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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 explains the first principles of the later philosophy.

Outline of this page ...

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 their definitions, the rules for their use, are (BB p. 25). Suppose we were asked to explain the meaning of the word 'mind' or 'holiness' ... the meanings of many words, especially in philosophy, appear vague and cloudy to us. The source of this is of our naive ideas about language meaning: (1) that all nouns are names, and (2) that the meaning of a name is the thing the name stands for, regardless of whether that thing is tangible or intangible.

A Move in a Game

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 that 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 grocer's 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, asking and buying apples at a greengrocer's is an example of a "primitive language game".

Note that the language to games comparison (a rule-based definition) is not the only way to define the word 'meaning'. There are many meanings of the word 'meaning' in our language. Wittgenstein chose one, one that is public and thereby makes language meaning objective (verifiable).

Common Names and "Family Resemblances"

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 'piety' as 'doing one's duty [or correct conduct] towards God' (Gorgias 507b) elicits the response: "But just what is one's duty; what exactly must one do?"

The general definitions found in dictionaries are too general to serve as guides in any and all circumstances -- in a word, the general definitions in dictionaries are not essential definitions. Judged by the school requirement, therefore, most words are without essential meaning, despite having general definitions.

The rational standard of speculation versus the empirical standard of logic of language

Plato merged the thought of Heraclitus and Socrates, and reasoned metaphysically, that the meaning of a common name must be the common nature it names.

But Wittgenstein, looking, and wanting to look, no farther than the facts in plain view, found -- as Plato looking at the same facts had found -- that common names that name common natures are not characteristic of our language. Wittgenstein illustrated this with the common name 'game'.

Note.--"Whatever we know we must be able to tell others" (Laches 190c) is the Socratic standard in philosophy, for philosophy is discourse of reason. If we are unable to explain to others what we claim to know and defend our explanation in cross-questioning -- then we don't know what we think we do.

The historical Socrates applied two tests to claims to knowledge: reason and public experience, meaning: verification by the facts in plain view. If what we look for in our common language is not there to be found, then the claim that it is there is refuted.

That is the difference between metaphysical speculation and logic: speculation is only put to the test of reason (consistency). Wittgenstein wanted "to say no more than we know" (BB p. 45). Speculation is not knowledge.

Note that no philosophy is free of standards -- standards that must be chosen (or assumed), e.g. Wittgenstein's selected meaning of 'meaning' and Plato's method of preconceptions. There is always the choice of a point of view..

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 there are many different kinds of games (e.g. badminton, checkers, solitaire), if games are defined by their rules, as there are many different kinds of words in our language (contrast the rules for the use of 'impatience', '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 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 unworkable or false accounts of word meaning:

The first is that words are names of things and that the meaning of a word 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 it is not the same thing to say that the meaning of the name of an object is often explained by pointing to its bearer (PI § 43), and to say that the meaning of a name is the bearer -- all the while presuming that all words, or even just all nouns, are names of things. The words 'beauty' (Greater Hippias), 'justice' (Republic Book One), and 'piety' (Euthyphro) are not names of things.

The second account is that common names are the names of common natures, and that the meaning of a common name is the common nature it names. The first account is a "grammatical fiction" (ibid. § 307), and the second account, if we are examining natural language, is very rarely true. The definition of 'simile' (as a comparison using the words 'like' or 'is') is not the model of common name definitions, but instead explanations of meaning through examples is.

In sum, 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, and 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 farther 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, as Wittgenstein chose to define the word 'meaning' (as the logic of language).

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"

A philosopher says: Look at things this way! (CV p. 61, remark from 1947)

Despite Wittgenstein's description of our use of the word 'game', the old perplexity persists: Why do we call them all 'games' -- i.e. what is the essential 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 and impossible to define.

But as we normally use the word 'meaning' a word that can convey meaning is not meaningless. Therefore a different meaning of the word 'meaning' is needed if we are to set aside our naive ideas about the way language works, to see that the word 'game' is neither meaningless nor indefinable. [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 name (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.

... 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 since Socrates is being awakened (Plato, Apology 30e-31a) to things you never thought about, and there are many of these in logic of language, which are often (but not always or always most profoundly) the root of philosophical problems. How concept-formation is possible in the case of common names is a problem to be awakened to ("... that never troubled you before ...").

The "critique of language"

Is an "indefinite boundary" no boundary at all -- is a game without fixed rules (i.e. definite boundaries), or sometimes with no rules at all (child's play), 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 must sometimes invent rules (boundaries) to make the meaning of a question clear if there is to be a distinction between sense and nonsense when we philosophize.

The first question in philosophy, the "critique of language" that "all philosophy is" (TLP 4.0031, tr. Ogden), is the meaning of 'meaning' that a philosopher chooses (or gives no thought to) for his thinking in philosophy.

Drawing lines between the resemblances in 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.

Plato and concept-formation

If the formation of concepts can be explained by facts of nature, should we not be interested, not in grammar, but rather in that in nature which is the basis of grammar? (PI II, xii, p. 230; cf. ibid. § 142; OC § 617)

Wittgenstein's "theory of family resemblances" does not explain (account for) concept-formation. It sets the question of concept-formation aside; it does not answer Plato's question of how there can be common names if there are no corresponding common natures in our world (Parmenides 135b-c). Because note: Wittgenstein gives no criterion for distinguishing one family from another family. The word 'family' in fact adds nothing to 'resemblances'. Wittgenstein's "theory" amounts to pointing out similarities (but everything is similar to everything else in some way or another).

