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Wittgenstein's Logic of Language

Chapters 7-10

Note: there are 13 chapters, divided over three Web pages. There is a Table of Contents, and an Introduction which characterizes the first principles of the later philosophy.

Outline of this page ...

• 7. The Rules of the Game, as in "language game"
  • Like a move in a game (Comparison of using language to playing a game: the rules of the game define the game's words)
  • Games and "Family Likenesses" (The resemblances between the bearers of a common name are similar to the resemblances between the members of a human family)
    • Differences and Similarities
    • "Most words are without meaning" (Unserviceable definitions of 'meaning')
      • "Look at language meaning this way!"
      • Don't ask for the meaning; ask for the use in the language (PG i § 23, p. 60)
      • As we normally use the word 'meaning', words with a use in our language are not meaningless
    • A common name, not a common nature
    • Drawing lines between the resemblances of the faces in a family (The same might be done with games)
  • Plato and concept-formation
    • Very general facts of nature and concept-formation
  • Further criticism of Wittgenstein's "family resemblances" metaphor
    • Classes as families
  • Endnotes Chapter 7
    • Rules and sense and nonsense (Playing the game wrong versus nonsense)
    • The relationship between our concepts and general facts of nature
    • A game has not only rules but a point
    • Logic and nuance. Rules and impressions
      • Logic of language and Philosophy (Choosing standards for meaning and nonsense (Wittgenstein), and for truth and falsehood or ignorance (Socrates))
• 8. Three kinds of rules of grammar: Reported, Invented, Assigned
  • Reported rules (descriptions of our normal use of words)
  • Counterfactual rules
  • Assigned meanings
• 9. Concept indefiniteness: concepts with vaguely-defined borders (limits) versus concepts with clearly-defined limits. Marked versus unmarked frontiers. (Concept fluidity: a path that ends in a clearing, leaving it unclear how to go on)
  • Concept indefiniteness (a "grammatical reminder")
  • The meaning of a name is often learned in the presence of the bearer of the name (ostensively)
    • Indefinite boundary
  • Grammar and things that never happen
  • Natural language is far from chess-like (i.e. governed by strict rules), despite logic making that comparison
    • Rules as the standard for verification (objectivity)
  • "Analytic propositions"
  • Vagueness and Impressions of Meaning
    • Meaning as use in the language, or not (PI § 43)
      • "Let the use teach you the meaning"
      • "Impressions of Meaning"
        • Induction and Definition and Impressions of Meaning
      • Natural language is natural history. Learning the concept 'game'. Tolerance for vagueness
  • Concepts, order and chaos (and concept-formation)
  • The grammar of the word 'beautiful' versus Aesthetics (Are there meaningful signs without grammars?)
    • Concept-formation ('beautiful', 'pretty', 'lovely')
    • Grammar without rules
  • Distinction between the concepts 'grammar' and 'logic' made clearer
  • Acquiring the concept 'beautiful' as an example of a "form of life"
    • The concept 'the beautiful'
  • Endnotes Chapter 9
    • Is the outcome the point of a game?
    • Ethics and Aesthetics contrasted
      • Wittgenstein's account of Aesthetics
      • The beautiful is not unequivocally the good
        • "Concept-blindness"
• 10. Meaning as a custom, usage, institution ("the characteristic formation of a pattern")
  • Custom versus ad hoc convention
  • Is this a game?
  • Grammar is "a Normal School"
    • The Stoic lekton
  • The relation between recurrent behavior and grammar
    • "Form of Life"
  • An objective distinction between sense and nonsense
    • And between 'meaning' and 'meaningless'
  • When eyeglasses are required to see
  • Kinds of language conventions

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7. The Rules of the Game

Although we use the words of our language without difficulty in the transactions of day to day life, when we turn to words in philosophy, we are very often unable to say what the rules for their use (their definitions) are (BB p. 25). Suppose we were asked to explain the meaning of the word 'mind' or 'time' ... the meanings of many words, especially in philosophy, appear vague and cloudy to us. This is because our naive ideas about language meaning are misunderstandings of the logic of language. Our naive picture: (1) all nouns are names, and (2) the meaning of a name = the essence of the thing the name stands for (whether tangible or "abstract").

A move in a game, as in "language game"

One way to get a clearer view of a word's use in the language (or grammar) is to describe the use of the word as if it were a move in a game (Z § 294), because both moves in games and words are given meaning by following rules.

For example, picture going to a corner greengrocers to buy apples (cf. BB p. 16-17). The grocer asks us how many apples we would like. And if we answer 'blue', then we are playing the game wrong (cf. OC § 446), because we are not allowed by the rules of this game to answer with a color-word -- i.e. the word 'blue' is nonsense, mere sound without sense, in this context. The rules of the game require us to answer with a number-word. [Note 6]

In Wittgenstein's jargon, buying apples at a greengrocer's is an example of a "primitive language game". (The language to games comparison is not the only way to define the word 'meaning'. There are many meanings of the word 'meaning' in the language. However, Wittgenstein chose one, the one that makes language meaning objective (verifiable).)

Common Names and "Family Likenesses"

At school we are taught that the meaning of a word is the essence of the thing, action or quality it names. And therefore English teachers ask children for general definitions, although those definitions rarely identify an essence -- because if they did there would never be any doubt about how a defined word was to be used (Euthyphro 6d-e). Plato's general definition of 'quickness' as "the quality which accomplishes much in a little time" (Laches 192a) is hardly unambiguous, and like the general definitions found in dictionaries it is too general to serve as an absolute standard. It requires examples to clarify it, and examples are never exhaustive. Therefore, judged by the school requirement, most words are without "meaning".

Plato merged the thought of Heraclitus and Socrates and reasoned metaphysically that the meaning of common names must be the common natures they name. But Wittgenstein, looking no further than he wanted, namely to the facts in plain view found, as Plato and later the Ockhamists had found, that common natures are the exception, not the rule. He illustrated this with the common name 'game'.

Differences and Similarities

Logic [the study of rules] looks at the use of language from one point of view only: "what happens considered as a game". (Cf. PG i §§ 32, 30, p. 68, 66)

But games and their rules are quite varied, as are the words in our language (contrast the rules for the use of the words 'love', 'giraffe', 'four', 'cold', and 'logic'). Games range from chess with its strict rules to the simple play of a child skipping rope or throwing a ball into the air and catching it.

