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Wittgenstein's Logic of Language

Chapters 1-6

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

Outline of this page ...

1. Wittgenstein's Use of the Words 'Logic' and 'Grammar'

Wittgenstein noted that using language is like playing a game. What characterizes a game is its rules. In his philosophy the study of rules is called 'logic' -- and the study of the rules of sense and nonsense in language is called 'grammar'.

This new use of the word 'grammar' was perplexing at first and so G.E. Moore asked Wittgenstein about it:

He said that "any explanation of the use of language" was 'grammar', but that if I explained the meaning of 'flows' by pointing at a river "we wouldn't naturally call this a 'rule of grammar'" ... that we would be using his "jargon". (cf. PP ii, p. 276)

Everything descriptive of a "language game" [a use of language comparable to playing a game according to rules] is part of logic. (OC § 56)

[In the second remark, 'logic' = 'grammar', but only because logic = grammar: the equation is the result of Wittgenstein's later investigations, not their presumption. The historical meaning of the word 'logic', the Greek maid-of-all-work word logos.]


We want to distinguish between language with meaning and language without meaning (we don't want our philosophy to be mere sound without sense). We may call this distinction the logic of language.

In Wittgenstein's philosophy, logic = grammar = use of words in a "language game". Understanding this revision of the concept 'grammar' is the foundation to understanding Wittgenstein's later work in logic-philosophy.


Parts of speech are both syntactic and semantic

Wittgenstein's extension of the concept 'grammar' to include whatever is needed to describe the meaning of language is not eccentric, if we recall that which part-of-speech a word is classified as belongs to that word's grammar. For instance, the part-of-speech 'noun' is defined as 'the name of a person, place, or thing'. So that, if we classify any particular word as a noun, we have already gone some way towards giving that word's meaning.

Elementary schoolbook grammar does, then, already have a semantic element. But Wittgenstein called into question schoolbook definitions, e.g. to ask whether by calling all nouns names -- whether of objects, emotions, numbers, ideas, and other so-called things -- we do not cover up deep differences in the ways we use words. And so, to ask whether our schoolbook grammar -- and the matter-of-course inferences we draw from it -- does not lead us to misunderstand the logic (i.e. the "grammar", in Wittgenstein's sense) of our language.

False analogies between forms of expression

"If the word 'mind' is a noun, then the word 'mind' must be the name of some thing. As the word 'book' is the name of some thing. And so if a book is on the table, then where is the mind? And if a book is made of paper, then what is the mind made of? And if a book is read with the eyes, then is thinking done with the mind?" Wittgenstein wrote, don't smile at these examples as at something foolish (PI § 351) [Note 1a] because false analogies like these create conceptual illusions and thus are often the stuff that philosophy is made on.

Our naive, far too simple picture of language meaning blithely absorbs the suggestions of syntax, allowing language forms to mislead us when we philosophize. In logical grammar not all syntactic nouns are names. The word 'mind' is one such noun.

'Where does the flame of a candle go to when it's blown out?' 'Where does the light go to?' ... We may say that we are led into puzzlement by an analogy which irresistibly drags us on. (BB § 56, p. 108)

Our investigation is ... a grammatical one. Such an investigation sheds light on our problem by clearing misunderstandings away. Misunderstandings concerning the use of words, caused, among other things, by certain analogies between the forms of expression in different regions of language. (PI § 90)

Wittgenstein called attention to parts of speech ("regions of language") that are not dreamt of in elementary schoolbook grammar. The words 'book' and 'mind' are not the same part of speech in Wittgenstein's logic.

