With Best Play for both sides Chess is a Draw--So Why Do We Play?

I repeat the word "fact" has several meanings. I do not have a "hunch" that chess is a draw. [you are putting words in my mouth to say that]

It really does not matter how many times someone says differently-chess is a draw with best play. It is a "fact" to me as the evidence is overwhelming.

It is unknown to many that chess is a draw.

What is your source for your various definitions of "fact"

"You know, the irony of this whole debate (seems like this often happens when it's about philosophy) is that I think we both agreed the entire time, but thought we disagreed with each other because we didn't know what the other person was arguing. "-Elubas

Yes, that's why professors at my University in the Phil. Dpt. grade heavily based on clarity of presentation for arguments (and of course logical inferences used, etc).  I really advocate clear definitions at the start of any sort of rational discussion to at least try to avoid such ambiguities that lead to mistaken disagreement.  Also, something I don't think has been brought up yet.  Is it possible that chess is simply and unequivocally drawn (given overwhelming evidence), or is there another alternative in that on move 1, white is in zugzwang (qua drawing, not losing).  Someone at the US Open posed this to me.  I have yet to make up my mind.  I think it is more interesting to ponder this for awhile, as we may make some kind of progress...

I like how "appeal to authority" is used as a positive when it's a logical fallacy :)...(I'll use Wikipedia just to annoy the flying pigs...): 

Fallacious examples of using the appeal include:

• cases where the authority is not a subject-matter expert
• cases where there is no consensus among experts in the subject matter
• any appeal to authority used in the context of deductive reasoning.

This thread would be a textbook example of #3.  If 95% of the subect matter experts once thought the earth was flat, that does not affect the reality of the situation in any way ;).

Maybe Ponz should change his name to Ptolemy :)...

 I know i'm goin' against the grain, and i don't care what any of you people think, but there is literally no concrete proof that chess has ever been perfectly played, and seeing as chess is a science just as much as it is an art-form, any statements that a perfect game of chess is a draw is baseless. 

On numbers:

Someone said that numbers are a concept/construct made up by humans...

No.  Numbers and mathematics are names and nomenclature for observable "things" and rules in our universe.  If you have 3 apples and 3 people, they each get one if you hand them out...it doesn't matter if the whole human race agrees on changing the number 3 to the number 2.  It would be like saying that the color blue is a concept.  It isn't.  The word blue, like every word in every language, is an approximation of something, and relies on shared agreement for communciation, but that doesn't not mean that part of the light spectrum that we agree is "blue" does not exist, or that light would suddenly reflect off matter differently or hit our retinas differently if we decided blue was something else.

Chess is an interesting case of this fallacy, however, because it has become an integral part of chess study to rely heavily on chess engines.  In a certain sense, we do not "know" what the computers tell us in any immediate sense (which some accept as the only acceptable form of knowledge).  It was a question in my Ordinary Language Philosophy class I took my first year of college whether my professor knew Godel's Incompleteness Theorem (he had known it well enough to explain it to others and prove it about 40 years ago).  What would constitute knowledge of the Theorem?  There is a similar vein to this discussion given it has a particularly epistemological inclination thus far.  Do we know that a variation is bad simply because a computer spits out x centipawns to the opponent's side (perhaps assuming the computer had perfect knowledge in the most God-like sense)?  It is a bit of a tricky subject to begin with so perhaps it is not so easy to grace Ponz with the epithet of Ptolemy...

Actually, I think appeals to authority can have their uses. Particularly when there is not enough information to determine the truth of something. So, sure, if it turns out that there is a forced sequence out there that wins for white, the fact that strong players believe there is none will not change that at all. However, since we don't have all of the information out there, seeing what strong players say can give a better idea of what the truth might be.

For the sake of argument let's say that 60% of the time authorities are right. I am certainly not claiming it's the believing that is causing the thing they are right about to be true. Rather, that the authorities are, generally, better able to make the best guess on their subject based on their understanding of it.

Perhaps there is some strong understanding (that I might not have), that allows great players to confidently make such a conclusion. Certain things might seem ridiculous to me because my understanding doesn't find merit in them; the question is, is this because they are actually ridiculous, or because my limited base of understanding can't appreciate its merit? So although I will be happy to raise any doubts about what an "authority" says, I have to wonder too, there is a definite chance that the reason I am coming to a different conclusion to them is because of my limited knowledge base.

No, it's not necessarily the case, but it's a definite possibility. It doesn't mean I will automatically drop my disagreements, just that I am more likely to take my disagreements with a grain of salt.

