# Would I be correct in assuming that all* things have a 'best'? [closed]

My friend and I broke into an argument because I said that there was a best opening chess move. He clearly didn't agree with me and after much debate I came to the conclusion/theory that:

For any two objects in the universe of the same type, if one of the two objects is better than the other in any aspect (faster, more massive, etc) then there exists another object of the same type that is the best in that aspect.

Because if we have two horses and have them each run their fastest one will clearly be faster than the other which leads me to believe that there is a horse somewhere in the world that is the single fastest horse. But because a single proton is (to the best of my knowledge) exactly alike and indistinguishable (besides its position) from another proton, there is no proton that is better than the other in any aspect.

Assuming that these assumptions are correct, I proceeded to argue that since it is clearly possible for one chess move to be better than another, there must exist some chess move that is the best. And to further define this best opening chess move I concluded that it would be the single opening chess move that leads to the most favorable outcomes for the player.

I am here to ask if my theory has any major flaws that I have overlooked, and as it seems somewhat philosophical where else to ask then here.

Edit: Sadly many fail to realize I am not asking what the best move in chess is. The chess scenario was merely used to demonstrate how I got to my question. And several people have said that 'best' is too broad so I feel that I need to clarify that when I say best I am referring to a specific characteristic that would be relevant to a specific argument. I am not saying there is a single best horse in the world, but rather a best horse in terms of speed, a best horse in terms of endurance, etc.

• Actually, when you come right down to it, this is a math question. The question is 'Do all orderings have upper bounds?', and the answer is no. For any two numbers, there is a largest one, and yet there is no largest number. So I am going to vote to close. – user9166 Oct 26 '15 at 3:19
• Seems related to philosophy... related to some of the ideas for example in the Ontological Argument. – James Kingsbery Oct 26 '15 at 3:49
• `...the best in that aspect.` That may be the only saving grace, though it doesn't help determine what is meant by "best". E.g., if weight is the aspect, does it mean that "heaviest"="best"? Or is there some notion that "ideal"="best"? – user2338816 Oct 26 '15 at 4:58
• Considering the argument at hand: there is a best chess move. Chess has a finite game tree. Therefore, either white can force win, or it can force draw, or otherwise his first move doesn't matter. This holds for any node in the game tree. Therefore, there is an optimal path down the tree for white. – user2953 Oct 26 '15 at 9:17
• Is there a best star? A best amoeba? A best frequency of electromagnetic radiation? A best metal? A best remote forest pond? A best serial murderer? A best technological disaster? A best cancer? A best strawberry? A best example of the best ___ ? – Niel de Beaudrap Oct 26 '15 at 9:29

Mathematically, there is not always a "best." Mathematics allows for many situations where one cannot specify a best. Consider the trivial example of "Real numbers which are less than 2." If I define larger numbers to be better, what's the "best" number? The answer, according to set theory, is that there is no such largest real number less than 2. If I were to take the set of real numbers less than 2, it has no maximum. It's a bit strange, and non-intuitive, but that's how mathematicians have chosen to define sets to operate (the original construction, by the way, is called a Dedekind cut, if you care to look at them).

Beyond such mathematics, there is also the issue of moves that are "best" in some circumstances, but very poor in others. Let's say you got a super-computer to crunch all possible chess games, and they found that 1. Nc3 "wins." However, when people try to play this "best possible game," it is recognized that it is notoriously hard to win starting with Nc3 as a human, because some of the lines black can play are full of situations that are hard for white to analyze, but easy for black. Alternatively, you might be particularly good at games starting with 1. e4.

Worth noting: whether chess has a winning line is an open problem today. We do have "endgame tables" which contain every possible position with a small number of pieces, along with the "best" move to play at each step. However, even in these tables, there's complexities. For example, very few of these tables can account for any rules which limit the number of moves before a draw occurs.

• thank you, your mathematical example helped disprove my theory and you seam to be the only person who acknowledged that when I say 'best' I was talking in terms of a specific characteristic. None the less, I was wrong and you proved it. – SemperAmbroscus Oct 26 '15 at 10:15
• To expand on the mathematics bit: suppose that for your definition of "better", move A is better than B (for example `1. e4` is better than `1. e3`), B is better than C (`1. e3` is better than `1. Kf3`) and C is better than A (e.g. `1. Kf3` is better than `1. e4`). Then amongst those three, clearly there is no "best". – CompuChip Oct 26 '15 at 14:40

If you have a good definition of "better" that provides a mathematical perfect ordering, and a finite number of "things", then yes, it can be proven that there is a "best" one. A mathematical ordering hast to have the transitive property, if a < b and b < c, a < c. A perfect ordering adds that for all a, b, such as a != b, either a < b or b < a (there are no ties between dissimilar elements). Caveat: if the ordering is not perfect (ie, there can be ties), then you could end up with a set of things that are best.

The source of the dispute is in the definition of "better". Let's take rock, papers, scissors. How do we define "better"?

• Against someone playing rock.
• Against a random player.
• Against the average of all the humans in the world.