Plato warns against mere resemblances when we are seeking to know the essence of a thing (Sophist 231a). If a concept (common name) is nothing more than a collection of various things that are alike in various ways but in no essential way, then there are limitless possible concepts, and the question of why our language consists of the actual concepts it does is not answered by Wittgenstein or the Ockhamists. But Plato believes there is a relationship between the concepts we actually have and reality itself, which is a view Wittgenstein shares in a limited way --

Very general facts of nature and concept-formation

If anyone believes that certain concepts are absolutely the correct ones ... then let him imagine certain very general facts of nature to be different from what we are used to, and the formation of concepts different from the usual ones will become intelligible to him. (PI II, xii, p. 230)

Wittgenstein offers a description -- not of how concepts are formed (i.e. their origins), but of what we find if we look at the everyday concepts of our language after their formation. Wittgenstein's family likeness analogy (metaphor) is not a theory, if by 'theory' is meant 'a speculative explanation of phenomena' (in this case, the phenomenon of concept-formation).

Ockham employs the principle of economy in explaining concept-formation: Plato and Socrates are both called by the common or class name 'man' because they are more similar to one another than either is to a donkey. No further explanation is needed: concepts are dictated by facts of nature. That may sound plausible in the case of 'man', but maybe not so plausible in the case of 'game'.

Further criticism of Wittgenstein's metaphor

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])

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 those 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 (a suggestion Guthrie refers to, Socrates (1971), p. 120) 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 that puzzle 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. A carpenter's tool chest contains the tools he needs for his work. These are different from the tools in an artist's paint box or in a farmer's barn. And because men use things to help them in their various kinds of work, that may explain the existence of the concept 'tool' DEF.= 'anything used to do anything'.

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.

Endnotes Chapter 7

Note 6: And not only a number-word, but a reasonable number, e.g. five but not five-hundred. There are different kinds of rules, of course; not all rules are rules of sense and nonsense (grammar). Some rules have their origin in what is practical, others e.g. in what is polite.

Rules and sense and nonsense (Playing the game wrong versus nonsense)

"... when a game is played according to its rules, moves in the game make sense (have meaning), and when language is used according to its rules of grammar, the language makes sense." The trouble with that simple summary or formula is that a wrong move may be made in a game without the move being without meaning. Contrast moving the bishop as if it were a knight with Wittgenstein's example of putting a paper crown on the chess king's head (BB p. 65); the first is a wrong move, while the latter is no move at all, i.e. it is without meaning.

If I ask the corner grocer for five-hundred apples, although I am breaking a rule of the game, I am not talking nonsense, whereas if I answer 'How many?' with 'Blue', I am talking nonsense. So that "playing the game wrong" is not the criterion (or sufficient criterion) for distinguishing sense (i.e. language with meaning) from nonsense. Rather, break some rules and you talk nonsense; but break other rules and you only play the game wrong -- i.e. what you say isn't without meaning (mere noise).

The source of verbal humor is playing the game wrong, language which is absurd but not meaningless -- otherwise there would be no joke. "Even a nonsense-poem is not nonsense in the same way as the babbling of a child" PI § 282).

So it is false to call any playing of the game wrong nonsense, because that would obliterate the difference between "played wrong" and "senseless". We understand what it is to stock and hand over 500 apples, but not 'How many?' -- 'Blue'. So a ruled-out move may be either foolishness or without meaning, with the response in both cases being, "I don't know how to go on with the game if you are going to make unreasonable demands or talk nonsense."

The relationship between our concepts and general facts of nature

The propositions 'There are physical objects' and 'Human beings can only jump so high' are of very different kinds. The first proposition is a rule of grammar (OC § 36) -- i.e. an explanation (description) of how words are used in the language: e.g. physical objects exist in contrast to mirages, hallucinations and creations of the imagination, which don't; other than as a grammatical proposition, however, that combination of words has no use in the language. (That grammatical account may appear rejected by Idealism; but there is a difference between (1) the proposition 'There are physical objects' as we normally use our language as judged by the facts in plain view, and (2) the philosophical thesis 'There are objects that exist independently of our perception of them' with the attendant question of the existential (or grammatical) status of the "thing in itself". That speculative thesis cannot be judged by Wittgenstein's standard of the facts in plain view.) In contrast, the statement 'Human beings can only jump so high' is a general fact of nature (proposition of fact).

Wittgenstein writes that a language game is without grounds (OC § 559), but he gives an example that seems to refute that thesis, namely the act of weighing cheese (PI § 142). And if some very general facts of nature were different from what they are, the way of life might be very different, e.g. the use of the word 'know' might be very different from what it is in our world in a world in which all human beings were without the sense of sight.

Not only rules but a point

There are different kinds of rules of the game, e.g. the rule in chess that if you touch a piece you must move that piece and not some other seems different in kind from the rule that the bishop is permitted only to move along diagonals through unoccupied squares. The rule that the volleyball must be returned to the opposition server under the net not over is similar to the touch rule in chess. Some rules appear to be outside the game itself (etiquette); nonetheless, they may be binding. (Cf. PI § 68)

Let us say: the meaning of a piece is its role in the game. -- Now before the start of any chess-game let it be decided by lot which of the players gets white. For this purpose one player holds a king in each closed hand and the other chooses one of the hands at random. Will it be reckoned as part of the role of the king in chess that it is used for drawing by lot?

Thus even in a game I am inclined to distinguish between essential and inessential. The game, I would like to say, does not just have rules; it has a point. (RFM i §§ 19-20, p. 108-109) [Note 7])

But if elements are inessential, then it follows that others are essential. What defines a game are its rules, but some rules may not be essential to the game, i.e. defining (That is an example of a "grammatical remark" or "reminder").

