have done so, and pointing out that this usage is incorrect. It is a factual statement that it has been called non-constructive, not an opinion. —David Eppstein (talk) 19:16, 3 April 2022 (UTC)


 * Thank you for your reply. I generally agree with your statement that "[It is NPOV to say] it has been called non-constructive, pointing to people who have done so, and pointing out that this usage is incorrect." but I disagree that this is what the article does. In particular, I don't think the article as it stands actually succeeds in pointing out that the usage is incorrect. This is where the NPOV failure comes in: "It has been called non-constructive" is not NPOV; "It has been called non-constructive but this is incorrect because etc." may be NPOV. This is really what my edit was attempting to accomplish, modulo that...
 * I'm not sure I entirely agree that Bishop was wrong (or is wrongly applied in the article). I think you may have missed the point in my first sentence; let me rephrase: As the SSA is defined in the article, the SSA is not a proof that the first player has a strategy. If it isn't a proof at all that the first player has a strategy, then it certainly can't be a constructive proof that the first player has a strategy. Over in classical mathematics land, this objection can be brushed aside because we really don't care about constructing the proof anyways; a wink is as good as a nod and the SSA-as-presented-here is as good as a proof of a strategy. But in constructive mathematics, this distinction suddenly becomes very important. You appear to be correct that there exists a constructive proof of the strategy by combining SSA with an instance of LEM. But it is the nature of using instances of LEM in constructive mathematics that all of the actual construction happens in the decision procedure. That is, if you take the proof which you point out exists, and you ask, "where in here is there actual construction of a strategy", you'll find the answer is, "in the proof of the LEM instance". So returning to our article here, it doesn't have anything about a decision procedure for strategies in finite games (nor do I think it should, but perhaps there's a way to work it in?). And therefore as far as this article is concerned, the SSA isn't constructive. Frankly I assume that all of this is precisely what Bishop meant, but maybe you have more context which suggests he was just mistaken, or he meant to exclude finite games in the cited passage, or whatnot.
 * To restate my position as succinctly as I can, there exists a constructive proof of a first-player strategy in certain games, but the SSA as presented here is not that proof, or at least is not the relevant part of that proof. This viewpoint is no doubt strongly influenced by my focus on the computational properties of constructive proofs, and you seem to have interpreted this as some confusion on my part about what constructive mathematics is. But this conception of constructive mathematics is not an "attempt[] to use this technical word incorrectly". In any case, if someone with this focus can draw a distinction between two things (such as the SSA and a complete constructive proof of a strategy), then it's not incorrect to state in the article that there is a distinction. Distinctions can exist independently of one's personal opinion about their importance.
 * So what I'd like to accomplish now is to fix the article to say the above, except minus getting into the weeds as I have done here. Again, this is what I was trying to do but you obviously disagreed. May I suggest you make the next attempt at improving the article? Belovedeagle (talk) 19:43, 3 April 2022 (UTC)
 * I'm certainly not saying that Bishop was incorrect. That is a misreading of what I have said and misses the point. All of this getting into weeds would be relevant for infinite games, where excluded middle becomes non-obvious. But strategy stealing is generally applied to finite games like hex. All of this foundational material is irrelevant there, because finiteness makes it irrelevant. There exists a perfectly valid procedure for constructing a winning strategy: perform a game tree search. Strategy stealing merely tells you what the outcome of this procedure will be, more quickly. —David Eppstein (talk) 19:58, 3 April 2022 (UTC)
 * I don't think this engages with my concerns at all. The obviousness of LEM here is not in question.
 * If you do not wish to engage with my concerns, that's your prerogative, but in that case I feel you would be obliged not to simply revert any future changes I may make along the lines I have suggested. I'm not yet confident that this will occur. So unfortunately I must ask you directly and impolitely, what changes am I permitted to make to this article in your view? Belovedeagle (talk) 20:05, 3 April 2022 (UTC)
 * Withdrawing above comment in light of an edit I missed. I am going to make a bold attempt to edit the original article now that I understand your position better; I hope you will interpret it in the spirit it is made even though it will probably look a lot like my first attempt. Belovedeagle (talk) 20:12, 3 April 2022 (UTC)