In the first case, it is obvious that there is a perfect ordering, and it is paper > rock > scissors.

In the second case, there is no ordering: all the possibilities are equivalent.

In the third case, since we are dealing with humans, not every option will come up with equal probabilities, so one of them will have a slightly better chance of winning. Let's say, for the sake of argument, that people have a tendency to pull rock first; ergo, the "best" option is paper. But this "best" option is only best if you are playing against all of humanity, there are plenty of players that will preferentially use scissors, and you will loose against them.

The same is applicable to chess. You can define the "best" opening as the one that will make you win more times after playing a hundred games against every other chess player on Earth; or you can define it as the one that will make more likely for you to defeat your friend; but they won't necessarily be the same; nor that it will guarantee you winning on any particular match. To further complicate things, your opponent will learn and adapt to your strategies, so the definition will change over time.

But, as in the rock-paper-scissors, comparison between openings don't offer a good ordering. If opening A wins opening B, and opening B wins opening C, we can't say what will happen between openings A vs C. We need a "fixed" player (always playing the same, or statistically averaged).

Note that this is much more clear in your examples: the speed of a horse is a very well defined quantity, and in that sense, an Arabian horse is better than a smaller, more compact Finnhorse. But if I want to play devil's advocate, I'd say that the track is through a mountain forest covered in snow and ice: now your slim Arabian horse is freezing, twisting its ankles on the irregular soil, and the Finnhorse is happily winning.

So, as with most philosophical debates, the problem is that you were talking about different things with the same words.

• "paper > rock > scissors" implies "paper > scissors", but this isn't true. Rock, paper, scissors does not have a mathematical ordering because of its circularity. Concerning chess: there are well-defined best moves to force win or win/draw or draw or otherwise it doesn't matter; this has nothing to do with whom you're playing against. Simply investigate the game tree. See my comment here. – user2953 Oct 26 '15 at 9:14
• @Keelan it does against someone always playing rock, as it is my first scenario. It doesn't against a random player. – Davidmh Oct 26 '15 at 9:16
• Ah, right, apologies. However, your statement about chess is still incorrect. – user2953 Oct 26 '15 at 9:18
• You're thinking about this from the point of view that we cannot compute the whole game tree. Mathematically however, every leaf in the game tree has either 'white wins' or 'draw' or 'white loses'. Therefore, one level higher in the tree, there is a best move, defined as the one that guarantees the best result (win > tie > loss). By induction, every node in the game tree has a best move. Therefore, the root has a best move. That is how you typically define 'best' in game theory. – user2953 Oct 26 '15 at 9:23
• Well, yes, but that's how you typically define 'better' in game theory. It guarantees the best possible result against a player with the same strategy. – user2953 Oct 26 '15 at 10:33

If you assume

• that only finitely many objects exists - which I consider a plausible supposition about our daily world - and
• that the values of each property under consideration form a total order, which implies that each two values can be compared,
• then for each property exists at least one object with maximal value.

Of course, there can exist more than one maximal object.

The conclusion rests on the supposition of finiteness. Then one can prove the statement by complete induction on the number of objects.

The problem in applying your statement in practical situations is to make sure, that the values of each property form a total order. In addition, e.g., in your horse example, one has to define over which distance the velocity is measured.

• @Keelan You are right. But I assumed the questioner is not interested in explanations about transitivity and antisymmetry :-) Nevertheless I edited the point. – Jo Wehler Oct 26 '15 at 22:13

I think the problem mostly dissolves when you realize that for many uses of best, there is a best for that is implied. For instance, presumably, the "best chess opening" is the one that is most likely to yield a win. But for other things, "best" is much less clear.

For instance, the best horse here in Japan might for some one be the one with the tastiest meat. Whereas you seem to assume running fast is the determination of the best of horses.

In an interesting way, this is a key problem for Plato in the definitions of the forms. What the best form of society would be is the key question of the Republic.

ps in the case of chess, I don't believe there's a consensus as to (a) whether there is a best possible opening and (b) among those who believe there is, what that opening would be.

The idea that something has a generic best relates to Aristotle's teleology, specifically the notion of final cause. According to Aristotle, all things tend towards the good, meaning both the end of all things and their own perfection. ("tend" here does not mean that they attain it, but that they are directed towards it).

This notion is central to Aristotle's ethics, but teleology is a bad word in many domains in contemporary science and philosophy.

Your currently revised claim relates to the existence of one best for each categorization. I think that contemporary math addresses this by claiming that there is no such thing as the largest number (etc) as suggested by jobermark's answer.

There's no reason why it is logically necessitated that the best exist unless we accept the condition suggested by Anselm et al. that existence is a feature of being the "best", but this doesn't work very well when the scope is narrowed from being itself, a point Anslem includes in his argument when addressing an objection about whether the best possible island must exist.