Consider ... the proceedings that we call 'games'. I mean board-games, card-games, ball-games, Olympic games, and so on. 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. (PI § 66)

Tennis and volleyball and badminton have nets in common, but volleyball has no rackets, and there is no ball in badminton. All three are played on marked grids, as are chess and hopscotch, but there is no net, racket or ball in chess or in hopscotch. There is no grid in jump rope, but there is hopping. There is no net in bridge and no playing cards in tennis, but bridge and doubles tennis are played by teams. There are no teams in solitaire (patience), but there are playing cards. There are no playing cards in chess, but one may play chess against oneself, and jump rope may be played alone or in groups. Fetch is sometimes played with a ball, and there is no winning or losing in fetch, but there is exercise in it. There is no exercise in chess and no dog, but there may be winning and losing.

There are countless similarities (but also dissimilarities) between particular games and between kinds of games. Compare games for yourself.

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. (ibid.)

Looking at games and finding there not something "in which they do not differ but are all alike" (Meno 72c), but only various similarities between games, Wittgenstein invented this simile:

I can think of no better expression to characterize these similarities than 'family resemblances' [or 'family likenesses' (BB p. 17)] ... And I shall say: games form a family. (PI § 67)

But then is Wittgenstein saying that the common nature or meaning of the word 'game' is the similarities among games? No, but that the word 'game' has no meaning -- if meaning DEF.= the common nature named by the word. The word 'game' is not nonsense ("mere sound without sense"), but its role in our language is also not to name a common nature.

"Most words are without meaning"

There are two ancient false or barren and unworkable accounts of word meaning:

The first is that words are names of things and a word's meaning is the thing it names. Plato: "You do not suppose that a man can understand the name of a thing when he does not know what the thing is" (Theaetetus 147b). But there is a difference between saying that the meaning of a name is often explained by pointing to its bearer (PI § 43) and saying that the meaning of a name is the bearer -- all the while presuming that all words or even all nouns are names of things. The words 'beauty' (Greater Hippias), 'justice' (Republic Book One) and 'piety' (Euthyphro) are not such names.

The second account is that the meaning of a common name is the defining common nature of a class of things, the common nature the common name names. The first account is a "grammatical fiction" (ibid. § 307), and the second, if we are examining natural language (in contrast to how words are defined in the natural sciences) is very rarely true (the definition of 'simile' as 'a comparison using the words 'like' or 'is'' would appear a counterexample, were it not that similes don't always explicitly contain those words).

Definitions of 'meaning' whereby most or all words are without meaning are only of negative use in trying to understand the logic or grammar of language. They mark off false paths.

"Look at language meaning this way!"

Setting those accounts aside, shunning metaphysical speculation, Wittgenstein looked at word meaning from a different point of view, namely to ask for a description of a word's use in the language as shown by the facts in plain view -- and only by those facts, going no further than those facts, and accepting those facts as they are (i.e. asking for "is" rather than "must be"). That description is the word's meaning, in the sense of 'meaning' DEF.= explanation of meaning.

How is the meaning of the word 'game' explained -- what does a "non-essential" or "meaningless" definition look like? It may be a single rule (an instruction) that shows the way to go on (PI § 151) if you don't know the way in a particular setting (ibid. § 123). Or the explanation may be made by pointing to synonyms or equivalent words -- or by giving examples.

Don't ask for the meaning; ask for the use in the language (PG i § 23, p. 60)

A philosopher says: Look at things this way! (CV p. 61)

We may use the word 'game' as Wittgenstein describes, but the old perplexity persists: Why do we call them all 'games' -- i.e. what is the meaning of the word 'game'? But that question is not a move in a language game -- unless the word 'meaning' is defined in an unserviceable way -- and then the only answer to our question is that the word 'game' is meaningless ... But a meaningless word that can convey meaning is after all not meaningless -- i.e. a different meaning of the word 'meaning' is needed if we are to describe (and set aside our false preconceptions about) the way our language works.

As we normally use the word 'meaning', words with a use in the language are not meaningless

If we are going to hold fast to the idea that a common name names a common nature, then if there is no common nature, the name will be meaningless -- and therefore impossible to define. But as we normally use the word 'meaning', the word 'game' is not meaningless (and undefinable). That is not the logic of our language. [Note 6a]

A common name, not a common nature

The word 'game' does not name a common nature, but more or less similar things are called 'games'. As more or less similar things are called uses of language. And like games they may in fact be very dissimilar, as examples of "proposition types" show. [Note 6b]

But if the doubt remains: "Still, games must have something in common (for otherwise they wouldn't all be called 'games')", then the answer is that there is indeed one thing that all games really do have in common: a word -- i.e. they are all called 'games'. Take that word away from us, however --.

Further, even if games all do have something in common, that something may not be defining (PI § 153), as indeed having the name 'game' in common is not. ("A game by any other name would be a game" ... or would it be?)

... how is the concept 'game' bounded? What still counts as a game and what no longer does? Can you state the boundary? No. You can draw one, because none has so far been drawn. (But that never troubled you before when you used the word 'game'.) (ibid. § 68)

Philosophy, after Socrates, is being awakened (Plato, Apology 30e-31a) to things you never noticed, and there are many of these in logic of language that are troubling (which is where my study of philosophy began), not only how concept-formation is possible in the case of common names.

That is the "critique of language" that "all philosophy is" (TLP 4.0031, tr. Ogden).

Is an "indefinite boundary" no boundary at all -- is a game without fixed rules (i.e. definite boundaries), or with no rules at all, not a game? (ibid. §§ 98-100). Because that is how the concepts of our natural language often are, and it is why in philosophical discussions we sometimes invent rules (boundaries) to make our meaning clear. We must sometimes recognize, sometimes make a distinction, between sense and nonsense when we philosophize.

Drawing lines between the resemblances of the faces of a family

Wittgenstein gave an explicit account of family resemblances among human faces: "And one would like to draw lines connecting the parts that various faces have in common" with various others as one might do with a collection of photographs (PI § 67). Lines might similarly be drawn between the resemblances between Wittgenstein's games examples.

