The following is a summary of Wittgenstein’s position, from Anthony Kenny’s book ‘Wittgenstein’ (1973):
“There is no characteristic that is common to everything that we call games; but we cannot on the other hand say that ‘game’ has several independent meanings like ‘bank’. It is a family-likeness term (pg 75, 118). Think of ball-games alone: some, like tennis, have a complicated system of rules; but there is a game which consists just in throwing the ball as high as one can, or the game which children play of throwing a ball and running after it. Some games are competitive, others not (pg 68). This thought was developed in a famous passage of the Philosophical Investigations in which Wittgenstein denied that there was any feature — such as entertainment, competitiveness, rule-guidedness, skill — which formed a common element in all games; instead we find a complicated network of similarities and relationships overlapping and criss-crossing. The concept of ‘game’ is extended as in spinning a thread we twist fibre on fibre. ‘What ties the ship to the wharf is a rope, and the rope consists of fibres, but it does not get its strength from any fibre which runs through it from one end to the other, but from the fact that there is a vast number of fibres overlapping’ (pi, i, 65–7; bb 87).
This feature of ‘game’ is one which Wittgenstein believed it shared with ‘language’, and this made it particularly appropriate to call particular mini-languages ‘language-games’. There were others. Most importantly, even though not all games have rules, the function of rules in many games has similarities with the function of rules in language (pg 63, 77). Language-games, like games, need have no external goal; they can be autonomous activities (pg 184; z 320).”
Actually, there is some contention on whether Wittgenstein thought all games needed to have rules, or not. Here is a quote some of his students took from him in some of his lectures in the spring of 1931:
What does it mean to use language according to grammatical rules? … There must be rules, for language must be systematic. Compare games: if there are no rules, there is no game, and chess, for example, is like a language in this sense. When we use language we choose words to fit the occasion.” — Ludwig Wittgenstein, Wittgenstein’s Lectures: Cambridge 1930–1932 ed. D. Lee (Chicago: University of Chicago Press, 1982), 48
But later, towards the end of his life in the beginning of the 1950s, in his work Philosophical Investigations (PI);
“he was to argue that there was, indeed, an analogy between language and games but that not all games are played according to rules. There are also those in which we ‘play aimlessly’ or ‘make up the rules as we go along’. Wittgenstein concluded that ‘the application of a word is not everywhere bounded by rules’.”,
as we are reminded by Hans Sluga in his book ‘Wittgenstein’. From this we may infer that Wittgenstein would also say that there exist some games which are not everywhere bounded by rules. Not only games with an incomplete rule-set, but also games that have flexible boundaries (as opposed to a structure).
The following is the relevant excerpts from Ludwig Wittgenstein’s book Philosophical Investigations (1953), starting from page 5, at § 7(links, emphasis in bold, and clarifications in brackets, are my additions):
3. […] And one has to say this in many cases where the question arises “Is this an appropriate description or not?” The answer is: “Yes, it is appropriate, but only for this narrowly circumscribed region, not for the whole of what you were claiming to describe.”
It is as if someone were to say: “A game consists in moving objects about on a surface according to certain rules . . .” — and we replied: You seem to be thinking of board games, but there are others. You can make your definition correct by expressly restricting it to those games.
7. […] We can also think of the whole process of using words […] as one of those games by means of which children learn their native language. I will call these games “language-games” and will some- times speak of a primitive language as a language-game.
And the processes of naming the stones and of repeating words after someone might also be called language-games. Think of much of the use of words in games like ring-a-ring-a-roses.
I shall also call the whole, consisting of language and the actions into which it is woven, the “language-game”.
54. Let us recall the kinds of case where we say that a game is played according to a definite rule.
The rule may be an aid in teaching the game. The learner is told it and given practice in applying it. — Or it is an instrument of the game itself. — Or a rule is employed neither in the teaching nor in the game itself; nor is it set down in a list of rules. One learns the game by watching how others play. But we say that it is played according to such-and-such rules because an observer can read these rules off from the practice of the game — like a natural law governing the play. — — But how does the observer distinguish in this case between players’ mistakes and correct play? — There are characteristic signs of it in the players’ behaviour. Think of the behaviour characteristic of correcting a slip of the tongue. It would be possible to recognize that someone was doing so even without knowing his language.
