Chess will never be solved, here's why

Euler now mentioned by @Elroch.
Euler was a great Swiss mathematician.
His equation e to the (i x pi) = -1 has been considered by some to be the most beautiful equation in all of math.  
Its called 'Euler's identity'.
Unfortunately - I have no easy way to type the equation in proper algebraic format.  
e is the base of natural logarithms.
i is the square root of minus one and is the base of complex numbers - if I recall it right.  It was called j when I studied it back then.
pi is of course ...  a transcendental number like e but much better known to the public than 'e'.
Volume of pizza pie with thickness 'a' and radius z ...
Pi x rsquared x a = Pi x z x z x a.  Which algebraically can be written
'Pizza'.  

#3041
"There is a set of first moves that win, a set that draw and a set that lose"
++ Yes, that is true. The set of first white moves that win is conjectured to be empty. The set of white first moves that lose may be empty. That leaves all 20 first white moves in the same subset of moves that draw. However, by human logic per Capablanca no move accomplishes as much as 1 e4 or 1 d4. Thus if 1 e4 and 1 d4 are proven to be in the set of moves that draw, then as a corollary 1 a4 cannot be in the set that wins.
If 1 e4 and 1 d4 are proven not in the set of moves that win, then the logically inferior moves like 1 a4 are not in that set either and the set of winning first white moves is empty as conjectured.

#3041
"But note also that chess is not mathematics. "
++ Chess is a game, but game theory is a branch of mathematics and thus solving chess is mathematics.
Maybe the analogon of Capablanca vs. AlphaZero would be Euler vs. Appel & Haken.
Appel & Haken used a computer to prove the Four Color Theorem, that is not more reliable than the proofs of Euler without computer. When Appel & Haken finally had proven the Four Color Theorem (longtime known to be true, but not yet proven), many mathematicians doubted the validity of a computer proof.

Since you missed this, I will post it again.

To weakly solve chess, the game-theoretic value of the game and a strategy to achieve that value must be determined. Being 100% sure of something without proof means that thing is considered an axiom. Using axioms like "the game-theoretic value of the game is a draw" and "this strategy is superior over that other" to prove in fact the axioms themselves, is a fallacy known as "begging the question". Excluding "inferior" strategies makes actually impossible to falsify the assumption of their inferiority.

Many posts ago you said:

I asked if you can provide papers supporting this statement, because we use in general only two values of truth: true and false. Are you sure you did not mistake "provability" for "probability", reading something about fuzzy logic? If that statement was true, a proof could not be true at a higher degree, compared to a knowledge already 100% true.

That calculation is flawed for "begging the question" and other reasons, but you refuse to address its many problems.

Projection again.

 "Using axioms like "the game-theoretic value of the game is a draw" and "this strategy is superior over that other" to prove in fact the axioms themselves, is a fallacy known as "begging the question"."
I think its also called circular reasoning.  And its a form of illogic.
@Haiaku is correct as usual. 
But @tygxc will 'get away with it' in a double-edged sense.
He won't concede anything - but continues to be exposed.

@tygxc is a very good chess player.  
In conversations that resemble chess games ... a square and what's on it (issue in the conversation) can be contested - or conceded - or ... simply shift activity to another square.
Each square can be considered to be a kind of game in itself.
So anytime @tygxc looks like he might be 'in trouble' on a particular square ...  he can simply shift his responses slightly. 
The other person 'waits' for a response but there isn't one.
So the closest @tygxc comes to concession - is silence.
What is very paradoxical about this though - is he is able to do this quite civilly.
More about that in a minute - but first:
we got this a few pages ago:

Various ideas:
1) 'how to debate' can be typed on google search
2) 'debate' is a broadly-used term on the website. 
There are few if any conversations on this website that are like proper debates in debating societies in Universities.
Nor even approaching the organization in political debates on TV between politicians running against each other for election to high political office.
In a 'true' debate you might even see the two sides switch positions.
Each 'team' will take the opposite position they took in the first debate and then the debate happens a second time.  But differently.
A panel that does not include any member of the two debate teams will vote on a 'winner' of each debate.  Plus maybe 'grade' the teams.
That panel also moderates.  Applies rules.  Maintains decorum and so on.

///////////////////////////
Again:

That post was addressed to @tygxc - not 'somebody'.
Point:  It seems that @tygxc has not responded to @Haiaku 's reminder of providing a 'paper'.  
If anybody tries to do @tygxc 's answering For him ...
after the conversation had already 'converged' on @Haiaku 's reminder to @tygxc ...
well the result of that is definitely more 'circles' because it greatly enhances @tygxc 's opportunity to sidestep the reminder.  Or obfuscates it.
But - extra ironic ...  interference by that third person - is from that same third person who bitterly complains about 'circles'.  

Again:  from @Haiaku to @tygxc 

Has there been any indication here that @tygxc has read that response 'paper' and responded to that reminder?
Just repeating den Herik's definition over and over is 'dodging'.
@tygxc 'interpreted' den Herik's definition.