We want to establish an order in our knowledge of the use of language ... To this end we shall constantly be giving prominence to distinctions which our ordinary forms of language easily make us overlook. (cf. ibid. § 108)

Thus Wittgenstein might have said about our schoolbook, that its grammar

seems to me to be always wanting to say that things which look different are really the same. Whereas my interest is in showing that things that look the same are really different. (cf. Recollections p. 157)


Wittgenstein's two meanings of 'grammar'

From this point on, I will use the word 'grammar' in Wittgenstein's way -- to include whatever is needed to give an account of the meaning of language (OC § 56). By 'grammar' I shall mean (1) the rules for using a sign, and also (2) the description we give of those rules. [Note 1b]

2. The False Grammatical Account

How may we account for the persistence of schoolbook grammar? Is it that as children we readily believe what all evidence suggests is not the case -- i.e. that the words 'book', 'idea', 'mind' and 'elf' are all names of objects? For as children we are never given ideas or minds or elves to touch or see or taste or hear or smell. Here is one possibility:

Where our language suggests a body and there is none: there, we would like to say, is a spirit. (PI § 36)

Take away from us the words 'idea', 'mind' and 'elf', and we are left with nothing to cling to; but give us those words and we seem able to grab hold of ghosts. (At the same time, about the meaning of "abstract terms", about the nature of "abstract objects", we feel a deep uncertainty.)

Instinct more than second nature

Our belief in this grammatical myth comes so naturally to us that it can be compared to instinct (or superstition). A piece of crumpled paper, forgotten to one side, suddenly begins to unfold, and we immediately sense a soul as the source of the movement.

It may be that way. But consider further. Consider that the first stories children are told are fairy tales. We are taught to imagine souls in the objects which we do see, e.g. brooms and coffeepots and stuffed animals; and we are taught to imagine objects we never see, e.g. ghosts -- but also long dead historical figures and far away or fanciful countries.

But also, consider this: that each of us has thoughts and feelings, or as we say "consciousness" -- i.e. our own invisible but real self (soul or mind) to which it seems we sometimes refer when we speak. (cf. PI § 358)

Grammatical myths and Natural history

We are thus predisposed by instinct, education, and apparently by experience to suppose that if we are talking, then we are talking about some object -- if not a visible one, then an invisible one. This is the persistent view or picture: the essence of speech is stringing together names of objects.

A statement of fact is a picture of the world. A picture shows the relationships between objects: it says: This is how things stand. To the objects in the world correspond the words of the statement. The objects are the words' meanings, and the objects in relationship to one another is the meaning of the statement. (cf. Tractatus Logico-Philosophicus 2.1-2.141, 4.5)

That was Wittgenstein's earliest thought about the logic of language, and his later logic is a correction of "grave mistakes in what i wrote in that first book," he says in the Preface to his Philosophical Investigations, which he begins with a summary of Augustine's picture of language --

"Words are names, and the meaning of a name is the thing the name stands for"

... the individual words in language name objects -- sentences are combinations of such names. -- In this picture of language we find the roots of the following idea: Every word has a meaning [which] is the object for which the word stands. (PI § 1)

It was Wittgenstein's view that this picture, which we imagine to be a picture of the facts of our language use, is not a true picture of the way we use the words of our language.

I say that this picture ... stands in the way of our seeing the use of the word as it is. (ibid. § 305)

If we are to see the logic of our language aright, we must break with the picture that: "all words are names and the meaning of a name is the thing the name stands for -- whether that thing is an object or a phenomenon, visible or invisible, tangible or intangibly abstract)." Otherwise we shall be like the child who, supposing that all pegs are round, tries to force cubes, stars and pyramids through round holes, a Procrustean act that cannot be done without distorting the pegs that are not round (if indeed any pegs are round, i.e. have as their meaning an object they name).

Studying the grammar of the expression 'explanation of meaning' will teach you something about the grammar of the word 'meaning' and will cure you of the temptation to look about you for some object which you might call the meaning. (BB p. 1)

How do we teach someone else the meaning of a word, e.g. how do we teach a child a new concept? Because that teaching is an explanation of meaning, and only some explanations are given by pointing to the bearer of a name (and those are of the least interest to philosophy).


It is not one thing, but a convergence of many things ("analogies between different regions of language" among them), which may account for the persistence of schoolbook grammar. But speculation like that is not logic; only linguistic facts are (Z § 447). Wittgenstein, like Socrates, wanted in philosophy "to say no more than we know" (BB p. 45), which is what 'speculation' contrasts with.

