Gérard TAILLE wrote:CDavis7M wrote:The 5 White stones on the upper side are alive because even though they can be captured by Black, they can newly form stones

and

that cannot be captured by Black. Moves like

are not uncapturable unless a move like

reduces liberties in capturing.
The 5 stones are capturable and it is those capturable stones that are the ones that can newly form stones that cannot be captured by the opponent because it is those stones (
) that reduce Black's liberties such that the uncapturable stones can be formed.
Seeing your argument "The uncapturable stones can be formed without those stones being captured at all" I can propose another example for which this argument does not exist...
Note my point that I underlined above.
Let's try to capture the 9 White stones. Indeed there is a new uncapturable stone

. But does a new uncapturable stone mean anything by itself? I don't think so because in an actual game-play position, new uncapturable stones can always be played somewhere on the board (filling dame, territory, etc).
$$B
$$ +-------------------+
$$ | X X X . O . X . X-X X X . O . X . X -X X X . O . X . X
$$ | O O O O O X X X X-O O O O O X X X X-O O O O O X X X X
$$ | X X X X X Q Q Q .-X X X X X Q Q Q 3-X X X X X . . . X
$$ | . . . . X Q . Q Q-. . . . X Q 5 Q Q-. . . . X . X . .
$$ | X X X X X Q Q Q 1-X X X X X Q Q Q X-X X X X X . . . X
$$ | O O O O O X X X X-O O O O O X X X X-O O O O O X X X X
$$ | X X X 2 O . X . X-. 4 . O O . X . X-. @ . O O . X . X
$$ +-------------------+
- Click Here To Show Diagram Code
[go]$$B
$$ +-------------------+
$$ | X X X . O . X . X-X X X . O . X . X -X X X . O . X . X
$$ | O O O O O X X X X-O O O O O X X X X-O O O O O X X X X
$$ | X X X X X Q Q Q .-X X X X X Q Q Q 3-X X X X X . . . X
$$ | . . . . X Q . Q Q-. . . . X Q 5 Q Q-. . . . X . X . .
$$ | X X X X X Q Q Q 1-X X X X X Q Q Q X-X X X X X . . . X
$$ | O O O O O X X X X-O O O O O X X X X-O O O O O X X X X
$$ | X X X 2 O . X . X-. 4 . O O . X . X-. @ . O O . X . X
$$ +-------------------+[/go]
Backing up, the real question is whether it is
these 9 White stones that
can newly form stones that cannot be captured by the opponent -- is there some game-mechanic in the Game of Go that gives those 9 stones the ability to form stones that cannot be captured by the opponent. Or is it actually some other stones that already have that ability give the game mechanics?
Let's see what happens when Black tries to prevent the formation of the new uncapturable stones with

. If Black tries,

will reduce his liberties of

and White can capture with

. So yes, those 9 White stones are living stones because they contribute to the formation of the new uncapturable stones.
$$B
$$ +-------------------+
$$ | X X X . O . X . X-X X X . O . X . X-X X X . O . X . X
$$ | O O O O O X X X X-O O O O O X X X X-O O O O O X X X X
$$ | X X X X X O O O .-X X X X X O O O .-X X X X X O O O .
$$ | . . . . X O . O O-. . . . X O . O W-. . . . X O . O O
$$ | X X X X X O O O 1-X X X X X W W W B-X X X X X O O O .
$$ | O O O O O X X X X-O O O O O B B B X-O O O O O . . . .
$$ | X X X 2 O . X . X-. 3 5 O O 4 X 6 X-. X X O O O . O .
$$ +-------------------+
- Click Here To Show Diagram Code
[go]$$B
$$ +-------------------+
$$ | X X X . O . X . X-X X X . O . X . X-X X X . O . X . X
$$ | O O O O O X X X X-O O O O O X X X X-O O O O O X X X X
$$ | X X X X X O O O .-X X X X X O O O .-X X X X X O O O .
$$ | . . . . X O . O O-. . . . X O . O W-. . . . X O . O O
$$ | X X X X X O O O 1-X X X X X W W W B-X X X X X O O O .
$$ | O O O O O X X X X-O O O O O B B B X-O O O O O . . . .
$$ | X X X 2 O . X . X-. 3 5 O O 4 X 6 X-. X X O O O . O .
$$ +-------------------+[/go]
This is easy to confirm. Consider if

did not have the ability to reduce the liberty of

. In this case,

does not capture Black's stones because

would have a liberty were it not for

.

cannot even be played, letting

capture White, preventing the formation of new uncapturable stones.
$$B
$$ +-------------------+
$$ | X X X . O . X . X-X X X . O . X . X-X X X . O . X . X
$$ | O O O O O X X X X-O O O O O X X X X-O O O O O X X X X
$$ | X X X X X O O O .-X X X X X O O O .-X X X X X O O O .
$$ | . . . . X O . O O-. . . . X O . O O-. . . . X O . O O
$$ | X X X X X W O O 1-X X X X X W O O X-X X X X X W O O X
$$ | O O O O O B X X X-O O O O O B X X X-. . . . . B X X X
$$ | X X X 2 O . X . X-7 3 5 O O 4 X 6 X-X X X . . . X . X
$$ +-------------------+
- Click Here To Show Diagram Code
[go]$$B
$$ +-------------------+
$$ | X X X . O . X . X-X X X . O . X . X-X X X . O . X . X
$$ | O O O O O X X X X-O O O O O X X X X-O O O O O X X X X
$$ | X X X X X O O O .-X X X X X O O O .-X X X X X O O O .
$$ | . . . . X O . O O-. . . . X O . O O-. . . . X O . O O
$$ | X X X X X W O O 1-X X X X X W O O X-X X X X X W O O X
$$ | O O O O O B X X X-O O O O O B X X X-. . . . . B X X X
$$ | X X X 2 O . X . X-7 3 5 O O 4 X 6 X-X X X . . . X . X
$$ +-------------------+[/go]
The 9 stones are live. This is similar to Example 4.
----------
Here we can see that

have no ability to form new uncapturable stones. There's no game mechanic that let's them contribute to the formation. It is the other White stones that already have that ability. They are already alive when considered separately.
$$B
$$ +---------------+
$$ | . X . . X X X |
$$ | X X O O O O O |
$$ | . O X X X X X |
$$ | . O X Q Q Q X |
$$ | X O X Q Q . X |
$$ | X O X Q Q Q X |
$$ | X O X Q Q Q . |
$$ +---------------+
- Click Here To Show Diagram Code
[go]$$B
$$ +---------------+
$$ | . X . . X X X |
$$ | X X O O O O O |
$$ | . O X X X X X |
$$ | . O X Q Q Q X |
$$ | X O X Q Q . X |
$$ | X O X Q Q Q X |
$$ | X O X Q Q Q . |
$$ +---------------+[/go]