A better definition would be the other way around:
A group is dead if the opponent can capture it even against strongest resistance.
WillerZ: This is a bad definition, as it implies that the opponent of the player with the dead group plays first.
A group has two eyes if the opponent cannot capture it because filling its second-to-last liberty would be suicide.
A group lives in seki if the opponent cannot capture it because filling its second-to-last liberty would be self-atari, resulting in two eyes for the group.
22.214.171.124: I agree - it seems to me that, since two eyes and seki are not the only way a group can be alive, being unable to attain them is not the only way a group can be dead. A proper definition would be that no matter what moves the group's owner makes, the other player can capture the group (although possibly at the expense of their own groups - gets a bit fuzzy there).
WillerZ: The two headed dragon has two eyes.
WillerZ: One could argue that all of those are dynamically seki or two eyes, in that there is a forced cycle in which both players play the same number of moves that can only be interrupted without loss by either side when the groups in question are temporarily two-eyed.
xela: "One could argue..."--that is the most important point here, that the definition at the top of the page leaves a lot of room for argument. If "dead" can be defined without reference to eyes or seki, then there is no room for argument. (Of course, we can still argue a little over the precise wording: "stones are alive if they can not be captured, and dead otherwise" is too vague.)
SL discusses the same over and over again, but why? Formal definitions of life, death, seki, eye, etc. are available in the Japanese 2003 Rules, its derivates and extensions, or via the two-eye-formation and two-eye-alive approach. --RobertJasiek
The text in the Chinese Rules is not a definition of life and death in a strict sense - instead it is a guideline for a procedure to be applied by the players. After all, they might also disagree. In fact, the procedure in case of disagreement comes closer to a definition. --RobertJasiek
Bill: The Chinese rules definition is pragmatic. As Robert says, it provides guidelines that players might use to reach agreement. Let's take a look at it.
At the end of the game,
Rules do not have to define life or death before the end of the game. Then the question is whether certain stones may be removed without capture. For area scoring, which the Chinese rules use, this question is not, strictly speaking, necessary, since play can continue until no dead stones are left on the board. However, people would like to avoid unnecessary play, and the rules allow them to do so.
A definition that applies at the end of the game can be simpler than one that applies during play, because there should be no unsettled positions at the end of the game. Stones should be either alive or dead. Still, end of game definitions are basic. A necessary condition for stones to be dead is that they may be captured or removed at the end of the game, but do not have to be captured before then, unless forced to do so. (Nothing is ever quite so simple as we might wish. ;-))
stones which both players agree
Life and death is a matter of agreement. Perfect play is not assumed. The definition is pragmatic, not theoretical. However, the agreement of the players is constrained.
could inevitably be captured are dead.
Inevitably is not strict language. There are some unstated assumptions here. One is alternating play. Another is that one player tries to capture the stones while the other player tries to save them. Another is that the players are trying their best. Another is that the defender is allowed to play first (or pass, if playing a stone would be disadvantageous). More formally, we might say that, under alternating play with the defender going first, for every possible play of the defender (including pass), there is a sequence of play that results in the capture of the stones. But that is a theoretical, not a pragmatic definition. It also fails to address certain problematic ko positions, such as moonshine life, which is dead by the Chinese rules. Like the Ing rules, the Chinese rules could say that passes lift ko bans, but they do not.
Stones that cannot be captured are alive.
Again, cannot is not strict language. The real point of this (by implication) is that there should not be unsettled positions at the end of the game. Stones are either alive or dead. If the defender cannot prevent their capture, they are dead; otherwise they are alive.
By removed Ing means essentially the same thing as captured in the Chinese rules. But the Ing ko rule is different, so that some stones may be regarded as dead under one rule set and alive under the other.
According to one theory of Ing rules interpretation, "can be removed" refers to the state of already being breathless. According to another theory, it refers to perfect hypothetical play. The latter would mean the same as "could inevitably be captured" in the Chinese rules.
Bill: The Ing rules state: "Stones with unreal breaths are dead." That is not the same as being breathless. (OC, it is not a definition of death, but of unreal breath.)
RobertJasiek: The Ing rules state: "[...] unreal breaths for non-life [...] Stones that have lost all their unreal breaths are said to be breathless. Removal: Breathless stones are taken off the board [...] Life and Death: Stones live or die according to whether they can be removed. Stones that can be removed are dead; stones that cannot be removed are alive. These are the only crieria for life and death. [...]"
To unwind this from the end: "These are the only crieria for life and death." <-> Life versus death depends on "can be removed" <-> Removal is taking breathless stones off the board, i.e., breathless stones can (may?) be taken off the board <-> "breathless" is the property of stones having lost all their unreal breaths. (One wonders whether also stones with other types of breaths could ever lose all their breaths, but this is side problem.) <-> Unreal breaths occur for / in / together with (?) non-life, where non-life is undefined, but this is not such a big problem because application of "unreal breaths" is only necessary under the property of stones (already) having lost all their unreal breaths, which defines breathless.
To summarize this reading, "death" equals "can be removed" equals "taking stones off the board" equals "the stones are breathless" equals "the stones have lost all their unreal breaths" equals "non-life". If we now set "death" and "non-life" equal as linguistic synonyms, we have detected a vicious circle. However, apart from this logical sin, the apparent intention is that "death" equals "already being breathless"
The other interpretation puts much greater emphasis on "can" and makes the unbelievable supporting claim that Ing rules would have been derived from Japanese rules (where the hypothetical possibility in a word like "can" plays a real, intended role) while everybody should know that they were invented to oppose and surpass in particular also Japanese rules and that Ing rules have the basic intention of being play-it-out rules whenever necessary. That Ing rules (and Chinese rules) carry much linguistic ballast about life and death with them is a remainder inherited from Japanese rules or their influence even in China and also explained by the much slower progress of Western style rules theoretical thinking, which has elegance and abstraction, within the Asian countries (except for Western style theoreticians like Ikeda, whose rules were not known to Ing).
Bill: Ing rules example (Diagram ) of dead stones with unreal breaths:
The White stones are dead.
RobertJasiek: Good argument. I have never looked at that example seriously, maybe because I concentrated more on rules. - Ok, what does the diagram mean? I suppose that not all breaths shown there shall be unreal. Unreal breaths are unreal for a particular player (unless we have an anti-seki). For the opponent, they are real breaths! To explain which breaths are unreal, one needs to apply methods of the Japanese 2003 Rules. Besides one has to correct similar design mistakes in the rules about multiple threat positions. - What is the relevance of the Ing Rules' "definitions" about life, death, and breath types? If the players are supposed to agree, may they agree as they like or do they have to agree strictly according to the life, death, and breath types "definitions"? - I begin to wonder whether Ing 1975 Rules were as good as their reputation is or whether they had the same dependency on life and death. I.e., were they simple area scoring rules or were they life and death area scoring rules?
Bill: I saw them, even wrote an article in the AGA Journal about them. I am not absolutely sure, but I think that life and death was not part of the 1975 rules. Ing did not become overly concerned with life and death before reformulating the ko rules, which require life and death to be settled for disturbing kos.
RobertJasiek: They also contain some life and death text, but I do not have the booklet at hand now. - If one is not pleased by rules depending on cycle length, then a disturbing ko / fighting ko distinction needs to depend on life and death in some sense. Ing wanted such.