Further criticism of Wittgenstein's metaphor

Spengler could be better understood if he said: I am comparing different periods of culture with the lives of families; within the family there is a family resemblance, while you will also find a resemblance between members of different families ... (CV (1998 rev. ed.) [MS 111 119: 19.8.1931]; cf. CV (1980) p. 14)

Wittgenstein's "family" resemblance simile -- namely, as the members of a human family resemble one another in various ways, so the members of a class resemble one another in various ways, although no particular one of these ways is essential to membership in the family or class -- is not a definition of 'meaning'. It is a comparison only, an after-the-fact-description of what we may find if we look at particular concepts (classes of things).

The criticism of Wittgenstein's simile is: what can be done with it in logic of language investigations? At best it is a grammatical reminder not to presume that there must be an essential quality or common nature definition for every common name, that an explanation of meaning may involve pointing out similarities that are not essential.

At worst Wittgenstein's simile may suggest that Wittgenstein's "theory of family resemblances" has solved the ancient puzzle of concept-formation posed by Plato, rather than, as it does, simply set it aside (PI § 47).

There are various criteria for inclusion in a human family (belief in common ancestry is the usual one, with adoption being another), but in the case of language there is only one criterion for inclusion in a family -- namely, bearing the same family name, regardless of how it may have been that our natural history bequeathed that name to anything.

Classes as families

It is not by chance that all these things have been put together ... (LC i, 4, p. 1)

"It is not by chance ..." In other words, it is done for a reason. But whereas that may be said about the invented vocabulary of natural science, in natural language reasons can only be attributed after the fact.

No more than we know

To say no more than we know (BB p. 45), i.e. what is public and verifiable by anyone, we ought to say no more than that there are various similarities between games, but that none of those similarities is defining of the common name 'game'. (To say more than that would be to think we know what we don't know, which is the cardinal vice in philosophy (Plato, Apology 22d-e, 29a; cf. Xenophon, Memories of Socrates iii, 9, 6 and iv, 6, 1).

The word 'family' may appear to explain, to make the meaning of common names clearer, whereas in fact it explains nothing and makes nothing clear.

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Endnotes Chapter 7

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8. Three kinds of rules of grammar: Reported, Invented, Assigned

The "rules of the game" play varied roles in games. (1) Sometimes the rules are explicitly referred to in the course of play. (2) At other times the players may follow the rules habitually without thinking about them, although they will be able if asked to state the rules or to teach someone else how to play the game. (3) And sometimes the players will not be able to state the rules, although they play the game more or less well enough; with respect to language, this is most often the case with psychological words, e.g. 'hope', 'love', 'sorrow', and what are confusedly called abstract terms or names of "abstract objects", e.g. 'concept', 'time', 'elf', 'mind'.

The rules of the language game -- i.e. the rules of grammar -- in philosophical investigations fall into three broad categories.

Reported usage rules

(1) First, there are the rules we derive from examples of actual uses of language signs (e.g. Wittgenstein's examples of games, which show that the meaning of the word 'game' is not a common nature). These will be statements of fact that any speaker of the language will admit to be true (Z § 211; PI § 599). For instance, that by the word 'thunder' we mean 'noise in the clouds', or that by 'flows' we sometimes mean the movement of a river.

Counterfactual rules

(2) Second, there are the rules of grammar we invent for the fictitious language games we create in order to compare those fictions with our normal language use. These fictitious objects of comparison alter very general facts of nature, to imagine e.g. a world in which all human beings are born blind -- how will their use of the word 'know' differ from ours (the point: to see the word 'know' as no more than a tool we use to do some work in our life)?

Imagine people who could only think aloud. (As there are people who can only read aloud.) (PI § 331)

[Consider the] procedure of putting a lump of cheese on a balance and fixing the price by the turn of the scale ... [But what] if it frequently happened for such lumps to suddenly grow or shrink for no obvious reason. (ibid. § 142)

Or suppose that disputes about the results of simple calculations in arithmetic frequently broke out among adults (ibid. II, xi, p. 225). What would language be like in such circumstances?

Inventing fictions sometimes shows us the foundations of our concepts -- because if we "imagine certain very general facts of nature to be different from what we are used to ... the formation of concepts different from the usual ones will become intelligible to" us (ibid. II, xii, p. 230b; cf. ibid. § 497b, RPP i § 46-48, Z § 350).

The only limit of concept-formation is imagination (logical possibility).

Assigned meanings

(3) The third category of grammatical rules are the rules we invent (assign) to resolve philosophical perplexity. When a word is commonly used equivocally or vaguely (i.e. when a word is a blunt tool we can do no work with), we may assign a particular meaning to that word, as e.g. Wittgenstein does with the word 'nonsense' in his later work , although that word is not commonly used in that limited way (Normally that word is often equivalent in meaning to 'foolishness').

Sometimes we may make a rule to resolve vagueness, e.g. as a rule that the word 'truth' is only to be applied to statements of fact or that by the word 'concept' we mean 'a set of rules' -- although at other times, the simple recognition that there is no rule will be the only resolution our perplexity needs -- if only we see this.

"The use of language in philosophy is not often, if ever, like a game played according to strict rules. It is not game-like." But we can, by making rules ("assigning meaning") , make it game-like and thereby answer our questions in philosophy. Always? Or does the nature of our existence sometimes make that impossible -- are there eternal questions, questions without answers in philosophy?

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9. Concept definiteness and indefiniteness. Concept fluidity

Our concepts are "fluid" -- as opposed to having well-defined borders; e.g. water is fluid but ice is not. Our concepts have more or less "blurred edges". These are similes Wittgenstein invented. They mean that any definition of a sign that we give -- or have given to us -- does not tell us how the sign is to be used in every imaginable case (PI §§ 68, 71). To define a word is to set limits, to more or less mark the boundaries, to is its use (or application).

Generally, we don't use language according to fixed rules, neither was it taught us that way. (cf. BB p. 25, PI § 292, OC § 139)

If we are unable clearly to circumscribe the concepts we commonly use, it is not because we don't know their real definitions, but because there is no real "definition" [clear limits] to them. (BB p. 25)

Recall that a game with fixed rules, e.g. a game like chess (or arithmetic), is what Wittgenstein compares language to. But our use of language, especially in philosophy, is often more unlike playing such a game than like playing one.

In discussing verbal and real definitions we accepted that 'thunder' means 'noise in the clouds'. But must clouds be present to justify calling an event thunder; must lightening be present? You don't know? The question is grammatical: what would anyone need to know in order to answer that question? More facts about a phenomenon, namely thunder -- or a rule for using a word, namely the word 'thunder'?