The meaning of language in philosophical logic is not something hidden

We must do away with all explanation [metaphysical speculation is imagination added to the facts], and description [of the facts in plain view] alone must take its place. (PI § 109)

And what is hidden from view -- as e.g. a reality speculated to underlie the facts in plain view, invented to explain perplexing facts about concept-formation (as e.g. the Theory of Abstraction or Plato's theory of Forms) -- is of no interest [Note 1c] to Wittgenstein's logic of language. That logic wants only a clear view of what is "open to the public" about language, its civil status (ibid. § 125) -- i.e. the conceived facts that by common consent are in plain view.

What is public -- in contrast to what is hidden or thought to be essentially private -- is objective (verifiable by anyone), and this allows Wittgenstein's "logic of language" to distinguish between sense (i.e. language with meaning) and nonsense (meaningless babble of words); the alternative is "whatever seems to have meaning", which is not an objective distinction.

What Wittgenstein did was to suggest different ways of looking at nouns -- e.g. that where there are no objects to point to neither are their names. This allowed him to give a different account of the grammar of nouns from "Every noun is a name".

The primaeval chaos (Ghosts)

We begin our study of logic with this picture of natural language: (1) that we regard all nouns as names, and (2) that where there is no object for a noun to name, there we feel an insensible something bears the name (PI § 36). Thus whoever defined 'noun' as the all-inclusive "A noun is the name of a person, place, or thing" had the same misleading picture of our language's semantic logic that we have.


A Logic of Language versus a Theory of Meaning (Plato and meaning)

It is nevertheless possible to give an account of our language in which all nouns are names of things. Philosophers have done this [Note 1d], and where there were no perceptible things to bear the names, they posited spirits, as does Plato with his "Ideas" or "Forms".

"Behind the appearances"

Philosophers invented metaphysical theories about the reality they presumed to be hidden behind our language (These theories are what Isaac Newton called "hypotheses" and Wittgenstein "explanations"), a reality that can explain concept-formation (PI II, xii, p. 230). They weren't happy to describe no more than the facts of our language in plain view, because they did not find in those facts what they thought needs to be there if our discourse (and indeed philosophy itself) is not to be "mere sound without sense" (Parmenides 135b-c).

Origin of the Theory of Forms (Archetypes)

Plato's theory of Forms seems to have been invented to solve the perplexing problem of common names, for it seemed to Plato that the meaning of a common name must be the common nature it names, that there must be common natures, even if they are not visible, Plato thought, if sense is to be distinguished from nonsense and there is to be knowledge. And so Wittgenstein and Plato are trying to respond to the same question, but in very different ways.

"In plain view"

Wittgenstein looked -- and wanted to look (hypotheses non fingo) -- no further than the facts in public view. And based on those facts, and on his own way of looking at things (i.e. Wittgenstein's selected meaning of the word 'meaning'), he saw that the meaning of language cannot lie in invisible or private things ("thought") that cannot be called to account [Note 1e] -- but only in the public use of language.

And that is a logic of our language, because what is public is objective (just as the rules of a game are public, verifiable). And that is how Wittgenstein's way of looking at language makes an objective distinction between sense and nonsense in the language we use in philosophy.


Wittgenstein would not have had the right to call his later work "the logic of our language", because what Wittgenstein does, according to my view of his work, is to look at language in a different way from the way other philosophers have done, from the way Socrates' logic of language (as distinct from Plato's speculations about language meaning) does, for example.

Refutation or Rejection

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

Or what is the alternative to my view -- that Wittgenstein discovered the "true" logic of our language -- by redefining words and inventing similes (making comparisons)? That he refuted the Greek account? But how does one refute Plato's picture of language, namely that "The meaning of a common name must be the common nature it names regardless of whether that nature is perceptible to the senses or not"? One cannot refute that picture -- because it is founded on a metaphysical principle that can neither be proved nor disproved, namely that there is an imperceptible reality.