Logic and nuance. Rules and impressions

No one would believe that a poem remained essentially unaltered if its words were replaced by others in accordance with an appropriate convention. (PG i § 32, p. 69)

But in Wittgenstein's logic of language, the poem's meaning would remain unaltered, because its 'meaning' in the sense of 'affective nuance' (or 'sensibility') does not belong to "meaning = use in the language = rules of grammar", and therefore the poem's meaning, in Wittgenstein's sense of 'meaning', would remain "essentially unaltered" despite the poem's words being replaced by others of equivalent meaning. The word 'spider' can replace the phrase 'friend of the cobwebs' with no change of meaning.

What interests us in the sign, the meaning which matters for us is what is embodied in the grammar of the sign.... In a certain sense one might say that we are not concerned with nuances. (ibid. i § 44, p. 87)

Is the meaning of words always told by the words alone (Z § 144)? But context can be quite wide, e.g. facial expressions. The telephone's disembodied voices: "People can't see you smiling." Is that you are smiling when you talk on the telephone essential to the meaning of your words? and then does your hearer not know the meaning of your words if that person doesn't know that you are smiling? Does tone of voice (which seems to belong to context) determine the meaning of the words 'I hate you', because those words may be used affectionately (as well as in many other ways).

What belongs to nuance, what to grammar? Is the test whether something can be stated in rules? (Can a poem's affective nuances be stated in rules? There may be formulas, but following them is no guarantee that you will attain the desired effect.)

Logic of language and Philosophy: Wittgenstein, Socrates, and choosing standards

What have these questions to do with philosophy (PI § 109)? Logic of language is the foundation stone of philosophy, and these questions point out the indefiniteness of the concept 'meaning' and the barrier that indefiniteness would present to distinguishing sense from nonsense in the language used in philosophy -- had not Wittgenstein selected a particular meaning of 'meaning' for his work in philosophy. If meaning were not objective, or could not be made objective, in my eyes at least, philosophy would be idle chatter, understanding an illusion.

Likewise if Socrates had not chosen the particular meaning of 'know' he chose, the meaning that makes knowledge in philosophy objective, we could only think ourselves wise when we are not (for we do, if unchecked, think ourselves wise).

It is because of the choices these two philosophers made that investigations in philosophy can be objective (verifiable), rather than more or less nebulously seeming to be sense rather than nonsense and seeming to be knowledge rather than ignorance (ibid. § 258). [BACK]

Note 6a: Neither the theory of abstraction nor Plato's theory of Forms defines common names by identifying their common natures. The presumption (preconceived idea) of both is that common names are neither meaningless (i.e. essence-less) nor unknown, only that knowledge of what their meanings are can be grasped but cannot be put into words.

Metaphysics is the philosophy of speculation (in contrast to going no farther than the facts in plain view as the historical Socrates and later Wittgenstein did). The view of the question of the meaning of common names of many Mediaeval philosophers shows in what way metaphysics is different from "saying no more than we know".

... whether genera and species are subsistent entities [i.e. whether classes and subclasses exist extra-mentally] or whether they consist in concepts alone; if subsisting, whether they are material or immaterial and, further, whether they are separate from sensible objects or not. (Copleston, A History of Philosophy, Volume II (1950), xiv, 2)

The essence of metaphysics is that it wants to go, using reasoning alone ("pure reason"), beyond the facts in plain view. In contrast, those facts are just what, and all that, Wittgenstein's logic of language wants. Verification by experience is part of Socrates' method, in contrast to the the stated method of Plato. [BACK]

Note 6b: How can knowledge be one thing, always the same (Theaetetus 145e-146a) if there are many branches of knowledge, some of which are unalike or even opposite to one another (Philebus 13e-14a)? Square and circle are both shapes, yet they are in some ways opposite to one other (ibid. 12e-13a).

Since a thing cannot be opposite to itself (have a self-contradictory essence), this observation (anomaly) refuted Plato's earlier view that the meaning of a name must be a common nature, and from the dialogs the literary character Socrates disappears to be replaced by the "visitor from Elea". [BACK]

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 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 abstractions or "names of abstract objects", e.g. 'idea', 'time', 'ghost', '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 found in common language games. Reports of these are 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 'a [natural] noise in the clouds', or that by 'flows' we sometimes mean the movement of a river. (We might use Socratic induction to gather these, as Wittgenstein does to show that there is no defining common nature of games, but we don't often use this method.)

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 rules alter very general facts of nature, to imagine e.g. a world in which all human beings are deaf -- how will their use of the word 'know' differ from ours? (the point in this particular example is 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 basic calculations in mathematics frequently broke out among adults.] (ibid. II, xi, p. 225)

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 fictional concept-formation is imagination (logical possibility). What is the limit of non-fictional concept-formation? The concepts of metaphysics (e.g. Plato's "Forms", Locke's "substratum") are examples of logical, not real, possibility because real possibility can be verified.

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 like a blunt instrument 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 the word 'nonsense' is equivalent in meaning, not only to 'an undefined combination of words', but also to 'foolishness').

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

Note that if language as used in philosophical problems is not game-like, 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?

9. Concept definiteness and indefiniteness. Concept fluidity

Our concepts are "fluid" as water is fluid but ice is not. Our concepts have more or less, not sharp, but "blurred edges"; they are not well-defined. 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 [inflexible] rules; neither was it taught to us that way. (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 definitions, but because there is no clear limit ("definition") to them.] (BB p. 25)

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 lightning be present? You don't know? The question is grammatical: what would anyone need to know in order to answer those questions? More facts about a phenomenon, namely thunder -- or a rule for using (applying) a word, namely the word 'thunder'?