65. […] And this is true. — Instead of producing something common to all that we call language, I am saying that these phenomena have no one thing in common which makes us use the same word for all, — but that they are related to one another in many different ways. And it is because of this relationship, or these relationships, that we call them all “language”. I will try to explain this.
66. Consider for example the proceedings that we call “games”. I mean board-games, card-games, ball-games, Olympic games, and so on
Actually “Olympic Games” is a slightly inaccurate translation by Anscombe’ who translated Wittgenstein from German to English. Because Wittgenstein didn’t use the words “Olympische Spiele” which would be the direct translation, but “Kampfspiele” which means “fighting-games” or “martial games”, like boxing, wrestling, fencing, jousting, etc. Such games were characteristic of the ancient Olympic Games though, to Anscombe’s credit. But this disambiguation is important, so we don’t think that Wittgenstein also was referring to contests such as running races, chariot races, jumping, throwing etc. which were also a part of the Olympic Games.
What is common to them all? — Don’t say: “There must be something common, or they would not be called ‘games’ “ — but look and see whether there is anything common to all. — For if you look at them you will not see something that is common to all, but similarities, relationships, and a whole series of them at that. To repeat: don’t think, but look! — Look for example at board-games, with their multifarious relationships. Now pass to card-games; here you find many correspondences with the first group, but many common features drop out, and others appear. When we pass next to ball- games, much that is common is retained, but much is lost. — Are they all ‘amusing’ [i.e. fun]? Compare chess with noughts and crosses. Or is there always winning and losing, or competition between players? Think of patience [i.e. Solitaire]. In ball games there is winning and losing; but when a child throws his ball at the wall and catches it again, this feature has disappeared. Look at the parts played by skill and luck; and at the difference between skill in chess and skill in tennis. Think now of games like ring-a-ring-a-roses; here is the element of amusement, but how many other characteristic features have disappeared! And we can go through the many, many other groups of games in the same way; can see how similarities crop up and disappear.
And the result of this examination is: we see a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities, sometimes similarities of detail.
67. I can think of no better expression to characterize these similarities than “family resemblances”; for the various resemblances between members of a [human] family: build, features, colour of eyes, gait, temperament, etc. etc. overlap and criss-cross in the same way. — And I shall say: ‘games’ form a family.
And for instance the kinds of number form a family in the same way. Why do we call something a “number”? Well, perhaps because it has a — direct — relationship with several things that have hitherto been called number; and this can be said to give it an indirect relationship to other things we call the same name. And we extend our concept of number as in spinning a thread we twist fibre on fibre. And the strength of the thread does not reside in the fact that some one fibre runs through its whole length, but in the overlapping of many fibres.
But if someone wished to say: “There is something common to all these constructions — namely the disjunction [it has this OR that] of all their common properties” — I should reply: Now you are only playing with words. One might as well say: “Something runs through the whole thread — namely the continuous overlapping of those fibres”.
68. “All right: the concept of number is defined for you as the logical sum of these individual interrelated concepts: cardinal numbers, rational numbers, real numbers, etc.; and in the same way the concept of a game as the logical sum of a corresponding set of sub-concepts.” — — It need not be so. For I can give the concept ‘.number’ rigid limits in this way, that is, use the word “number” for a rigidly limited concept, but I can also use it so that the extension of the concept is not closed by a frontier. And this is how we do use the word “game”. For how is the concept of a game bounded? What still counts as a game and what no longer does? Can you give the boundary? No. You can draw one; for none has so far been drawn. (But that never troubled you before when you used the word “game”.)
“But then the use of the word [“game”] is unregulated, the ‘game’ [the language-game] we play with it is unregulated.” — — It is not everywhere circumscribed by rules; but no more are there any rules for how high one throws the ball in tennis, or how hard; yet tennis is a game for all that and has rules too.