With best play from both sides, white would achieve checkmate one move faster than black.  White would always win.

yes sorry thread is out of hand

Dear Jaaas,

A dictionairy shows the way a word is used. It is not the truth what a word means, it shows its use on average. If the word is used within a small group of experts differently then in daily life yet less times then the threshold for the dictionairy, then will that word usage not return in a dictionairy. Even if it is correct or better or more precise or just different then what is used in daily life or shown in the dictionairy.

Take for instance the word second. The second of a chess player is not mentioned in the dictionairy. Does it mean that that meaning of the word does not exist? No, only that this particular meaning is below the threshold for making its appearance in the dictionairy.

If you take a thorough look at the four definitions, then can you see that the first three definitions are equivalent and boil down to the first one. Something must have happened. The last one, the proven one, is different. That one requires knowledge and that one is imo not a proper definition of a fact.

To proof that a woman was not a witch had you throw her chained into the water. If she drowned, she was not a witch. That is a fact. Right.

The theory of Newton could proof a lot of things, but not the planetairy orbit of Mercury. Does that make the orbit of Mercury not a fact? Does that proof that the orbit of Mercury is not happening? Or does that make clear that with proper reasoning a proof can not be used to establish a fact?

A proof does not proof the fact, but the theory which is used to create the proof. That is the use of a proof: to show the explanatory power of a theory.

Looking at more than one game when there is no proof that a draw would result with perfect play, or any proof that white (or black) would win in a perfect game is going nowhere.  This whole discussion is a waste of time because humans will never play perfect chess.  And the day that happens will be a very sad day indeed.

LoekBergman got back to me via PM regarding the ongoing discussion - I thought I might as well post a part of the reply here, as I believe it makes points I was making earlier in this thread more clear and systematic. Perhaps it will be of help and might shed a new light at the issue for someone.

* * *

In my opinion, the fundamental misunderstanding lies in the confusion of

•  the existence of a fact for itself (and, by extension, the truthfulness of a statement asserting this fact), versus
• the logical meaningfulness (or a lack thereof) of a statement about that fact being made by a certain entity under the circumstances it was made, based on that entity's knowledge (or a lack thereof) about said fact.

Let me illustrate this in the following way.

You will probably agree with me, that according to scientific knowledge regarded as facts, we may assume that the Earth has been orbiting is parent star, the Sun, since a few billion years.

Now, let us imagine that a caveman a hundred thousand years ago had made the following statement:

"It is a fact, that this huge cluster of rock I am dwelling on is round in shape, and is running around the fiery light in the sky."

Now, let us answer the following questions:

1. Was the statement the caveman made reflecting the truth when it was made?

Answer: Yes. Obviously, as it seems. Albeit (and this is crucial!), we are able to tell, because we know now that the Earth orbits the Sun (and we also know, by hindsight, that this was the case 100,000 years ago).

2. Was the caveman's statement logically meaningful when it was issued?

Answer: No (this is very important, and is the core of the point I was attempting to make all along). The caveman himself had no means whatsoever to obtain any evidence which would either prove or disprove the truthfulness of his statement. As such, given that the statement's truthfulness was undetermined at the point it was made, it could not be rightfully (from a purely logical point of view, any concerns such as law or ethics are irrelevant here) claimed by the caveman or any of his fellows to be either true or false (even though we by hindsight know now that it did then, as it does now, reflect reality).

3. Did the fact, that the caveman had no real knowledge whether what he was stating was true or false (due to him having no chance to obtain hard evidence confirming or contradicting his statement) have any influence on whether at that point the Earth was actually orbiting the Sun or not?

Answer: No. This is so obvious, that I presume no further contemplation of this question is necessary.

As we can see, the meaningfulness of a statement (i.e. whether there is enough grounds to assume it being either true or false) made under certain circumstances is very dependent on the actual circumstances under which it is made - and this is a matter completely separate from whether the statement actually is true or false. Even though the caveman's statement is now, by hindsight (i.e. under the present circumstances), known to have been true, it's truthfulness was undetermined at the time it was made, and as such the caveman had no right to call it a fact.

In this sense, the meaningfulness of a statement under specific circumstances could also be referred to as its relative derminability, or meta-truthfulness.

* * *

Now let's fast-forward, and put this into a perspective of the actual matter discussed in the forum topic in question.

Member Ponz111 makes the following statement:

"It is a fact, that a game of chess, if played perfectly by both sides, will inevitably end in a draw."

(While this is not an actual word-for-word quote of him, I'm sure that Ponz111 himself would agree that this essentially is what he has been asserting.)