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

"... or a rule for using the word 'thunder'?" What would be the source of that rule -- would it necessarily be the phenomenon itself? Is thunder the cause of lightning or is lightning 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.

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 the meaning of that word goes. What the child learns is not a strictly defined concept.

Concept indefiniteness (a "grammatical reminder")

There is no rule to answer every question we might ask about the grammatical ("as defined by rules of grammar") meaning of the word 'thunder' or other names of phenomena. Wittgenstein said that his "grammatical remarks" are "reminders", here a reminder that in most cases there are not rules to define a word's use everywhere and always (PI §§ 84-85).

Note that there is a special 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. For example, rules were made to resolve contradictions in the Paradox of the Cretan Liar and algebraic equation.

The sciences, both early and later, may assign strict limits to concepts, but our natural language does not. (Definition in natural science.)

"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. 230) that things like that do not happen. Our concepts (words) do their work within our life (ibid. § 116; Z § 173), not in every set of circumstances that may be dreamed up.

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 language 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. (CV p. 27, remark from 1937)

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

In this context 'explanation' = 'speculative accounting for the presumed facts', as exemplified by the Theory of Abstraction: that by an unspoken induction and a mysterious abstraction, the result of which cannot be put into words, the common natures or essences, which common names are presumed to name, are grasped by the mind.

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

Rules as a standard (objectivity)

But how can Wittgenstein make an objective distinction between sense and nonsense if language use doesn't follow strict rules -- because aren't strict rules what make meaning objective? That question would appear 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. (PI § 68)

That is how Wittgenstein's project in philosophy differs from Plato's method of preconceptions: it accepts the facts in plain view as the ultimate facts ("nothing is hidden"). What is objective (verifiable) is whether or not there is a rule ("regulation"). That is how the distinction between sense (defined language) and nonsense (undefined language) is objectively made.

Many or most of our concepts are open-bordered ("the concept is not closed at the frontier") (ibid. § 68), and this limits 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.)

However, simply 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 normally exist (cf. Z § 466). Making rules allows us to bring clarity or resolution to philosophical problems; thus our work doesn't have to be obstructed by the normal state of the concepts that are our common currency.

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; others are pointing out hypostatization (i.e. when abstractions are mistaken for independently existing things) and when adverbs or other parts of speech are without reason transformed into nouns ("names of things").

"Analytic propositions"

Can a parakeet give birth to a giraffe?

Can a horse give birth to a calf (baby cow), or is any offspring of a horse a foal (baby horse)? (Cratylus 393b-c)

If the answer is that "any offspring of a cow is a cow, regardless of whether it is in all other respects a horse", then is the question a grammatical question, i.e. does it ask for a rule for using a word, or does the question ask for an hypothesis about a phenomenon?

The proposition 'It is not biologically possible' would be an hypothesis, not a proposition that can be known (verified) independently of the test of experience, which an analytic proposition or truth, by definition, can be.

The "analytic" account of language meaning seeks to define words by introspection, i.e. subjectively -- (Wittgenstein said about the Rationalists, "they let the words speak to them") -- to find "whatever seems right" (PI § 258) from the impression a word makes. (Further: defining words by pondering.)

Plato's question is not answered by musing, but by asking whether there are rules of grammar for events that, although they can be described, never happen.

If 'analytic proposition' is defined as 'a proposition that is known to be true solely by an analysis of its ideas (regardless of what the origin of those ideas is)' [Note 7a], then is the proposition 'If you know what is meant by the word 'cow', if you examine that idea, then you know that a cow can give birth only to a cow' analytic?

How would I know? Because in fact it lies entirely in the realm of "whatever seems right is going to be right" (ibid.) along with everything else involving essentially inexpressible ("what is meant by", "the idea") elements. And whatever seems right is not a standard by which to distinguish sense from nonsense.

As we normally use our language, the proposition 'The offspring of a cow is necessarily a cow' is (1) as a report of grammar, a fiction (because there is no such rule), and (2) judged as a statement of fact, it is undefined language (because there is no defined test of its truth).

'A cat is a feline, a dog a canine' may be called an analytic proposition, if analytic propositions are simply definitions, explanations of the use of words. Whenever the predicate is synonymous with the subject, the proposition is called "analytic" might be the rule (definition). But 'cow' and 'offspring of a cow' are not synonymous -- or are they? (There simply is no rule.)

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 definition? Why don't I know? Surely I speak English. Why can't I define this common word?

How does a child learn to use the word 'city'? How would we teach the child -- is there something we know that we can't tell the child? (ibid. § 69) No, every explanation of meaning we can give ourselves, we can give the child too (ibid. § 210). We often say the word 'city' -- don't we know what we are talking about?

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 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 geography 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 an imperfect way to define most words, but instead the normal way, because, as we find if we look, most words do not have essential meanings (definitions). Similarities or resemblances there usually are.

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 the language is not that of ostensively defined names. It is the logic of the "use in the language" class that is misunderstood and that generates philosophical confusion when analogies are made from the name-bearer class to the use-in-the-language class (I give the example of 'book' to 'mind'; Augustine-Wittgenstein: 'river' to 'time').

Invent, not Discover

When in philosophy we (or philosophers) invent a rule for the purpose of resolving perplexity that would continue were it not for the new rule -- i.e. when we redefine a cloudy concept, we mustn't think that we have somehow discovered the concept's true limits; what we have done is to make a rule, a meaning, not discover one that already exists.

[Philosophy's] aim is to remove particular misunderstandings; not to produce a real understanding [of the meaning of a word] 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 (BB p. 69), and therefore if we want to describe that meaning we must describe our way of life. However, that is just 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 word divorced from its use as a tool in our life.