69. How should we explain to someone what a game is? I imagine that we should describe games to him, and we might add: “This and similar things are called ‘games’ “. And do we know any more about it ourselves? Is it only other people whom we cannot tell exactly what a game is? — But this is not ignorance. We do not know the boundaries because none have been drawn. To repeat, we can draw a boundary — for a special purpose. Does it take that to make the concept usable? Not at alll (Except for that special purpose.)
71. One might say that the concept ‘game’ is a concept with blurred edges. — “But is a blurred concept a concept at all?” — Is an indistinct photograph a picture of a person at all? Is it even always an advantage to replace an indistinct picture by a sharp one? Isn’t the indistinct one often exactly what we need?
Frege compares a concept to an area and says that an area with vague boundaries cannot be called an area at all. This presumably means that we cannot do anything with it. — But is it senseless to say: “Stand roughly there”? [Wittgenstein further argues that it is not senseless, and that vague boundaries can be useful.]
75. What does it mean to know what a game is? What does it mean, to know it and not be able to say it? Is this knowledge some- how equivalent to an unformulated definition? So that if it were formulated I should be able to recognize it as the expression of my knowledge? Isn’t my knowledge, my concept of a game, completely expressed in the explanations that I could give? That is, in my describ- ing examples of various kinds of game; shewing how all sorts of other games can be constructed on the analogy of these; saying that I should scarcely include this or this among games; and so on.
76. If someone were to draw a sharp boundary I could not acknowledge it as the one that I too always wanted to draw, or had drawn in my mind. For I did not want to draw one at all. His concept can then be said to be not the same as mine, but akin to it. The kinship is that of two pictures, one of which consists of colour patches with vague contours, and the other of patches similarly shaped and distributed, but with clear contours. The kinship is just as undeniable as the difference.
77. And if we carry this comparison still further it is clear that the degree to which the sharp picture can resemble the blurred one depends on the latter’s degree of vagueness. For imagine having to sketch a sharply defined picture ‘corresponding’ to a blurred one. In the latter there is a blurred red rectangle: for it you put down a sharply defined one. Of course — several such sharply defined rectangles can be drawn to correspond to the indefinite one. — But if the colours in the original merge without a hint of any outline won’t it become a hopeless task to draw a sharp picture corresponding to the blurred one? Won’t you then have to say: “Here I might just as well draw a circle or heart as a rectangle, for all the colours merge. Anything — and nothing — is right.” — — And this is the position you are in if you look for definitions corresponding to our concepts in aesthetics or ethics.
In such a difficulty always ask yourself: How did we learn the meaning of this word (“good” for instance [or “game”])? From what sort of examples? in what language-games? Then it will be easier for you to see that the word must have a family of meanings.
78. Compare knowing and saying.
how many feet high Mont Blanc is —
how the word “game” is used —
how a clarinet sounds.
If you are surprised that one can know something and not be able to say it, you are perhaps thinking of a case like the first. Certainly not of one like the third.
82. […] But what if observation does not enable us to see any clear rule, and the question brings none to light? […]
83. Doesn’t the analogy between language and games throw light here? We can easily imagine people amusing themselves in a field by playing with a ball so as to start various existing games, but playing many without finishing them and in between throwing the ball aimlessly into the air, chasing one another with the ball and bombarding one another for a joke and so on. And now someone says: The whole time they are playing a ball-game and following definite rules at every throw.
And is there not also the case where we play and — make up the rules as we go along? And there is even one where we alter them — as we go along.
100. “But still, it isn’t a game, if there is some vagueness in the rules”. — But does this prevent its being a game? — “Perhaps you’ll call it a game, but at any rate it certainly isn’t a perfect game.” This means: it has impurities, and what I am interested in at present is the pure article. — But I want to say: we misunderstand the role of the ideal in our language. That is to say: we too should call it a game, only we are dazzled by the ideal and therefore fail to see the actual use of the word “game” clearly.
101. We want to say that there can’t be any vagueness in logic. The idea now absorbs us, that the ideal [i.e. the essence of a game] ‘must’ be found in reality. Meanwhile we do not as yet see how it occurs there, nor do we understand the nature of this “must”. We think it must be in reality; for we think we already see it there [when we are able to talk about ‘games’, and readily intuitively classify something as ‘a game’ or ‘not a game’].