The meaning of a name is often learned in the presence of the bearer of the name (ostensively)

What would be the source of that rule -- would it necessarily be the phenomenon itself? Is thunder the cause of lightening or is lightening the cause of thunder (or is neither the cause of the other)? Alice seems not to know (Through the Looking-Glass, ix), nor need she know in order to use the word 'thunder' correctly -- because as we normally use the word 'thunder', that word is not defined by the cause of the phenomenon. We learn to use the word 'thunder' in the presence of the phenomenon we call 'thunder' -- and that is as far as an explanation of the meaning of that word goes.

Children are not given a verbal definition of the word 'thunder'. They learn to use that word in the presence of thunder -- i.e. the word 'thunder' is taught ostensively. And that is as far as the invariable explanation of meaning goes in this case. What children learn is a fluid concept.

Concept indefiniteness (a "grammatical reminder")

There is no rule to answer every question we might ask about the grammatical, the "as defined by rules of grammar" meaning of the word 'thunder' or other names of phenomena. Wittgenstein said that his "grammatical remarks" are "reminders", as the remarks here may serve as a reminder that in most cases there are not rules to define a word's use everywhere and always (PI §§ 84-85). The boundaries of the everyday concept 'thunder', for example, are verbally vague, indefinite, rather than well-defined (Natural science, both early and later, may assign strict limits, but our natural language does not).

There is another, although distinct, kind of case where if I don't know how to go on, a rule must be made to tell me how to continue, a rule no one foresaw the need for. Examples are algebraic equation and the Paradox of the Cretan Liar.

"Indefinite boundary"

Is a child's throwing a ball into the air and catching it to be called (classified as) a game? There is no rule. (PI §§ 69, 83) Or is the word 'game' defined such that "For a child to be playing a game, it must be following strict rules"? (BB p. 25)

In most cases, at what point the border guards will fire is indefinite. But can it be that they will never fire if you try to cross the frontier: Is "a game with no rules" what we call a 'game'? (If there is a difference between language with meaning and language without meaning, what is that difference?)

Grammar and things that never happen

Friedrich Waismann [cf. OC § 513] imagined that a cat grew to the size of a house and began barking -- was such a creature still to be called a 'cat'? But should it surprise us that grammatical rules do not exist to cover things that in fact never happen (PI § 87)? Grammar has no aim but language, and our language no aim but to be a tool in our hands. (ibid. §§ 80, 497)

It is a very general fact of nature (ibid. II, xii, p. 230a) that such things do not happen. Our concepts do their work within our actual life, not in every set of circumstances we may dream up. Or again, according to Wittgenstein, our language has its proper place, is at home (ibid. § 116), only in our life (Z § 173).

Natural language is far from chess-like, despite logic making that comparison

... are we to say that we don't really attach any meaning to this word, because we are not equipped with rules for every possible application of it? (PI § 80)

... in philosophy we often compare the use of words with games and calculi which have fixed rules, but cannot say that someone who is using language must be playing such a game. (ibid. § 81)

Wittgenstein's comparison or "analogy between language and games" (PI § 83) doesn't require that the use of language -- i.e. of signs (spoken sounds, marks on paper, sand or clay, gestures, the physical aspect of language only) -- follow strict rules (as most games, including primitive language games, do) if it isn't to be nonsense (mere noise, scribble). There is no "must" in Wittgenstein's grammar, but instead only descriptions of the facts in plain view.

The ideal [namely a game played according to strict rules] loses none of its dignity if it is presented as the principle determining the form of one's approach [i.e. as a] good unit of measurement [or object of comparison]. (CV p. 27)

Grammar does not tell us how language must be constructed ... It only describes and in no way explains [speculatively accounts for] the use of signs. (PI § 496)

Explanation = speculative accounting for the facts, in this context is exemplified by the theory of abstraction, which is that by an unspoken induction and a mysterious abstraction, the result of which cannot be put into words, common natures or essences are known by the mind (This shares Plato's requirement that the meaning of a common name be a common nature).

In contrast, the use of language that is in plain view is the (grammatical) meaning of language, the meaning grammar describes as if it were describing the rules of a game, regardless of what those rules are found to be. Nothing is hidden (ibid. § 435) or inscrutable (mysterious). That is the definition of 'meaning' Wittgenstein chose for his thinking in philosophy, the first of philosophy's three requirements.

Rules as a standard (objectivity)

But how can Wittgenstein make an objective distinction between sense and nonsense when language use doesn't follow strict rules -- for aren't strict rules what make meaning objective? It appears that question is devastating to Wittgenstein's project in philosophy.

"But then the use of the word is unregulated; the "game" we play with it is unregulated." -- It is not everywhere circumscribed by rules. Can you point out the boundary? No. You can draw one; but none has so far been drawn. (PI § 68)

That is how Wittgenstein's project in philosophy differs from Plato's method of preconceptions. What is objective (verifiable) is whether or not there is a rule. That is how we make the distinction between sense and nonsense. Many or most of our concepts are open-bordered ("the concept is not closed at the frontier") (ibid. § 68), and this somewhat sets limits to their usefulness as tools for reasoning, and yet we do use them for reasoning soundly within those limits -- when we see those limits. Beyond that, however --

Should it be said that I am using a word whose meaning I don't know, and so am talking nonsense? -- Say what you choose, so long as it does not prevent you from seeing the facts. (ibid. § 79)

"Seeing the facts" is all logic wants to do. "And when you see [the facts of our language use] there is a good deal that you will [no longer presume about our language]" (ibid.).

But describing the grammar in common use of our vocabulary is not always the end of philosophy, because sometimes in philosophy -- in order to clear up conceptual confusion -- we may draw boundaries where none exist in normal usage (cf. Z § 466).

Because grammar -- the standard of rules -- is only a clarifying tool in philosophy. It is not philosophy itself, and it is not philosophy's only tool. Others are e.g. Socrates' method of seeking contradictions in meaning by cross-questioning claims to knowledge, and Wittgenstein's method of showing the confusion misleading syntactic analogies cause in philosophy; another is pointing out hypostatization (i.e. when abstractions are imagined to be real entities).