That is to kidnap a word from "the language game that is its original home" (PI § 116), the place where the word has meaning, according to Wittgenstein.

The presumption: "Language follows thought and thought follows things" (Copleston), and that it is those "things", e.g. "mind" and "time", that philosophy is about. But it is only in a mistaken conception of language meaning that the words 'mind' and 'time' are the names of things at all.

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).

In the Socratic dialogs Plato tries to guess the meaning of words as one thesis after another is proposed and refuted. Plato assumes that abstractions (e.g. 'beauty', 'justice', 'piety') are the names of things, although returning these terms to their original homes (as 'beautiful', 'just', 'holy') shows that they do not function as names there. That is "what we find if we look". Was Plato, then, talking nonsense -- was he "using words whose meanings he did not know" -- because isn't doing that "talking nonsense"? (ibid. § 79) Then why does he seem not to be talking nonsense but only to be perplexed about the nature of things (beauty, justice, holiness, courage, self-control), as we naively read his work? To reply "mutual ignorance of the logic of language" sounds presumptuous and pretentious. Which doesn't make it untrue (cf. 'geometric point'). [Note 7b]

"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 is the meaning of the word 'gentleman'? Can one 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 (i.e. describing or making rules for the use of) a word.

One would like to say: whatever is going to seem right to me is right. And that only means that we can't talk about "right" here. (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 in Wittgenstein's sense of 'grammar'.)

Logic asks for the language facts that are open to the public, the rules that are recognized by all speakers of the language (BB p. 65) however sketchy those rules may sometimes be (PI §§ 79, 88).

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

Induction and Definition and Impressions of Meaning

The form of expression 'What is some thing?' (e.g. "What is a city?" "What is a gentleman?") points the way deeper into confusion rather than the way out. "I would say that piety is ..." as in Plato's Euthyphro. But Plato has Socrates put Euthyphro's impressions to the test to see if they are everywhere consistent with what Euthyphro believes about the gods. And this may show what Euthyphro means by the word 'piety' -- or that Euthyphro doesn't know what he means (i.e. that he does not know what he thought he knew).

What Socratic induction, from the point of view of logic of language, does is to seek the boundaries of our concepts, e.g. 'piety', because those limits belong to the description of a word's normal use in the language, the use which "anyone knows and must admit" (Z § 211).

Concepts, Order and Chaos

Note that it is the boundaries of our concepts that induction may discover. An abstract term ('piety') is not the name of an abstract object ("piety") that can be known independently of the definition of a word, as if the boundaries of a phenomenon existed before they were drawn by language. Induction does not discover the natural boundaries of phenomena (although it sometimes appears that it does -- which may test the thesis that concepts define phenomena, not phenomena concepts, that phenomena without concepts are a chaos).

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 indefinite, but we would not say that about the grammar of 'love'. The definiteness and indefiniteness of our concepts arose as part of our natural history (ibid. § 18), and indefiniteness just has sometimes to be accepted as "the given" (ibid. II, xi, p. 226) in conceptual investigations (i.e. investigations of the grammar of words).

Learning a natural language may be learning to accept concept indefiniteness, acquiring a tolerance for many kinds and degrees of vagueness -- or it may be acquiring deep and abiding perplexity (something else that "turns a man into a philosopher" (Z § 455)).

Facts of nature that can explain concept-formation

Despite this being the grammar of the word 'game' we inherited when we inherited our language, we would not say that solitaire (patience) and table tennis belong in the same category based on their compelling similarities or "family resemblances".

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?

Our inherited language would be "the ancient city of language" (ibid. § 18), that was built up naturally, with twists and turns as the need arose. It is from the ancient city of language that all problems of philosophy arise, as Wittgenstein limits the concept 'philosophy' and illustrates with selected examples that appear to justify that limit.

"Facts that can explain the formation of concepts" (PI II, xii, p. 230) -- what might 'explain' mean here? 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, as had Aristotle.) There may seem a few such concepts, e.g. 'object' and 'space' and 'movement' or 'change' -- but are those forced on us by the nature of things (and maybe of our five senses) or by the nature of the human mind (Kant)?

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." The concept 'beautiful' doesn't work that way.

Don't we sometimes give reasons for saying that something is beautiful? But must anyone find those reasons compelling -- i.e. agree that those reasons force anyone to apply the word 'beautiful' to the example? The grammar of the word is not that way.

As children we are given aesthetic judgments. "Don't the ribbons in my little girl's hair look beautiful!" But in later years the girl can point to a photograph of that day and say, "I looked horrible!"

If we are to give an account of the way the word 'beautiful' is used in our life, then whatever we find belongs to "everything descriptive of the language game" (OC § 56) (although is this particular use of language in any significant way comparable to a game?)

The creation of beautiful things

Can rules be given for the creation of beautiful things? The classical Greek sculptors did have rules for carving the female body [Note 8] -- can we then state rules here for applying the word 'beautiful'? That would be a possible concept, but it would not be ours. Indeed, anyone might respond: "In my eyes at least, idealized proportions are not beautiful." The grammar of our word 'beautiful' (a description of how we use that word) doesn't rule out that judgment.

By nature (instinct), it seems, human beings as individuals have likes and dislikes. But 'beautiful' is not synonymous with 'liked and 'disliked'. And a description of the grammar of 'beautiful' must include this "very general fact of nature", because it might be -- and sometimes is (e.g. women's fashion) -- otherwise.

"Most people find this beautiful." But is that how we learned to apply the word 'beautiful' -- by appealing to the judgments of "most people", i.e. 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)

It is a fact of natural history that people living in a given place and time usually do agree in their aesthetic judgments, e.g. there have been near-universally admired starlets. And possibly if it were not this way we would not have the concept 'beautiful' that we do have (ibid. § 351). The absurdity is that it would be impossible to define the word 'beautiful' except by means of disputable examples, starlets notwithstanding (nearly all ≠ all).