Now, let us answer the following questions:

1. Was the statement Ponz111 made reflecting the truth when it was made?

Answer: Undetermined. As there is presently no knowledge of a method which could enable anyone to prove soundly and beyond any doubt whether a hypothetical perfectly played by both sides game of chess would specifically end in either a draw, a win for White, or a win for Black, nobody can possibly assess the truthfulness of that statement at this time. All we know right now is that one of the three above possibilities certainly must be, and as such, is true, but which one of them it actually is, is simply unknown under the present circumstances. Any number of opinions, even by those who are universally considered authorities on the subject matter (in this case, chess masters and grandmasters), is just that - a collection of opinions does not constitute a hard proof, especially not in a case that is as fundamentally based on logic as chess is.

2. Was the Ponz111's statement logically meaningful when it was issued?

Answer: No. As the truthfulness of the statement is undetermined under the circumstances it was made under, i.e. at present time (as shown in the answer to question #1), the statement is not logically meaningful. As such, any assertions of the statement being specifically true (which calling it a "fact" would boil down to) or specifically false made under the current circumstances are logically invalid.

3. Does the fact, that Ponz111 (or anyone under the present circumstances) has no real knowledge whether what he has stated is true or false (due to him having no chance to obtain hard evidence confirming or contradicting his statement) have any influence on the specific inevitable outcome of a game of chess played perfectly by both sides?

Answer: No. The specific inevitable outcome of a game of chess played perfectly by both sides is determined by, and only by, the rules of the game. There is obviously no influence someone's knowledge (or, specifically, our present lack thereof) about this outcome could possibly have on what the outcome actually is (quite to the contrary, the outcome needs to be specific in the first place for any specific knowledge of it to be able to possibly arise).  Knowledge obviously has no influence on the fact itself, but has a (decisive) influence on whether the truthfulness of statements concerning the fact can be determined under the given circumstances.

A more general summary (which, hopefully, helps to clear the confusion for good):

A fact makes knowledge about that fact possible. In turn, knowledge about the fact makes it possible to determine whether a statement concerning that fact is true or not.

If under certain specific circumstances the knowledge (i.e. the link between the fact itself, and the determinability of it being a fact) about a fact is missing, the truthfulness of specific statements about that fact made under these specific circumstances is undetermined (irrespectively of whether that fact can be determined as being specifically true or specifically false under other circumstances which provide the necessary knowledge).

* * *

I hope the example and the subsequent fitting of its reasoning into the context of the matter debated over in the forum thread makes as much sense to you as it makes to me. Still, should anything remain unclear, don't hesitate to point it out and, if possible, I will try to explain it further.

Regarding paradoxes: you're right that a statement, besides being true or false, can also be self-contradictory, i.e. paradoxical. However, for a statement to be self-contradictory it must be self-referencing in the first place - though not every self-referencing statement must be self-contradictory, as we shall see below.

The sentence "This is true", assuming that the word "this" contained in it refers to the whole sentence itself, can be either true or false, not leading to any paradox. All the sentence states is asserting itself, thus there is no knowledge which would allow to determine its logical value - it's truthfulness is undetermined (just like the caveman's statement about the Earth orbiting the Sun from the perspective of 100,000 years ago, or Ponz111's present-day statement about chess being inherently drawn with best play on both sides), with the exception that it is universally undetermined, i.e. under any circumstances (precisely because of it's lack of any content beside its self-assertion).

The sentence "This is false", on the other hand, is self-negating rather than self-asserting, and as a result it is self-contradictory, i.e. paradoxical. While its truthfulness could be called "undetermined" as well, it's a different type to those seen thus far, as a paradoxical statement can be neither true nor false.

Here a comparison of the two determinable (each under specific circumstances) statements we have been dealing with before, as well as the two non-determinable, self-referencing statements:

Caveman's statement:

• Truthfulness under original circumstances: Undetermined, no way for the entity who stated it to obtain knowledge that would verify it
• Truthfulness under present circumstances: Determined as true
• Statement determinable? Yes, its truthfulness ultimately depends on the laws and the physical reality of (at least a part of) our universe

Ponz111's statement:

• Truthfulness under original (present) circumstances: Undetermined, currently no way for humanity to obtain knowledge that would verify it
• Truthfulness under possible future circumstances: Determined as either true (if the game of chess with best play on both sides inherently drawn), or false (if the game of chess with best play on both sides is inherently decisive either in favor of White or in favor of Black )
• Statement determinable? Yes, its truthfulness ultimately depends on the rules of the game of chess (but the precise determination of it seems to be a staggering task)

"This is true"

• Truthfulness under any circumstances: Undetermined, can always be either true or false
• Statement determinable? No, no content besides self-assertion

"This is false"

• Truthfulness under any circumstances: Undetermined, can be neither true nor false (paradoxical)
• Statement determinable? No, no content besides self-negation

[Edit: whoops, I ended up pasting more than I intended, as the stuff concerning self-referencing statements was not actually part of this thread. Whatever, perhaps it's informative to someone too.]