To state that an opinion is "accurate" is to state that it is fact, which is itself a statement of fact. You have once again effectively reverted my original change without adequate discussion, even though this time you did not use the 'undo' button literally. Belovedeagle (talk) 20:56, 3 April 2022 (UTC)
 * FWIW, the reason I said "accurately described" is because I agree that "described" would be a better way to explain the situation if it could be done in an NPOV. So if someone can find a way to say "accurately described" in a way that we can agree is NPOV, that would be a superior compromise than what I have tried, which is to claim the fact is true in a strict sense, which isn't even quite right or perfectly encyclopedic. Belovedeagle (talk) 21:24, 3 April 2022 (UTC)

I will admit to not even vaguely understanding the idea that there's an NPOV problem here. The original text was clear, accurate, and light on jargon. The replacement at present uses much more technical language and consequently is less clear and harder to follow, without being better in any sense I can readily determine. I suggest reverting to the version before the recent edits. --JBL (talk) 22:39, 3 April 2022 (UTC)


 * I agree the latest version is overall worse, which is of course why I didn't start with it. David Eppstein above said best what the article should have done, but in my view did not do: "There is nothing NPOV about saying it has been called non-constructive, pointing to people who have done so, and pointing out that this usage is incorrect." The original article only did 2 out of 3. For a version which meets not only those requirements but also yours, https://en.wikipedia.org/w/index.php?title=Strategy-stealing_argument&oldid=1080538860 is a good place to start! Iterating on that will be more likely to resolve all issues. Belovedeagle (talk) 22:50, 3 April 2022 (UTC)
 * This does not help me understand what you think was wrong with the original. Can you state, as briefly and clearly as possible, what you think was problematic about the original wording?  (Also I think "I changed it in a way that I know is bad" is almost always a sign of a poor decision-making process.) --JBL (talk) 23:19, 3 April 2022 (UTC)
 * Normally NPOV comes into play when we state opinions as facts. But NPOV also requires that we do not state facts as opinions. Original article stated, "However, it does not provide an explicit strategy for the first player, and because of this it has been called non-constructive." "X has been called Y" is a construction we use (per NPOV) to launder opinions into facts. The use of this construction in the original article incorrectly presents "[SSA is] nonconstructive" as an opinion.
 * Normally we'd fix the problem by just turning "X has been called Y" back into just "Y" when "Y" is actually a fact. But in this case it's more complicated, because if we just say "SSA is nonconstructive", that is very much an incorrect fact, and not at all what Bishop meant, because of missing context. I am trying to find a better wording of the underlying correct point which Bishop was making.
 * Let me go through the points of my original edit which I feel fixes this problem and is better than the final version (though still needing improvement):
 * "It does not provide an explicit strategy for the first player" - I think we are agreed above that this is a true claim which is the correct version of "SSA is nonconstructive".
 * "and so is not a constructive proof of such a strategy" - This connects the corrected claim back to the original claim "SSA is nonconstructive" which is found in the cited source. To an expert, this reading of Bishop may be straightforward; to the reader, it may need this gloss.
 * "However, in games where there can be no draw, the law of the excluded middle may be applied making a non-constructive proof that the first player has a winning strategy." - explains why the SSA is actually fine constructively, in the broader context where we know that the decision procedure exists
 * If there is a flaw with this version so severe that there is consensus against it, I would really appreciate an explanation. The edit summary of the original revert only restated point #3 above; since that was (therefore) in agreement with the text of the edit it has not led me to understand what the problem was. This lack of explanation is the poor decision-making process in question. Belovedeagle (talk) 00:08, 4 April 2022 (UTC)
 * Like JBL, I'm finding the original easier to follow than the current version. The current version uses more words and more involved syntax to say the same thing, in a way which requires more background experience to understand. XOR&#39;easter (talk) 00:56, 4 April 2022 (UTC)