But aren't there examples about which people must agree? For example, 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.

Concept-formation ('beautiful', 'pretty', 'lovely')

What is pretty cannot be beautiful. -- (CV p. 42, remark from 1942)

If I say that something is pretty, I will not also say that it is beautiful. A pretty face, for example. But how I decide what is pretty, what is beautiful, is beyond me (I haven't the foggiest idea): there are no grammatical rules to follow. None whatever; I leave it to whatever suggests itself (PI § 607). How did we learn to use these words? By imitating what others say and do? But what we learn isn't something that can be put into words, i.e. stated as rules -- and we would not accept it as an account of our concepts if it were stated in rules. (Certainly nothing Wittgenstein wrote can account for, or even suggests an explanation, of concept-formation in the case of 'beautiful'.)

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'.

Possibly 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 the word 'beautiful' may amount to no more than a "gush word". For others, e.g. the German Romantic Movement, it has been the center of life (Franz Schubert and his circle).

How words are understood is not told by words alone. (Z § 144)

But also by the difference they make in the things human beings do, how they 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"). That 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 'beautiful' 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 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 of the word 'beautiful' in our language. Would we point to examples of things we judged 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 that she is seated. 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 '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'

What is remarkable to logic of language about the word 'beautiful', despite Wittgenstein's dismissal of that word as having an unimportant role in aesthetics, is that it is an example of a human form of life that one cannot participate in unless one has the concept 'beautiful' and that the way to acquire that concept is not by learning rules of a game. (Cf. acquiring the concept 'humor').

[Wittgenstein would call this discussion "stupid" (LC i, 36, p. 11), because this is not the way he wanted to discuss aesthetics. But our interest here is not the subject of aesthetics -- but language meaning ("grammar"), and discussion of the concept 'beautiful' is instructive for that purpose.]

If we want to explain the meaning of 'beautiful', 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 (Z § 211), e.g. checkers is a model board game.

By the Socratic standard, we could say that we know that the girl in Renoir's painting is sitting in the balcony, but we don't know that the girl is beautiful.

An indefinite class (concept) is not a closed list

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. bridge ("card games"), table tennis ("ball and net games"), and so on.

However, also compare the case of 'beautiful', because acquiring the concept 'game' requires more than just memorizing a list -- you must also be able to add new games to the list.

What do we call "catching on" ("Now I know how to go on" (PI § 151)) 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. (ibid. § 199)

Endnotes Chapter 9

Note 7:

Is the outcome the point of a game?

Is even the game of chess everywhere bounded by rules, because there is no rule about whether the chess pieces are to be moved with the right hand or the left. What would be the point of such a rule? What is the point of the rule that a bishop may not move through occupied squares? (Because that game can be imagined too.)

A rule for moving the bishop (and the other chessmen) is essential to chess; a rule for which hand the bishop is to be moved with is not. How do I know what is pointless? Which hand the bishop is moved with does not affect the outcome of the game, and in chess the outcome of the game is the point.

But if a game is played "just for fun" without keeping score, as table tennis may be, is it then not a game?

Chess with Bishop's Option: player may move his bishop through squares occupied by his own pawns -- but he must sacrifice his pawns to do this, as if he were a feudal lord riding over his serfs in battle. (Other imaginary options.)

[BACK]

Note 7a:

Analytic judgments are those in which the predicate is contained, at least implicitly, in the concept of the subject. They are said to be "explicative judgments" [Kant, Critique of Pure Reason B, 11; A, 7] because the predicate does not add to the concept of the subject anything which is not already contained in it ... [The] truth [of analytic judgments or propositions] depends on the law of contradiction [because we] cannot deny [an analytic] proposition without involving ourselves in logical contradiction. Kant cites as an example "all bodies are extended" [because] the idea of extension is contained in the idea of body. [As an example of a judgment that is not analytic, Kant cites "all bodies are heavy" because] the idea of weight or heaviness is not contained in the concept of body as such. (Copleston, A History of Philosophy, Volume VI, xi, 3)

How does Kant know that "all bodies are extended", because according to Euclid a geometric point is a body without extension? Is the judgment "all extension is bodily" analytic, because Descartes said "there can be no extension which is extension of nothing", and yet Pascal demonstrated the existence of vacuums, which are extensions of nothing? "How do you know?" That is the question with Kant's concept 'analytic proposition'. [BACK]

Note 7b: When Plato speaks of "the immortality of the soul", is he talking nonsense if the word 'soul' is not a name of a thing (an "abstract object")? Would Wittgenstein be obligated to say that Plato is? If the word 'soul' is not the name of a thing, then its meaning will be its use in the language, not "the thing the word names". (Is the soul's immortality a grammatical question, a question of assigning a meaning to nebulous language?)

The accusation of materialism

Is a materialist world-picture at the root of Wittgenstein's thinking about language? And if reality does not consist only of what is perceptible to the senses, does it follow nevertheless that language can be used to talk about -- assign names and speculate about -- what is imperceptible?

Why Wittgenstein's lifetime aversion to metaphysics -- why do both his early and later accounts of language meaning, although opposites, claim that metaphysical speculation is nonsense? (If Wittgenstein's world-view was pantheistic (materialist pantheism), would that affect his views about language?)

An underlying materialism, or a down to earth ("facts in plain view") account of language meaning? What right has Wittgenstein to go no farther than the facts in plain view? The right of someone who wants to make the distinction between sense and nonsense objective. And a logic of language based on what is hidden "on the other side of the sky" (Plato's Forms and Frege's "geometric heaven") or on what is hidden in the mind cannot do this.