It's a well thought out post, jaaas, and I agree with the general point. Indeed, if a caveman claimed as a fact that the earth revolved around the sun, or something equivalent, if he had no reasons or evidence to make such claims, then for his situation it was silly for him to make such a statement. It would just be dumb luck that he turned out to be right in that case.

Regarding the "proving" of something, yes, at the very least a hard proof is needed if you want 100% certainty about something (unless perhaps the truth is axiomatic). However, I would argue you can predict a lot about something even without even close to a maximum amount of info.

For example, why is it that a grandmaster is so confident that an extra rook in an endgame, with some pawns for both sides and kings for both sides (and nothing else), wins for the side with rook, if he only has a, relatively speaking, extremely limited experience with such positions? Perhaps there are trillions of positions/branching variations that are as I described -- certainly, the GM couldn't have looked at, let alone analyzed, all of them. And yet, the GM assesses his chances to win so confidently. The point I'm trying to make is that sometimes you can know a lot about something (albeit not 100%) even if you haven't even come close to analyzing every single possibility in a situation -- he's taking a tiny sample of those possible positions and yet he is able to make such confident claims about nearly all of them.

There have been billions of chess games played. If either White or Black had a win from the initial position then there would be some games where either side won without his opponent making a mistake.

Since there is not even one such game out of billions, I would think this pretty much proves chess is a draw

I guess jaaas would argue that it is just 1 billion out of 10^60 positions or something like that.

The medieval "proofs" of witchcraft were not actual proofs, as they were dogmatic in nature. They were non-self-evident statements accepted without a sound proof and spread as supposed "fact" by means of zealotry (i.e. dogmatized). I suppose there is neither a need nor point to throw that kind of stuff into the mix if we are discussing matters to be taken seriously from a scientific point of view.

The nature of the orbit of Mercury was confirmed to be fact by a combination of astronomical observations and calculations. What was further desired was an explanation of its peculiarity - Newton's laws of physics happened to be insufficient for this. More recent knowledge has been able to explain it sufficiently.

A practical assessment of such a position is never 100% complete, unless you know that the defending side will either be checkmated soon in a predictable way, or that the winning side will be able to make further material gains so as to be able to win trivially without commiting blunders.

On the other hand, there are (not necessarily obvious) positions were the defending side would be able to establish a fortress and thusly secure a draw. Also, there are other positions where the rook could be trapped and eventually lost with optimal play on both sides - the side seemingly defending would thus turn out to be able to win.

Perfect position assessment requires the knowledge of the outcome of perfect play from the position by both sides, and that is what only tablebases could provide thus far. To determine the outcome of a perfect game played from the starting position we would need nothing less than a functional equivalent of 32-man tablebases (the tablebases themselves in the current sense are rather infeasible to be procured, as I hinted at here). How real such a prospect is to be realized is not something I would suspect any of us to ever know.

Truth be told, statistical probability is just an estimate, and by no means razor-sharp evidence.

As mentioned above, to determine the outcome of a perfectly played chess game we would need a functional equivalent of a 32-man tablebase, if only for the single position which constitutes the Array (starting position). Tablebases aren't computed based on fortune-telling, or on estimates relying on statistical probability. The computational algorithms leading to a acquiring a set of data which constitutes a tablebase require 100% exactness, just as scientifically accepted logical methods which allow to prove mathematical theorems beyond any doubt.

Have you taken a science class? Did you pay attention to science classes?

Einstein : E=mc^2. The Last Fermat Theorem, etc. Michellson : Ether vs Light speed. Darwin: Evolution Theorem.

They were not true (under some circustances), but they hadn't been proved to be false.

Have you ever heard of hypothesis?

Hypothesis has been used so that man can reach the moon and soon Mars? These men and women risk their lives just to prove some hypothesis ( or can I say the truth? )

So what if a hypothesis has not been proved yet? Man will seek it out.

Ponz didn't make up the statement or did he? He might have just quoted someone or some books. Yet he tried his best. You cannot blame him for trying. I will blame him if he doesn't try.