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Vagueness and Impressions of Meaning

What is the meaning of the word 'city' (PI § 18)? Is it based on number and height of buildings or on population, for example? Is there an essence -- does the word 'city' have an essential meaning or general definition? Why don't you know? Surely you speak English. Why can't you define this common word?

How does a child learn to use the word 'city'? How would you teach the child -- is there something you know that you can't tell the child? (ibid. § 69) No, every explanation of meaning you can give yourself, you can give the child too (ibid. § 210). We often say the word 'city' -- don't we know what we are talking about; is that word "mere sound without sense"?

Common names that are defined ostensively do not belong to the first class of cases Wittgenstein cites in the following quotation (ibid. § 43); they belong to the class of names and bearers, the second paragraph of the quotation.

When we look for a rule and find that there is none, we can only note the absence of a rule -- or invent a rule to fill the absence.

Invent a rule is what the writers of a geography books do when they define the word 'city' based e.g. on population; they invent a standard. That standard is not a rule we normally follow in using the word 'city', but a rule that defines that word's use in the context of the book.

To teach a child to use the word 'city', we might use a picture book. But will it always be clear to us whether a given picture is of a city or not -- will we always know what to tell the child? Must a city have this or that specific quality? Many tall buildings, businesses, busy streets? Then are not the ruins of Pompeii a city; is Florence, Italy, not a city; was the ancient "city-state" of Athens not a city; was Atlantis not a city; is a beehive a city, or only "like a city"?

"Must a city have a specific defining quality?" That is a request for a definition, a further explanation of meaning, of the word 'city'. But no such further rule exists. Then what shall we tell the child? Well, what did we tell the child about the word 'thunder?'

When we define words by pointing out examples, that is not a deficient way to define most words, but instead the standard way, because, as we find if we look, most words do not have essential meanings (definitions). Resemblances there usually are.

Common names that are defined ostensively do not belong to the first class of cases Wittgenstein cites in the following quotation; they belong to the class of names and bearers, the second paragraph of the quotation.

Meaning as use in the language (or not)

For a large class of cases -- though not for all -- in which we employ the word 'meaning' it can be defined thus: the meaning of a word is its use in the language.

And the meaning of a name is sometimes explained by pointing to its bearer. (PI § 43; cf. the nominalist definition of 'meaning')

The class of words whose meanings are explained by rules for using them is the class of words whose use in our language is not that of ostensively defined names of objects. It is the logic of language of that large class that is misunderstood, that generates philosophical confusion when we try to make analogies from the name-bearer class to the use-in-the-language class (I gave the example of 'book' and 'mind'; Augustine-Wittgenstein: 'river' and 'time').

When in philosophy we (or Wittgenstein) invent a rule to clear up conceptual confusion -- i.e. when we assign borders to (redefine) the grammar of a vague or cloudy concept, we mustn't imagine that we have somehow discovered the concept-sign's true meaning. The rules we make in philosophical investigations belong only to those investigations, and they are only made for the purpose of resolving perplexity that would continue were it not for the new rule. And what we have done is to make -- i.e. invent -- a rule, a meaning, not discover one that already existed.

[Philosophy's] aim is to remove particular misunderstandings; not to produce a real understanding for the first time. (PG i § 72, p. 115)

Our investigation does not try to find the real, exact meaning of words; though we often do give words exact meanings in the course of our investigation. (Z § 467)

"Let the use teach you the meaning"

In Wittgenstein's logic of language, the meaning of a natural language sign is the work we use it to do in our life (BB p. 69), and therefore if we want to describe (or give an account of) that meaning we must describe our way of life. However, that is exactly the opposite of what we do in philosophy, e.g. with words like 'mind' and 'time'. We imagine that their meaning is "analytic", discovered by analyzing a disembodied concept -- i.e. a concept-word divorced from its use in our life. Our presumption: "Language follows thought and thought follows things" (Copleston), and that it is those "things", e.g. mind and time, that philosophy is about (Indeed, it is only in philosophy's portrayal of language that the words 'mind' and 'time' are the names of things at all). But, according to Wittgenstein, any grammatical account is false that allows words to be kidnapped away from the use in our life that alone gives those words meaning. (PI § 116)

One cannot guess how a word functions. One has to look at its use and learn from that .... Let the use teach you the meaning. (ibid. § 340; II, xi, p. 212).

"Impressions of Meaning"

Sometimes we feel that we have only an impression of a word's meaning (The comparison is to the indefiniteness of Impressionist art where line is indefinitely defined by color), the meaning of the word 'gentleman', for example. "What does the word 'gentleman' suggest to you?" We sometimes answer "I think of a gentleman as being ..." or "A gentleman to me is ..." As if this were a question of defining something familiar -- but a bit cloudy -- that was difficult to grasp hold of, rather than of defining a word: "What is a gentleman?" versus "How is the word 'gentleman' used in our language?"

One would like to say: whatever is going to seem right to me is right. And that only means that here we can't talk about "right". (PI § 258)

We could call this the 'impressionist meaning' of a word. It is not the meaning of the word 'meaning' used by Wittgenstein's logic of language, however.

What a word suggests to someone's imagination is not a definition in logic -- a word may suggest many different things to many different people, and if that were the meaning of 'meaning' logic used, then there would be no objective distinction between sense and nonsense, because none of those "meanings" would (or, indeed, could) be incorrect. (To 'define' is to 'set limits': Where there are no limits to mark off what is incorrect, there is no grammatical definition.)

Logic asks for the public rules that are followed by all speakers of the language when using a word (cf. BB p. 65). These rules are in many cases sketchy (PI §§ 79, 88). But they are the rules we live and think by, and they are what Wittgenstein used to define the word 'meaning' (the tool of his logic that he called 'grammar').

(We can make "sketchy rules" definite, and sometimes in philosophy, if we are to get anywhere with our thinking, we must, although note that what we do then is to invent, not discover, rules.)

Natural language and the concept 'game'. Tolerance for vagueness

Learning one's native language is learning concepts that are some more, some less, definite. 'Stand roughly over there!' (PI § 71) is intentionally vague, but we would not say the same about the grammar of 'game'. The indefiniteness of the grammar of that word arose as part of our natural history (ibid. § 18), and that indefiniteness just has to be accepted as "the given" in the equation of the word's grammar (ibid. II, xi, p. 226).