It is there -- like our life. (OC § 559)

Not, I would say, as if that were necessarily all there is, only that it is all we know there is -- the emphasis is always on proof, verification, the limits of knowledge (the shoreline and the vastness we suppose lies beyond it).

Isn't it curious that, although I know I have not long to live, I never find myself thinking about a "future life". All my interest is still on this life and the writing I am still able to do. (Recollections p. 169)

The phrase 'future life' may be meant ironically or not. Plato has Socrates, shortly before he is to die, discuss the nature and final disposition of the soul in the Phaedo (as he somewhat does also at the end of the Apology), Plato's "house of cards" that Wittgenstein claimed to be knocking down ("destroying") (PI § 118). To be focused when death overtakes one with "the writing I am still able to do" is not the same as to be focused "on this life" -- as if there were nothing beyond that to think about in philosophy.

It has puzzled me why Socrates is regarded as a great philosopher. (Recollections p. 115)

Plato might have wondered why Wittgenstein is regarded as a philosopher at all. Is Plato's thinking in philosophy really not "all that is interesting, great and important" (PI § 118) rather than mere "houses of cards"? [BACK]

Note 8: the fine art historian Kenneth Clark (1903-1983) wrote:

One of the few classical canons of proportion of which we can be certain is that which, in a female nude, took the same unit of measurement for the distance between the breasts, the distance from the lower breast to the naval, and again from the naval to the division of the legs. This scheme we shall find carefully maintained in all figures of the classical epoch ... (The Nude: a study in ideal form (1956), i)

Ethics and Aesthetics contrasted

Ethics and aesthetics are different in this respect: in ethics we can give a list of rules, and if a person follows those rules, we say that the person is, if the rule (definition) is that a good person is one who does good, a good person. But if we do the same in aesthetics, if we give a set of rules to someone (such as the Greek rule for modeling the female nude), even if the person follows those rules, the person will not necessarily produce a worthwhile work of art. The outcome of art is not knowable in advance. (The TLP says that "ethics and aesthetics are the same" [6.421], but they are not the same in this respect.)

Again, although in both ethics and aesthetics we may make judgments of worth ("value"), in ethics our judgments are applicable before the fact (before the deed is done), whereas in aesthetics our judgments are only applicable after the fact (of a work's creation).

Using the word 'value' to characterize both ethics (which, according to Wittgenstein, concerns absolute ends which cannot be disputed) and aesthetics does not make their relationship clearer, except that maybe in Wittgenstein's view there would be no disputing either "absolute ends" or "taste" (beauty). (Is aesthetics about values?)

Similar to art in this way is natural language: we can state formulas (rules of syntax) for the creation of English sentences, but following those rules is no guarantee that we won't create nonsense ("worthless" language, "sound without sense").

Wittgenstein's account of Aesthetics

Wittgenstein's remarks about aesthetics are different from his logic of language because they are barely focused on the use made of language and almost entirely on circumstances in our life in which aesthetic judgments are made, in many instances entirely without the use of words.

We are concentrating, not on the words 'good' or 'beautiful', which are entirely uncharacteristic, generally just subject and predicate ('This is beautiful'), but on the occasions on which they are said -- on the enormously complicated situation in which the aesthetic expression has a place, in which the expression itself has almost a negligible place. (LC p. 2)

I must say that I do not respond to music in words (maybe in tears) and when I put a painting (reproduction of art) on my wall, I don't say anything, certainly not 'This is beautiful'. The response to art, pictures, music, as to natural phenomena, sky, shore, beautiful women, is immediate and more or less intense. Of course a first impression may not be the same as a later judgment one makes, but is this "enormously complicated"? Subtler things may not have a place in every life. [BACK]

Note 9:

Strange that whole epochs cannot free themselves from the grips of certain concepts, 'beautiful' and 'beauty' e.g. (CV p. 79, remark from 1949)

But Schubert's aim in composing music was precisely to "attain beauty", which was the ideal he shared with his companions in art. Would the work they composed have been different had that not been their ideal? There is much in our life that is ugly and morally deformed, and art can portray that too.

The beautiful is not unequivocally the good

Dostoyevsky characterized the Incarnation as "beauty coming into the world". But it says in Isaiah [53] that the messiah ("the suffering servant") was not beautiful: "there was no beauty in him". What Dostoyevsky meant was goodness came into the world. But he always compared a "beautiful" -- i.e. good -- soul to a beautiful body, e.g. the Sistine Madonna in Dresden.

That is a different example of being in "the grips of" a concept, for about Dostoyevsky's simile it is possible to say that Romanticism undermines ethics by confusing beauty and goodness.

Of course Wittgenstein's remark might be directed back at him: how strange that certain epochs or individuals cannot free themselves from the grip of certain concepts, e.g. 'God', which was a concept Wittgenstein could not "free himself from the grips of" but instead could only speak of "concept blindness".

"Concept-blindness"

What must the man be called, who cannot understand the concept 'God', cannot see how a reasonable man may use this word seriously? Are we to say he suffers from some blindness? (RPP i § 213)

This discussion brings out that we are talking about "ways of life", ways of thought, about the role concepts play in our life, directing and expressing our interests (PI § 570). [BACK]

10. Meaning as a "Usage"

The relation between grammar and sense and nonsense is shown by this: that a sign -- a spoken sound, a 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' (sounds or marks with meaning) and 'nonsense' (sounds or marks without meaning).