 * I have removed some of the jargon by bringing back parts of my original change. I think the only way I will learn if the bits I brought back are acceptable is to try them. Belovedeagle (talk) 01:05, 4 April 2022 (UTC)
 * This analysis hinges on a strange and unnatural reading of the phrase "and for this reason has been called". I reject your reading of this phrase.  As a result, it seems clear that your are directed to fixing something that isn't broken.  I think you should stop boldly doing that until you can find anyone else to agree with you that there's an actual problem. -- JBL (talk) 11:11, 4 April 2022 (UTC)
 * Consensus is not required for changes. So far no one has engaged constructively here; I've gotten exactly zero suggestions how my original changes could be better (only that they're bad). Because of this the discussion seems to be purely for the sake of appearance rather than genuine. (Clarified below.) I'd love to work with someone genuinely on this article, but I can't force you to engage. Belovedeagle (talk) 23:41, 4 April 2022 (UTC)
 * Specifically, the reason I don't think that the BRD-type discussion is actually happening here is that the purpose of such a discussion is for me to better understand your concerns with my changes. "The article is fine as is" is not a concern with my changes, it's a concern about making any changes at all. This isn't to say you didn't have valid concerns about any of my changes; you did and I agreed with them and so I changed my changes again to try to improve based on your feedback. That was good. But then you reverted my improvements without explaining what was wrong with the new version other than that you felt I should ask permission first. That was not good. Belovedeagle (talk) 23:51, 4 April 2022 (UTC)
 * Someone has objected to every change you've made because they make the text worse, in various ways. Once your changes have been objected to, the onus is on you to find a consensus.  So far, you have yet to convince anyone that there is anything wrong with the section you've been editing, which is about as far from establishing a consensus to make changes as is possible. --JBL (talk) 00:07, 5 April 2022 (UTC)
 * Can you please explain why the most recent change made the article worse? I understand you tried to explain by saying "bizarre formatting" in the edit summary but I don't understand what that is supposed to mean, and this leaves me feeling that it may have been an excuse to restore your preferred version of the article - but I honestly do want to be proven wrong if it means a way forward. Belovedeagle (talk) 00:16, 5 April 2022 (UTC)
 * Your message contains a clear violation of WP:AGF, which now brings to 3 or 4 the number of distinct ways in which your behavior is disruptive. DE has already warned you but in a slightly oblique way, so let me be very clear: if you don't figure out how to interact more appropriately, I will seek administrative intervention.
 * That said: your use of emphasis was bizarre, and a reader, coming to that text, will find it confusing. "On its own" as opposed to what, and why is that phrase so important?  (I'm not asking you these questions, I'm trying to convey to you what a reader who happens not to be living in your head will experience upon reading them.)  Separately, the phrase "a constructive proof of a winning strategy" is somewhere on the spectrum between awkward and wrong.  Of course, the fact that your edits don't make things better is not terribly surprising given that you have yet to articulate a convincing basis to believe that there is something here that could be improved. --JBL (talk) 00:41, 5 April 2022 (UTC)
 * I apologize, I have been very frustrated because I felt this change is trivial. I appreciate that you are now providing feedback.
 * I do not think I will be able to "articulate a convincing basis to believe that there is something here that could be improved" to your satisfaction; but I think there is an easy workaround: if I suggest a change which is in your view neutral, it seems like that should be okay too per policy. Or you can suggest a compromise of your own.
 * What about "However, insofar as it does not provide an explicit strategy for the first player, it is non-constructive."? This avoids the formatting and the problematic phrases. It explains exactly what is required for "it is non-constructive" to be true; namely, that we are only considering the fact that "it does not provide an explicit strategy". Belovedeagle (talk) 01:19, 5 April 2022 (UTC)
 * If "it does not provide an explicit strategy" is the entire meaning of "non-constructive" here, then why bother saying "non-constructive" at all? Why not just say, "However, it does not provide an explicit strategy for the first player; this raises the question of how to actually compute a winning strategy"? All that saying "non-constructive" does is bring in another technical term, in a way that benefits pretty much nobody. Readers who don't know what "constructive" means will get nothing, and readers who are familiar with constructivism will be confused. XOR&#39;easter (talk) 03:45, 5 April 2022 (UTC)
 * I had the same thought; I was concerned however that it will amount to completely abandoning the language used in the citation. That was certainly not my original intention, but maybe it is the best solution...
 * So, yes, I do support the proposed language "However, it does not provide an explicit strategy for the first player; this raises the question of how to actually compute a winning strategy". If anyone later figures out how to put the citation quote back in, that would just be icing on the cake. Belovedeagle (talk) 03:56, 5 April 2022 (UTC)