Learning a natural language may be learning to accept concept indefiniteness, acquiring a tolerance for many kinds and degrees of vagueness -- or it may mean acquiring deep and abiding perplexity (something else that "turns a man into a philosopher").

Concepts, Order and Chaos

... facts of nature that can explain concept-formation. (PI II, xii, p. 230)

We would hardly say that solitaire (patience) and table tennis belong in the same category based on their compelling similarities or "family resemblances". (But recall that concepts define phenomena, not phenomena concepts; phenomena without concepts are blind; unconceptualized phenomena are a chaos.) Yet table tennis and solitaire both are in the category 'game' -- according to the grammar of the word 'game' we inherited when we inherited our language. What more do we know about it?

Suppose we did not have a word 'game' or 'games'. Suppose what we call "card games" were simply called 'cards', and games that were played with rackets, e.g. tennis and badminton, were simply called 'rackets'. Then we would have two entirely distinct categories, {rackets} and {cards}. Would we then feel compelled by the facts to join those two categories together under a broader category?

'... that can explain the formation of concepts' -- It's not clear what 'explain' would mean. What we can do is to describe the concepts we actually have and how they might be different. But can any facts of nature ("percepts") compel us to form particular concepts? (Ockham thought so.) There may seem to be a few such concepts, e.g. 'object' and 'space' and 'movement' or 'change' -- but are those forced on us by the nature of things or by the nature of our own thinking (Kant)?

Our inherited language would be "the ancient city of language" (ibid. § 18), in contrast to the newer suburbs where, as in the natural sciences, the inventors of the new language purposively give their terms essential ("one thing common to all") definitions. But the oldest parts of the city of language were built up naturally, with twists and turns as the need arose. And it is in the ancient city where all the problems of philosophy arise, as Wittgenstein limits the concept 'philosophy'.

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The grammar of the word 'beautiful' versus Aesthetics

Are there meaningful signs without grammars? No -- not as 'grammar' is defined in Wittgenstein's jargon. But there are grammars (descriptions of use in the language) that contain no rules. E.g. the grammar of 'beautiful'. No rules can be given for its application, nor can its application be justified by "family resemblances" (as can be done in the case of e.g. 'chair'). "E is beautiful. -- Why? -- Because it resembles A, B, C, and D." No, the concept 'beautiful' doesn't work that way.

But don't we sometimes give reasons for saying that something is beautiful? Certainly. But must anyone find those reasons compelling -- i.e. agree that those reasons force one to apply the word 'beautiful' to the example? No, the grammar of the word isn't like that.

As children we are taught (given) aesthetic judgments. "Don't the ribbons in my little girl's hair make her beautiful! Look in the mirror." But in later years the girl can point to a picture from that day of her childhood and say, "I looked horrible!"

The 'can' here is grammatical (i.e. it "belongs to everything descriptive of the language"). If we are to give an account of the way the word 'beautiful' is used in our life, then this is what we find.

Greek sculptors did make rules for carving "beautiful" bodies [Note 8], and here we can give grammatical rules for the application of the word 'beautiful'. But they will not belong to the rules of the grammar that describes our use of that word; i.e. the Greek sculptors' concept is not our concept 'beautiful'. Anyone can respond: "Those idealized propositions are not beautiful." The justification for such a response is that the speaker's native language is English, and English grammar allows that judgment -- i.e. that language is not nonsense.

"Most people find these sculptures beautiful." -- But is that how we learned to apply the word 'beautiful', by appealing to the judgments of "most people", by taking a vote? That would be a concept 'beautiful' (i.e. a grammar for the word 'beautiful') -- but it is not ours. (Cf. Z § 431)

But mustn't people agree in their aesthetic judgments, because would there be a concept 'beautiful' if they did not? It is a fact of natural history that people living in a given place and time usually do agree. And if it were not this way, then we would not have the concept that we do have. (ibid. § 351)

But aren't there places where people must agree? E.g. we don't call just anything a 'chair'. "Anyone knows and must admit that this is an example of a chair" (cf. ibid. § 211). Concepts are only either more or less well-defined. 'Beautiful' is one extreme.

Grammar without rules

The word 'grammar' means "any explanation of the meaning or use of language" (in Wittgenstein's jargon), and an explanation of meaning is a definition. And therefore there may be many kinds of definitions.

If we want to say that 'beautiful' is a sign "without a grammar" or an "indefinable sign", that is because we see that an account of its grammar made by analogy to words belonging to describable parts of speech will be a false account -- or because we have a too limited concept 'definition'.

The meaning of the word 'beautiful' is shown by the way of life of those who use the word 'beautiful', e.g. in their attitude towards the things they call 'beautiful'. For some times and places 'beautiful' has amounted to no more than a "gush word". For others, e.g. the German Romantic Movement, it has been the center of life.

"How words are understood is not told by words alone" (Z § 144) -- but also by the difference they make in the way human beings live. Concepts not only "direct our interest" -- they are also "the expression of our interest" (PI § 570). [Note 9]

In order to get clear about aesthetic words you have to describe ways of living. What belongs to a language game is a whole culture. (LC p. 11, 8)

Various ways of life could possibly be shown on stage (cf. "play-acted definitions"). However, this might require not one scene, one act, but many scenes, many acts. It would not be an account given in rules, and we would not naturally call it a definition (although that would be its function: an explanation of meaning).

Distinction between the concepts 'grammar' and 'logic' made clearer

Is 'beauty' a word without a grammar? That depends on how broadly we want to define the word (how broad we want to make the concept) 'grammar'. Words are our tools. What work do we want to do with the word 'grammar'?

The question in this particular case isn't whether there are rules -- there are none -- but whether we can even give a description of how the word 'beauty' or 'beautiful' is used. But isn't that what we have done above? Go back to G.E. Moore's account of Wittgenstein's jargon: "any explanation of the use of language" is "grammar". But not every explanation of meaning is the stating of rules.

If, as I said, by 'logic' Wittgenstein means 'the study of rules', then there are words that have a "grammar" but do not have a "logic" in his jargon. So that what I called "Wittgenstein's identification of logic with grammar" should instead be: his partial identification of those two concepts -- i.e. his redefinitions of the words, or revisions of the concepts, 'grammar' and 'logic'.