To the question "What gives a sign meaning?" an answer Wittgenstein gave 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. (But was Wittgenstein's claim made 'in the stream of life"? Was it a "move in a known language game"? Or was it an example of "trying to grasp the essence of the thing" (PI § 116), i.e. of language meaning?)

And what of philosophy?

What then of philosophy, the critique of thought and view of our life from outside "the stream of life"? -- Or is Wittgenstein's later work "nonsense", as the TLP claims itself to be, meaningless language that conveys meaning? Wittgenstein's claim is both a statement of intention (of how he is choosing to look at language meaning) and a statement of fact. As a statement of fact whether it is true will depend on which examples we have in mind.

But if it is a statement of "what the meaning of language really is", then the "only in the stream of life" thesis, like the "only in the language game that is its original home" (PI § 116) thesis, appears arbitrary -- because there are many kinds of explanations of meaning. It would be a requirement, not a result of investigation (ibid. § 107).

As always, examples are the true masters to follow in philosophy: they are a principal method for testing philosophical theses -- when they are not selected to prove a point, purposely excluding anomalies. While Wittgenstein can point to the example of "private language", I believe I have presented examples, and more examples, of real (not merely illusory) philosophical problems and shown that their language is not nonsense.) [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 aspect of language.

But to give a true account of Wittgenstein's use (or definition) 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 .

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:

Lawyer: You testified earlier that on Thursday afternoon you saw Mr. Anselm walking in the park. But now you say that what you saw was Mr. Anselm standing behind the trees overlooking the sidewalk.

Witness: Yes, what I meant was that he was sort of walking.

Lawyer: I suggest that your previous testimony was false, and that what you now describe as Mr. Anselm's behavior is not what anyone calls 'walking' -- "sort of" or otherwise.

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, a game where you do what you like whenever you like (like Humpty Dumpy). But now, can we suppose that Caprice were the only game? (PI § 199)

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

Were all 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. Wittgenstein's 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 these 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. Language is based on consistency, regulations.

The Stoic "lekton"

The meaning (lekton) is what the Greek understands but the barbarians do not, although they hear the sound, when Greek is spoken. (Sextus Empiricus, Adv. Math. viii, 11-12)

The Greek 'understands' (the single-quotes here mean this is a definition) because he knows the rules of the game, as in "language game" -- in this case 'knows the rules' = 'plays the game correctly'.

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'.

"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 "way of life" -- i.e. we do not have here the "characteristic formation of a pattern" of our 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 indefinite -- i.e. can the word 'sorrow' be applied to just anything? A word whose grammar were that indefinite 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 small child's babbling is not language. Were it correct to utter the sign 'I am here' in any and all circumstances, the sign would be nonsense (OC § 10; PI §§ 117, 514).

But why must? The question is: isn't it correct to use 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. (Here 'used correctly' = '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 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 played according to rules (conventions) and words to tools used to do some work in our life and (maybe) thinking: these comparisons make the distinction between with meaning 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 best general explanation of the distinction is made 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, that general explanation is only for orientation; it is not a formula: 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 the soul is entombed in the body", this is not a serviceable distinction.

Unserviceable too is the TLP's definition of 'nonsense' which consigns most of our language to the rubbish bin despite that language's ability to convey meaning.

Another alternative to Wittgenstein's logic of language would not make the distinction between sense and nonsense 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 meaning 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 definition of 'meaning' that is not rule-based a logic of language 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 way. It is important to be aware of this, of this particular pair of eyeglasses. Wittgenstein's definition of 'meaning' is one definition of 'meaning', not the definition of 'meaning'. Others meanings of 'meaning' exist.

To whom does the truth belong?

Who decides whether a particular example of language is nonsense or not? We don't decide what is true or false by taking a vote -- that is not our concept 'truth' -- (regardless of the practice of law courts). For example, regardless of what the teaching establishment's textbooks say, the word 'point' is not the name of an object of any kind (It is not "the name of a geometric object of no extension", but "a unique address in the plane"). That is what reason can demonstrate, not what tradition and the majority claim.

But if the reasoning of the individual decides these questions, then what makes the distinction between sense and nonsense objective?

Well, but we are not here, as we were with the grammar of the word 'beautiful', i.e. without rules to guide us. Whoever has learned to think rationally can decide these questions (where the evidence enables a decision) -- and what you cannot say is that there is an alternative rationality. (Everything rational has the same foundation, namely the principle of contradiction in meaning and what is consistent with it.)

There is reason to say that knowledge belongs to the community, namely because the standards (rules) of evidence belong to the community -- but in the Western philosophical way of life, i.e. our way of life, knowledge belongs, rather, to the rational part of the community. We don't call just anything a distinction, or knowledge, or verification (regardless of what the "populace" may say).

Knowledge belongs to the rational part of the community: that is what makes it objective. And that is why any rational individual can judge the truth for himself and defend his judgment by using rational rules of evidence against refutation.

That is our way of life, but it is not the only way of life on earth. It is not the way of life of primitive man (nature spirits, taboos, fetches, magical causality) or of superstitious man (dreams, oracles, omens). Although there were fully rational Greeks, the Western community only became fully rational during the Enlightenment; before that it burned witches.

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 particular 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)

Endnotes Chapter 10

Note 10a: While I accept that "use in the language" is often the most useful definition of 'meaning' for philosophy -- e.g. it allows us to break with the mistaken notion that all words are names -- I do not accept Wittgenstein's claim that use in the language must be practical use ("only in the stream of life"). That claim makes what has always been called philosophy impossible. However, not only is philosophy possible, but there is nothing in our life that is more important than philosophy. There are theses and answerless questions that are not mere conceptual mirages. Language is not solely the possession of primitive man. [BACK]

Next chapter:

11. 'Nonsense' and Contradiction

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