All Wittgenstein could do was say: Look at language-meaning my way! because that way makes language-meaning public, which is in accord with Socrates' standard for philosophy, namely that if we cannot tell others what we know, then we don't know what we are talking about. [Note 1f]

"Grammatical fictions"

That we do in fact use common names despite their not naming common natures (as Wittgenstein shows by describing the grammar of the word 'game') is enough for Wittgenstein:

The point is that this is how we play the game. (I mean the language game with the word 'game'). (PI § 71)

He does not seek to explain that phenomenon (i.e. to speculate about concept-formation).

Nonetheless, if our language is looked at the way Wittgenstein's logic of language does -- i.e. by comparing the facts in plain view about our language to games played according to conventions (rules) -- then it is not nonsense to talk about "the false grammatical account". Because then --

If I do speak of a fiction ... it is of a grammatical fiction. (ibid. § 307; cf. II, xi, p. 200b)

As for example, if Wittgenstein says that the word 'mind' is the name if an object of any kind, he is not saying what the mind really is, but that the proposition 'The word 'mind' is the name of an invisible object' is an example of a grammatical fiction, a combination of words allowed by syntax, but a false description of the way the word 'mind' is used in our language. (And to say that is to point out a fact about our language, not about the world independent of our language, despite our maybe wanting to say otherwise.)

If I am happy to go no further the facts in plain sight, if I am willing to accept Wittgenstein's logic of language, then it makes sense for me to talk about "grammatical fictions". But on the other hand, if there is a metaphysical use of language (ibid. § 116) in addition to our ordinary one, then a description of the use of the word 'mind' or 'soul' (psyche) may be very different in metaphysics, and I may not be able to speak of grammatical fictions.

3. The Distinction between a Sign and the Meaning of a Sign

The relation between rules of grammar and sense and nonsense (BB p. 65), is shown by this: that a sign -- a sound, an ink mark -- as such is without meaning. What gives the sign meaning?

Logic has a simple, special notation. Logic distinguishes between a sign (By the word 'sign' Wittgenstein meant: spoken sounds, marks on paper, gestures, figures in the sand, the purely physical aspect of language -- i.e. the words, phrases, sentences, and so on, of language), and the sign's meaning.

In contrast to when we use a sign (as we use a tool) to do its work, when I want to refer to the sign as a sign, I place single quotation marks [speech marks] around it (cf. PI § 37). For example: the sign 'flows' has five letters, is a word of the English language, sometimes can be defined by pointing at a river. This contrasts with e.g. "The River Ota flows into the Inland Sea" where the sign 'flows' is used in a geography textbook to state a fact about the River Ota. Likewise 'What is the meaning of life?' and 'What is the meaning of 'life'?' are different questions.

In some countries single quotation marks are used to mark quotes (and also e.g. to replace the word 'so-called' [scare quotes]). British writers -- including Wittgenstein's translators -- often mark signs with double quotation marks, e.g. the sign "flows". (You have to look and see, and think about it, however.)

On this site I always use single quotes when I want to refer to a sign as such; I even modify quotations from books to make them follow my practice here. I do this for the sake of emphasis, to make a sharp contrast to the everyday practice where I live (where double quotes are used). -- Because the distinction between a sign and its meaning is essential to Wittgenstein's logic of language (as it was to Bertrand Russell's).

We could, of course, make any convention we liked. We might e.g. enclose the sign in asterisks, e.g. The word *flows* rhymes with *glows*. The important thing is to clearly mark the distinction, not how the distinction is marked.

If you are in doubt about whether to use single quotes, remember that you should be able to replace the single quotes with an expression like 'the ink marks' or 'the sound', e.g. you should be able to replace '*Flows* is an English verb' with 'The pattern-of-ink *flows* is an English verb'.

'November' is longer than 'July', but July is longer than November.