Acquiring the concept 'beautiful' as an example of a way or "form of life"

Imagine we wanted to explain the concept 'beauty' or 'the beautiful' to someone who did not have that concept -- that is to say to someone who did not know how to use the word 'beautiful' in our language, who did not know that word's meaning. Would I point to examples of things I thought beautiful?

We might point to paintings like Fragonard's A Young Girl Reading or Renoir's La Première Sortie, but no one need understand what we are pointing to; someone might reply, "Yes, I see a girl. I see a chair. But I don't see this third thing you call 'beautiful'." We might point to the girl's eyes, her brow, the color and freshness of her skin, her hair, her chin, the shape of her face and the line of her jaw, but those are only facts, and beauty isn't a fact.

And we couldn't say that the girl was "lovely to look at" or "pleasing to the eye", because, although we use each of those expressions slightly differently, 'lovely' and so on are grammatically analogous to 'beautiful' or 'beauty' -- i.e. they have a similar rule-less grammar. If someone doesn't have the one concept, presumably he is not going to have the others either.

The concept 'the beautiful'

That is what is logically interesting about the word 'beautiful', despite Wittgenstein's dismissal of that word as having an unimportant role in aesthetics. Because it is a very good example of a human form of life that one cannot participate in unless one has the concept 'beautiful' and the way to acquire this concept isn't simply by learning rules of a game (Cf. acquiring the concept 'humor').

If we want to explain the meaning of 'beauty', we have to point to examples -- but we must do this with many or most other words as well. The difference is that here one cannot point to universal models that must be admitted by anyone who speaks the language, e.g. bridge is a model card game. That is why this word 'beautiful', the grammar of it, is interesting to logic of language. (In Socrates' context, you could say that we know that bridge is a card game, but we don't know that the girl in the painting is beautiful.)

Because contrast the case of 'beautiful' with teaching someone the concept 'game', where we can point to an objective list of games -- i.e. to a list of what everyone who has learned English calls 'games' -- e.g. checkers ("board games"), table tennis ("ball and net games"), and so on.

But even in this example, acquiring the concept 'game' requires more than just memorizing a list and being able to point to similarities between the members of that list -- because you must also be able to add new games to the list. What do we call "catching on" in elementary algebra -- e.g. learning to use x the unknown? You have to be able to find the x in problems you have not seen before, not just in those you have. ("To understand a language [game] means to be master of a technique" (PI § 199).)

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Endnotes Chapter 9

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10. Meaning as a "Usage"

The relation between grammar and sense and nonsense is shown by this: that a sign -- a spoken sound, an ink mark on paper -- as such is without meaning. What can give a sign meaning? (Z § 143; PI §§ 431-432)

Wittgenstein's logic is a study of rules of sense and nonsense undertaken to solve philosophical problems, but its foundation is a definition, a way of setting limits or boundaries to the concepts 'sense' (language with meaning) and 'nonsense' (sounds or marks without meaning).

To the question "What gives a sign meaning?" One answer Wittgenstein gives is: the sign's role in our life. The description of that role is the sign's grammar or meaning. "Only in the stream of life has language meaning" (Malcolm, Memoir (1984), p. 75). To divorce a sign from our life is to divorce it from its meaning.

That is a selected definition of 'meaning'. But it is also a statement of fact, although whether it is true will depend on what examples we have in mind. (What it is not is a statement of "what the meaning of language really is", which would be metaphysics, not logic.) [Note 10a]

Custom versus ad hoc convention

In the discussion of the distinction between a sign and the meaning of a sign", the word 'sign' was defined as: spoken sounds, marks on paper (ibid. § 431) lines in sand, gestures (Z § 651, e.g. a movement of the hand, a shrug of the shoulders), the purely physical aspects of language.

But to give a true account of Wittgenstein's use (or uses) of the word 'meaning' a further determination of the grammar of 'sign' needs to be made: a distinction must be made between a sign with a well-established use in the language (custom) and a mere arbitrary combination of sounds or marks or gesticulations.

The sentence 'The man walks' can serve as an example of the former, and the sign 'zazoz' as an extreme example of the latter. Whereas we can state that the meaning of 'zazoz' will depend entirely on how we choose to define that sign, if we are to give a true account of our language, then we cannot say the same about 'The man walks'. Why is this so? Picture the following cross-questioning in a court of law:

Our concept 'walking' (i.e. the grammar of that sign) is somewhat indefinite -- but not that indefinite. The word 'walking' is a word of the English language, the meaning (or use in the language) of which has been established by common practice -- and for that word to be applied with meaning -- and not be meaningless noise -- new applications of that word must resemble (to a greater rather than a lesser extent) established applications of that word, such e.g. as strolling or putting one foot in front of the other. Must -- why must?

Is "Caprice" a possible game?

If we compare language to games, where what interests us about a game is its rules, ask yourself if it is possible to play a game where everyone "makes up the rules as he goes along", changing them at the slightest whim. Of course there might be such a game; call it Caprice where you do what you like whenever you like (like Humpty Dumpy). But now, can we suppose that Caprice were the only game that was ever played? (PI § 199)

A capricious -- i.e. arbitrary, undefined (ruleless) -- language would not be a language; it would be sounds and marks without meaning. That is the connection between rules and meaning (sense and nonsense) (OC § 61-62).

Were language a game without rules, telling lies would not be possible -- nor would telling the truth. The lawyer assumes that the witness knows the rules of the game -- the language game with the word 'walking' -- and that the lawyer has caught the witness "cheating", i.e. not following those rules; the lawyer assumes that everyone who has learned our language will recognize this. And the lawyer has the right to make these assumptions -- because English is a language, not just a collection of sounds or marks.

What interests logic is not what a word suggests to a particular individual, because then a word might have countless "meanings", but how the word must be used by everyone who knows the language -- i.e. logic asks for our held-in-common, public rules for a word's use (i.e. the word's normal use in the language), because it is by means of those rules that we distinguish sense from nonsense verifiably.

Grammar is a Normal School

"I don't know what you mean by 'glory,'" Alice said.

Humpty Dumpty smiled contemptuously. "Of course you don't -- till I tell you. I meant 'there's a nice knock-down argument for you!'"

But 'glory' doesn't mean 'a nice knock-down argument,'" Alice objected.