There are a number of factors here complicating the claim for this argument to be constructive, including: While I don't think we should treat the question of constructivity as a complicated matter that we should avoid in general, I don't see the sources to provide an adequate treatment of this topic in this article. I recommend that we keep our treatment short, avoid claims we can't source, and provide hyperlinks to related topics so that the interested reader can explore what little we do have to say that might be helpful. &mdash; Charles Stewart (talk) 05:37, 5 April 2022 (UTC)
 * 1) This doesn't describe a precisely defined proposition that could be constructive or nonconstructive. Instead, this is presented at the level of a heuristic argument that might yield a correct argument in some game situations, or fail to apply in others. It can be applied simply, or it can be adapted.
 * 2) The article documents that the first game the argument was applied to was the game of [hex]]. This is a game with a finite game tree so in this case, we can apply quantifier elimination so there is no distinction between classical and constructive existence proofs. Likewise, the longest presented argument in the game involves a class of positions of chess, which is normally played with some rule that prevents infinite game trees.
 * It is quite clear that Belovedeagle is entirely correct and that the other editors are wp:tag teaming Leche de Pan (talk) 06:56, 5 April 2022 (UTC)
 * On the whole I'd prefer not to get this kind of assistance from new accounts, as, unfortunately, even when entirely genuine it leads to the appearance of sockpuppetry. I have seen no evidence of intentional tag-teaming. Belovedeagle (talk) 07:22, 5 April 2022 (UTC)
 * , I advise familiarizing yourself with WP:AGF. XOR&#39;easter (talk) 13:40, 5 April 2022 (UTC)

Would it help this discussion to find high-quality sources discussing how the strategy-stealing argument in infinite games relates to intuitionistic logic or the axiom of determinacy or related foundational issues, if it does? I only saw a small number of dubious-looking papers in a quick search but maybe I wasn't using the right keywords. At this point, without sources, we have no basis for saying anything about whether the people calling this argument non-constructive are doing so with any connection to constructivism in mathematics or whether they are merely using the word with some other colloquial and non-technical meaning (it doesn't provide a construction). —David Eppstein (talk) 07:26, 5 April 2022 (UTC)


 * "merely using the word with some other colloquial and non-technical meaning (it doesn't provide a construction)"
 * I think it may be the heart of the disagreement that this is really different from the "technical meaning" as you would call it. It is trivial (but surprising to newcomers) that the SSA is constructively valid. But if it doesn't provide a construction for a strategy, then it is constructively valid proof of what? On its own, for one proposition, and not another, as you explained. Alongside a decision procedure, for both propositions. For us, in practice, a trivial distinction. For the article, what SSA actually proves goes to the very heart of the topic.
 * So, the question is what should the article have to say about that? As XOR'easter pointed out, the article currently "benefits pretty much nobody" re the above. That's a fair enough paraphrase of my original objection to work with. Since the SSA really is constructive, then let's just delete the unclear suggestion that it's not. Figure out how to put it back later if we find a source more appropriate for the audience than Bishop's expert-directed quip. Belovedeagle (talk) 08:00, 5 April 2022 (UTC)
 * Again, our own philosophical maunderings are irrelevant here. We need sources. Do you have any? —David Eppstein (talk) 15:54, 5 April 2022 (UTC)
 * My suggestion is to remove the "non-constructive" claim. I am not suggesting to add anything to the article. Are you suggesting that we should find a source that says "the Wikipedia article on SSA is confusing and this should be deleted"? I currently can't tell if you agree or disagree this suggested change should be made, or are neutral, or if your reply has anything to do at all with the text it's under. Belovedeagle (talk) 20:06, 5 April 2022 (UTC)
 * The claim that it is called non-constructive is sourced. What published sources are you bringing to bear for your assertion that we should say something different in its place? —David Eppstein (talk) 20:56, 5 April 2022 (UTC)
 * I am not asserting we should say anything at all in its place. In fact I'm not asserting anything, I'm seconding a suggestion.
 * As I have already tried to explain, it is not possible to have a published source for deleting confusing content from an article.
 * Also, the claim that it is called non-constructive is not sourced. To have a source for that claim we would need to have something saying "Bishop said in [cute] that SSA is non-constructive". What we actually have is a source saying "SSA is not constructive". I don't really care about the distinction myself as it's irrelevant to the discussion, but since it appears to be very relevant to you, please do note the distinction. Belovedeagle (talk) 21:25, 5 April 2022 (UTC)