But @tygxc has no compelling obligation to consider the other paper provided.
Even in a proper debating society in a University - he would not have to do so.
Nor in a court of law in front of a jury.
He might have to acknowledge official 'receipt' of the paper -
which is called 'Discovery' I believe ...
or - has to indicate whether he accepts or objects to 'Exhibit A' or whatever.

but in jurisdictions - a lawyer is not directly compelled to read evidence.
He could lose business - get his reputation hurt ...  but would any judge anywhere have grounds to find him in contempt or get him disbarred ?
Extent of obligation: 
"Your Honor - I acknowledge to the Court that Defense has no objection to Exhibit A."
He then can ignore Exhibit A completely if he chooses.

Here's another circular assertion from @tygxc 
From post #177 - way back in January:  Here:  https://www.chess.com/forum/view/general/chess-will-never-be-solved-heres-why?page=9#comment-67001537

"Checkers was solved by only the square root of the number of legal positions. Hence it is plausible to apply the square root in chess too to account for all positions rendered irrelevant."
No its Not.  Nice try though.  
How many of these has he made? 
Maybe they can all be summarized in one list.

'adjective' yes. 
But the constant and consistent projection from the individual is remarkable. 
Every time he does something - its 'the other person doing it'. 
Close to 100% of the time.  He'll even project his projecting too.   
But that's part of chronic projection though. 
If he admits it - how can he continue?
It might even extend to his trying to deter use of the word.
One is not to say it ? 
And 'is not to disagree with him nor criticize any post he makes'? 
A kind of 'emperor has no clothes but you mustn't say it' situation.

#3046
"Provability is a higher degree of truth.
I asked if you can provide papers supporting this statement, because we use in general only two values of truth: true and false. Are you sure you did not mistake "provability" for "probability", reading something about fuzzy logic? "
++ Yes, I am sure the phrase was 'provability is a higher degree of truth'. It figured in a feature article in Scientific American about unsolved mathematical problems including at that time Fermat's Last Theorem. It also discussed ramifications of Gödel's incompleteness theorems.
I cannot unfortunately provide volume, no., or page: I have no eidetic memory allowing total recall.

And now 'Godel' too?  (some assert that Kurt Godel effectively argued or 'proved' for a real possibility of 'reverse time travel' ?)
'Godel' help us !!

Actually Truth is a higher level of provability.

This is only slightly ironic: in mathematics, this is meaningful because of the existence of alternative axiomatisations. Goedel's incompleteness theorem showed that no finite scheme of axioms can fully represent any mathematical system sufficiently rich to include the natural numbers.

What happens in practice is that any given axiom scheme in incomplete in that there are statements about the natural numbers that true but not provable in that scheme. An axiom can be added to fix such a hole, but there will always be another example.

To avoid any confusion note that this does no harm to the present discussion. We are talking about very simple statements that would be provable in any formal system representing the finite structure of chess. This is _much_ simpler in a fundamental sense than the natural numbers, which are intrinsically infinite.  But what we are discussing is a formal proof of a fact about this finite structure called "chess" (with some chosen rule set). That is the strict and appropriate meaning of "solve".

Hi @Elroch !
Regarding 'proof' and its realities:
There's something that could be called 'objective proof' and there's lots of that around.
But then there's a flip side of proof.
Which isn't quite like the silliness of "if a tree falls in the forest but there's nobody around to hear it then it makes no sound" ...
not quite as 'silly' as that.

It goes like this:  its a kind of analysis of 'proof' behaviour.
And some optional connotations of the word 'proof'.
I'll put it as a question:
Does 'proof' require cooperation from the person to whom something might or might not be proved to?
I would say ...  Yes.  Its not proof unless whoever finds it such.
Even the proof there is no greatest prime number -
a very very Neat proof ...
well whoever can simply refuse to follow the logic of it.
"No - that's Not Proof !"  And then even assign his own 'defaults'.
We've seen that here.  

It's probably worth bearing in mind the notion of a mechanised proof. This is one where the axioms are encoded and every logical step verified by computer in full detail.

Normal mathematical proofs have the character that they could feasibly be mechanised.

For example, this has been done for both of Goedel's main theorems.

I looked at that linked site for a bit.
'Mechanized proof'.
Could a computer prove the 'no greatest prime' argument ?

I would guess yes.  Using computerization of mathematical logic.
But only a guess.  I would think the computer would need much 'help' from a human programmer - to so prove.  
Makes me wonder - do computers solve differential equations ... and very tough integrals - where just substituting values for variables in  formulas isn't going to work ... ?
Maybe differential equations have changed a lot nowadays ...

Not only "could", pretty sure that has been done. I think all of Euclid has been mechanised. Here is a paper about mechanical verification of book I.

Even there - 'proof' to whoever might still 'require cooperation' by the provee.
Yes - I realize that the 'proof' still exists if whoever refuses to accept it.
But there's something about the word that connects with 'it takes two to tango'.
Pi would still be a constant without anybody around to know that it is.
Einstein apparently didn't need anybody to agree with him initially or at all - for his fundamentals to exist and be valid.
(ein ...  a ... 'one')
But for 'proof' something about that word implies 'at least two persons participating and with some degree of cooperation'. 

Regarding a chess engine defeating itself after being given material odds ...
Perhaps it would be better to have it play such against different engines.
Otherwise - it supports its own flaws.
In the research projects though - maybe that would slow down the 'solved' stuff too much.