If the rules of Humpty Dumpty's language (Through the Looking-Glass, vi) were the same as the rules of Caprice, then his language would not be a language, because it would consist only of signs (in this case, sounds) that were impossible to define, 'impossible' because their "meaning" would depend solely on Humpty Dumpty's whim of the moment. A language whose grammar were in constant flux would not be a language. Grammar (rules, definitions) requires regularness, stability.

The relation between recurrent behavior and grammar

The grammar of our language does consist of conventions -- but not of "mere conventions". The grammatical conventions of our language are not merely rules that are tossed up and let drop, but rules that have been established day after day -- usually for years and years, often for all our lives. This becomes especially clear if we consider the "language games" with words that Wittgenstein considers in the philosophy of psychology, words such as 'sorrow' and 'hope' (words whose grammar might, if not be stated in rules, be play acted as an explanation of meaning).

"Form of Life"

The term 'language game' is meant to bring into prominence the fact that the speaking of language is part of an activity, or a form of life. (PI § 23) To imagine a language means to imagine a form of life. (ibid. § 19)

A "form of life" or way that human beings live considered as a "custom, usage, institution" (ibid. § 199), or as natural history: a persistent pattern of human life, which may either be dictated by nature or, in some cases, chosen.

The word 'sorrow' is applied to a pattern which recurs, with different variations, in our life.

If someone's bodily expression of sorrow and of joy alternated, say with the ticking of a clock, we would not have here the characteristic formation of the pattern of sorrow. (cf. ibid. II, i, p. 174)

Imagine a man who wept piteously one moment, and laughed merrily the next moment, and so on and on. First, we would certainly regard him as a madman. And second, we really wouldn't know whether or not to call his crying 'sorrow' or his laughter 'joy'. Not only are there no rules for applying those words here, but also no natural extension of our concepts suggests itself to us. This behavior is not our "form of life" -- i.e. we do not have here the "characteristic formation of a pattern" of human life.

We would not know what to do with such a man. And if he uttered 'I am sad' one moment and 'I am joyful' the next moment and so on, we would not understand his "language", although we heard the sound.

Could someone have a feeling of deepest sorrow for the space of one second -- no matter what preceded or followed that second? (cf. ibid. § 583)

"Could someone ...?" is a grammatical question. It means: can the word 'sorrow' be applied in these circumstances? Is the concept that fluid -- i.e. can the word 'sorrow' be applied to just anything? A word whose grammar were that fluid would not be a word; it would not have a grammar; it would be meaningless scribble, noise.

An objective distinction between sense and nonsense

If an objective distinction is to be made between sense and nonsense -- if there is to be a logic of language, then mustn't it be correct to apply a sign in some circumstances and not in others?

If we made the rule 'Say the word 'zazoz' in any situation you please', we would not be making what Wittgenstein called a 'rule of grammar'; a child's random babbling is not language. Were it correct to utter the sign 'I am here' in any and all circumstances, that sign would be nonsense (OC § 10; PI §§ 117, 514).

But why must? The question is: isn't it correct to apply a sign in some circumstances and not in others? If the answer were not yes, then there would be no language, only the noises that are made by animals. (The word 'correct' here means 'with meaning' (Z § 297).)

And 'meaning' and 'meaningless'

The chapter began with the question: what gives a sign meaning? But if 'meaningful' does not contrast with 'meaningless', then this question is nonsense.

"How do I know that the color red can't be cut into bits?" That isn't a question. (PG i § 81, p. 126-7)

I.e. it is nonsense, an undefined combination of words. Anyone might, of course, invent a use for that combination of words, but it has no normal use in the language: it is not a defined move in any of our language games.

I would like to say: "I must begin with the distinction between sense and nonsense. Nothing is possible prior to that. I can't give it a foundation." (ibid.)

"I must begin with ..." But Wittgenstein still has to make the distinction. This he does with similes, specifically with comparisons of language to games and words to tools: these comparisons make the distinction between with and without meaning.

An objective (verifiable) sense-nonsense (meaning-meaningless) distinction belongs to the facts we find when we look at language, if we look at language through Wittgenstein's lenses. The distinction is best explained by comparing using language to playing a game: If a game is played according to its rules, moves in the game have meaning; similarly, if language is used according to its rules of semantic-grammar, the language has meaning. And contrariwise (although there are exceptions).

When eyeglasses are required to see

It is not a result of investigation: it is a requirement. (PI § 107)

It is like a pair of glasses on our nose through which we see whatever we look at. It never occurs to us to take them off. (ibid. § 103)

The question is: how are we to take these glasses off? There is no way to do that without adopting an alternative "logic of language", some explicit or implicit other way of distinguishing meaning from meaningless. (Plato's way is wholly metaphysical: the correct names of things (i.e. the names of Forms) have objective meaning (namely the Forms themselves), but as there is no way to know what those names are or what their meanings are "so long as we keep to the body", this is not a serviceable distinction. Unserviceable also is the TLP's definition of 'nonsense' that consigns most of our language to the rubbish bin despite its ability to convey meaning.)

In such a "logic of language" the distinction between sense and nonsense might not be objective (there would be no semantic rules of grammar). A sign would "make sense" if, as W.E. Johnson says, someone were inclined to say "It has sense for me" (BB p. 65). That is an example of an alternative to Wittgenstein's logic of language -- an alternative, that is, if we are willing to call a logic without rules a logic at all.

Which shows that the particular rules-based way of looking at language meaning-- namely through grammar and sense and nonsense -- is Wittgenstein's logic of language. It is important to be aware of this, of this particular pair of eyeglasses. Wittgenstein's logic is a logic of language, not the logic of language, not the only possible one.

Does the verification of meaning belong to the tribe or to the individual alone? Does knowledge, the meaning assigned to the word 'know', belong to the tribe? We don't call just anything a distinction, or knowledge, or verification. There are deeds in name only: abracadabra. And who is "we"? Whoever has learned to think rationally, and what you cannot say is that there is an alternative rationality.

Kinds of language conventions

If we want to say that it is misleading to speak of "customs, usages, institutions" -- because if a sign is meaningless, it is only because we have not given it a meaning, a use in the language, but left it undefined -- that is because we have certain examples in mind, and not others. But this is correct: the only demand logic makes of rules of grammar is that they be followable -- which is why we cannot simply utter a rule without describing how it is to be followed. (PI § 380; PG i § 82, p. 127)

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Endnotes Chapter 10

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Next chapter:

11. 'Nonsense' and Contradiction

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