200. It is, of course, imaginable that two people belonging to a tribe unacquainted with games should sit at a chess-board and go through the moves of a game of chess; and even with all the appropriate mental accompaniments. And if [we] were to see it we should say they were playing chess. But now imagine a game of chess translated according to certain rules into a series of actions which we do not ordinarily associate with a game — say into yells and stamping of feet. And now suppose those two people to yell and stamp instead of playing the form of chess that we are used to; and this in such a way that their procedure is translatable by suitable rules into a game of chess. Should we still be inclined to say they were playing a game? What right would one have to say so?
204. As things are I can, for example, invent a game that is never played by anyone. — But would the following be possible too: mankind has never played any games; once, however, someone invented a game — which no one ever played?
205. “But it is just the queer thing about intention, about the mental process, that the existence of a custom [i.e. a rule], of a technique, is not necessary to it. That, for example, it is imaginable that two people should play chess in a world in which otherwise no games existed; and even that they should begin a game of chess — and then be interrupted.”
But isn’t chess defined by its rules? And how are these rules present in the mind of the person who is intending to play chess?
208. Then am I defining “order” and “rule” by means of “regularity”? — How do I explain the meaning of “regular”, “uniform”, “same” to anyone? — I shall explain these words to someone who, say, only speaks French by means of the corresponding French words. But if a person has not yet got the concepts, I shall teach him to use the words by means of examples and by practice. — And when I do this I do not communicate less to him than I know myself.
562. But how can I decide what is an essential, and what an in-essential, accidental, feature of the notation? Is there some reality lying behind the notation, which shapes its grammar?
Let us think of a similar case in a game: in draughts a king is marked by putting one piece on top of another. Now won’t one say it is in-essential to the game for a king to consist of two pieces?
563. Let us say that the meaning of a piece is its role in the game. — Now let it be decided by lot which of the players gets white before any game of chess begins. To this end one player holds a king in each closed fist while the other chooses one of the two hands at random. Will it be counted as part of the role of the king in chess that it is used to draw lots in this way?
564. So I am inclined to distinguish between the essential and the inessential in a game too. The game, one would like to say, has not only rules but also a point [i.e. purpose].
567. But, after all, the game is supposed to be denned by the rules! So, if a rule of the game prescribes that the kings are to be used for drawing lots before a game of chess, then that is an essential part of the game. What objection might one make to this? That one does not see the point of this prescription [i.e. rules need a purpose to make sense, to be evaluated]. Perhaps as one wouldn’t see the point either of a rule by which each piece had to be turned round three times before one moved it. If we found this rule in a board-game we should be surprised and should speculate about the purpose of the rule. (“Was this prescription meant to prevent one from moving without due consideration?”)
568. If I understand the character [purpose, or type] of the game aright — I might say — then this isn’t an essential part of it.
((Meaning is a physiognomy.))
[i.e. Meaning is an assessment based on outward appearances.]
(p 206) Here is a game played by children: they say that a chest, for example, is a house; and thereupon it is interpreted as a house in every detail [including the rules that accompany something being a house]. A piece of fancy [i.e. fiction] is worked into it.
Final note from Wikipedia:
“The essential point of this exercise is often missed. Wittgenstein’s point is not that it is impossible to define ‘game’, but that even if we don’t have a definition, we can still use the word successfully.”
Actually, I’d argue, based on one if the first paragraphs I quoted from Wittgenstein above (§ 65, and rendered below), that while the former may be his main point, he actually also asserts that it is impossible to define ‘game’ in a way of something that is common to all games. Since he uses precisely ‘game’ as an example to illustrate why the same thing holds for language in itself. This interpretation is corroborated by Stanford Encyclopedia of Philosophy’s rendition of Wittgenstein. More importantly, in Wittgenstein’s own words (from § 65, leading up to talking about ‘a game’):
“I am saying that these phenomena have no one thing in common which makes us use the same word for all, — but that they are related to one another in many different ways”.