"The lines that no one has explored down to the tablebases yet, are unkown elements."
++ Many positions with more men than 7 are known draws or losses as well.
Many endgames with opposite colored bishops are known draws.
Many positions with huge material differences like a queen up are known wins.
"Missing the point" fallacy.
"how do we know that the positions in S are draws?"
++ For all positions of 7 men or less and even some positions with 8 men it is known from the table base. For some endgames like opposite colored bishops it is known from analysis. For some middlegame positions with huge imbalance it is known from experience and from logic.
Quoting out of the context and missing the point.
"you have no reason to believe that there will ever be a reliable proof." ++ A matter of money.
First of all, it is an epistemological matter.
"All analyses will be impossible to check." ++ And for Checkers and Losing Chess?
As above.
"To me the only real proof is an exhaustive one" ++ Connect Four has been solved independently in two different ways: an exhaustive one by Allen and a set of 7 rules by Allis. I believe weakly solving chess will be a combination of both.
Both are exhaustive. See the last section in this post.
"If one million mathematicians do all agree that T is a theorem, they might all be mistaken."
++ This has been heavily debated for the Four Color Theorem, but in the end it was agreed.
Missing the point.
"A statement like "chess is a draw because of the equalizing tendency" really cannot be considered scientific, or nearly as reliable as a computer-assisted proof by exhaustion."
++ That is vague.
In the second an third section of my previous post I addressed the problems with that statement. As for the reliability, an overgeneralization from a small sample of positions and games has a high probability to be proven false. We can make the following example (maybe someone else here already made it or a similar one, I do not recall well): we have 10²⁰ balls in a basket, few red, the other white; we pick randomly 10000000 balls; the red balls are 1/100000000000 (10⁻¹¹) of the total; the probability p to pick only white balls is approximately p = 0.99999999993. If we do not know a priori that there are red balls in the basket, by inductive reasoning we could well conclude that there is no red ball at all.
Computer-assisted proofs can be affected by glitches, but those proofs can be reproduced, there are methods to verify them, the probability that a glitch occur must be multiplied by the probability that the occurrence is crucial to the proof... In sum, they are much more reliable.
@Optimissed spoke of "full paradigm" for chess, but besides the fact that the word "paradigm" can be used in different ways, if the paradigm is the product of inductive reasoning, it has the same limits of the inductive reasoning.
++ That is vague.
However: white is 1 tempo up, experience shows 3 tempi are worth 1 pawn, 1 pawn is enough to win a game by queening it, 1 tempo is not enough to win, makes sense.
Overgeneralization and missing the point.
Also: 1 e4 e5 2 Ba6 white is a bishop down. A bishop is worth 3 pawns. A bishop is enough to win. 1 e4 e5 2 Ba6 is a win for black. That is without an exhaustive calculation to checkmate in all lines.
Overgeneralizations. And in that position my Lc0, after 25 million nodes (which is not bad for "her", as you know), still gives White 3.9% chances of winning.
In order to logically use knowledge A to prove something, you have to show that A is already proven; to prove A you can use logic and other proven knowledge B, and so on, down to axioms. Axioms are taken as always true, logic is taken as always true, so if you use them to prove something, that thing is taken as always true. That's what an exhaustive proof is: it is valid in any case. Unfortunately, the knowledge you plan to use is not always true and it is not proven that it would be, with optimal play, because optimal play has not been determined yet. The alpha-beta algorithm is always true: it is proven that it produces the same results of a minimax, so you can use it to cut off lines as soon as the search reaches the endgame. But knowledge as "a bishop is worth 3 pawns" is not always true, it is not exhaustive, so one can use it only for move ordering, when solving chess, not to cut off lines.
#3939
"sacrifices were sometimes valid "
++ Of course sacrifices are sometimes valid. But 1 e4 e5 2 Ba6 is no such time.
That is also why the good assistants are needed.
"Give me five years, good assistants and the latest computers
- I will bring all openings to technical endgames and "close" chess." - GM Sveshnikov (+)
The task of the good assistants i.e. (ICCF) (grand)masters is to launch calculations preferably from 26-men positions, but also to end calculations in clearly drawn, or clearly won positions, where they would agree on a draw or where they would resign in a real (correspondence) game.
You're talking of billions of chess positions, assessed by humans. You still think it can be done in five years and these others you're talking to cannot even work out that something's amiss. Something's amiss with their own critical abilities.