• I didn't mean to sound broad when I say the best I meant best in the context of any specific argument. While your right that there is no overall best I assume that any two parties arguing the best of something already have a specific characteristic in mind. – SemperAmbroscus Oct 26 '15 at 1:47
• Often they don't... or they don't agree about what is best. That's why they argue. Less frequently, there's arguments where people disagree about the best means to accomplish something. – virmaior Oct 26 '15 at 2:23

While at face value, this easily admits counterexamples (for example, when A and B are both better than C, but neither is better than the other), it's worth noting that it does echo a concept with a long and distinguished history in philosophy: It's (in essence) a version of an argument (for example, in the Republic, Book VII, following the Allegory of the Cave) that Plato uses to argue for the necessary existence of perfect Ideals that transcend ordinary reality, to the effect that if we compare one thing to another, and find it superior, it must be because we are comparing both to a perfect model that exists, not in the ordinary world, but in an abstract perfect realm.

While this theory may sound odd to modern ears, it was hugely influential in the history of philosophy, and still holds some currency in the worlds of both theology and abstract mathematics.

The nature of best in chess can be theorised specifically because the rules are known outright.

Here's one way to detect the best opening move for human players - simply play all possible games upto say 200 moves (since we expect humans to tire well before then, typically games take less than a 100 moves).

Then tabulate the proportion of wins for each different opening move...

This is very rough and doesn't take into account that human players consider opening moves as part of a 'book' of opening strategies such as the Queen or Kings Gambit; or that they take into account their opponents psychology - which is made more explicit in games like poker...

Similar in mathematics calculus tells us the best point as the numerically maximal point; or more recently category theory tells us the best point with regard to some partial ordering which is not necessarily numerical - but even with all this mathematical technology a physicist can't say to a mathematician: we have two theories QM and GR please (partially) order all possible theories which are consistent with these two and find us the best...

• This logic fails because of a basic failure of statistics: en.wikipedia.org/wiki/Nontransitive_dice Doing the statistics will definitely give you multiple, different, nontransitive situations at several points. So the statistics end up having no predictive value. – user9166 Oct 26 '15 at 2:32
• @jobermark: yeah, that's why I said very rough; I didn't want to get into a fine analysis - but simply to indicate sometimes it can be helpful. – Mozibur Ullah Oct 26 '15 at 2:36
• I am not asking about the best chess move specifically, I only used that scenario to describe how I arrived at my question – SemperAmbroscus Oct 26 '15 at 2:39

I have no education in philosophy so I will just try to approach this from a logical perspective.

"Best" is the superlative to "good". It's the highest order of what we perceive to be good. But that's just it, whether something is good or not is really a matter of the view of a person (or group) and thus subjective. Even if we would find the same things to be good, we might have applied different criteria that just turned out to have a similar result. We could still disagree on what "best" is.

Furthermore, "best" in no way has to mean biggest in an ordinal comparison. Simple example: I prefer large computer screens to small ones. That does not mean that I'd consider the currently biggest screen "best".

So, since we will not find a common understanding of what "good" means, we will certainly not agree on what "best" is so your definition is flawed.

I think what you meant to say was that each object has something we can measure and, looking at this single measure, there will be an object that is highest ranked. So we would get the following definition:

For any two objects in the universe of the same type and with at least one ordinal measurable property, if one of the two objects's properties is in a higher order than the other, there must be a single object of the same type with a property value that is in the highest order in comparison.

In my opinion, only now the philosophical debate can start.

Personally, I see several issues with this definition. For one, I don't see how you can justify your chess theory with it. Also, the definition is not taking into account the time aspect. To add an "at any given moment in time" might ease this. But most importantly, I am not sure whether the underlying thought can be true. I'm actually pretty sure that there will be many points in time where we will have two objects or more of the same type that together are highest ranked in one specific property (i.e. speed, size etc.). I guess at this point it then becomes a question of how to measure differences that are almost infinitesimal.

• What does time have to do with chess? The state of a chess game is uniquely described by the positions of the pieces. If you mean working with a chess clock: this is just an additional dimension. How is it relevant for the best move in a game whether it's 2 or 3 o'clock? – user2953 Oct 26 '15 at 10:42
• @Keelan It's not. OP created a theory that according to his own statements is generally valid. He chose to use chess as a specific example but said himself that he does not want this restriction. So, my comments are on the theory itself (or rather the flaws in it). As I stated, I personally don't see how this theory can be applied to chess as objects and actions are not comparable. So, a theory on objects cannot apply on actions, too. – vic Oct 26 '15 at 10:50
• You don't answer my question. Let me clarify: what is "the time aspect", and how should it be taken into account (either in general or with an example)? – user2953 Oct 26 '15 at 14:23
• @Keelan You asked "how is it relevant for [chess]", I answered "it's not". I was referring to OP's claim that there are objects, e.g. horses, that have a characteristic that can be be measured and considered to be "best", e.g. "fastest". Time is relevant here. Horse X can be the fastest today, it might not be the fastest tomorrow. – vic Oct 26 '15 at 14:29
• That's not really an inaccuracy of the OP's theory. You're not saying more than "'better' has to be defined properly". – user2953 Oct 26 '15 at 16:14