These examples are, of course, not the point of this notation. The point is to force us, when we are thinking about philosophical problems, to ask whether we are using language to talk about something other than language itself. Am I talking about the River Ota -- or am I only giving a definition of the word 'flows'? This is the essential question to ask especially in the context of philosophy ... although in many instances using this notation, rather than making anything clearer, will be just one more way of confusing ourselves.

By the word 'concept' I always mean 'rules for using a sign', not a nebulous "abstract" ghost conjured up by ink marks or sounds. (And so by 'concept' I don't mean the TLP's "symbols", for that notion suggests that the meaning of a word is an imperceptible aura that a word carries about with it regardless of where it goes.)


The Contrast Between an Object and the Rules Governing its Use

We are talking about the spatial and temporal phenomenon of language ["words and sentences in a quite common or garden-variety sense"], not about some non-spatial, non-temporal phantasm. But we talk about it as we do about the pieces in chess when we are stating the rules of the game, not describing their physical properties.

The question 'What is a word really?' is analogous to 'What is a piece in chess?' (PI § 108)

The "physical property" of chess is the wood (e.g.) of its pieces; that is the "spatial and temporal phenomenon" of chess. The "physical property" of language is the sounds or ink marks of its signs; that is the "spatial and temporal phenomenon" of language. In either case it is the public rules governing the use of this "physical property" (whether it is wood or ink or sounds) that logic is the study of. And thus there are no "real definitions" in logic: logic defines words, not things (objects or phenomena).

That is as close as Wittgenstein comes to stating the "metaphysical presuppositions" of his later logic of language (in contrast to his theories about the origins of philosophy, which in my view falsely claim an ALL from a SOME). What is most noteworthy is that this statement, this point of view (way of looking at language), is not in the least metaphysical -- i.e. speculative about the reality behind "the appearances".

The subject of Wittgenstein's logic of language is no more hidden from public view than the subject of a guide to home bread-baking is --

Mix together the water, yeast and salt, and add just enough flour so that the mixture can be kneaded with your hands.

There is no speculation here about the mechanics of the dough's elasticity ("gluten strands"). Wittgenstein's logic of language is like that. [Note 1g]

4. Wittgenstein's Meaning of 'Meaning'

A sign -- a sound, an ink mark -- as such is without meaning. What gives the sign meaning?

Wittgenstein began the Blue Book with the question "What is the meaning of a word?" (BB p. 65) And we must be clear from the very first which meaning of the word 'meaning' is the concern of Wittgenstein's logic of language. There are many meanings of 'meaning', many uses for that word in the language. Wittgenstein chose one, one that allows us to make an objective distinction between sense and nonsense in philosophy.

[According to G.E. Moore's notes, Wittgenstein said] that the sense of 'meaning' of which he held these things to be true, and which was the only sense in which he intended to use the word, was only one of those in which we commonly use it ... (PP i, p. 257)

Wittgenstein's logic is a selected definition of meaning, one that is best explained by comparing language use to playing a game: if the game is played according to the rules, the moves in the game have meaning; similarly, if language is used according to its rules of "grammar", then the language has meaning.

Logic is about only the conventional meaning of signs -- i.e. the meaning that is given when the rules (conventions most often co-incidental) for using signs are given. This can be called a sign's "grammatical sense" (Cf. PP iii, p. 312); 'sense' = 'meaning'.

Explanations of meaning

A word's grammatical meaning is given, in an especially clear way, when explanations of meaning are given in the course of everyday life. E.g. the case of 'flows' above: pointing to a river in answer to the question "What do you mean by 'flows'?"

Let's only bother about what's called the explanation of meaning, and let's not bother about meaning in any other sense.

An explanation of meaning is not an empirical proposition ... but a rule, a convention. (PG i § 32, p. 68-69. [Wittgenstein's old and new ways of thinking contrasted])

"The meaning of a word is what is explained by the explanation of the meaning." -- I.e. if you want to understand the use of the word 'meaning', look for what are called 'explanations of meaning'. (PI § 560)

Verbal and ostensive explanations of meaning

Grammar describes the use of words in the language. So it has somewhat the same relation to the language as the description of a game, the rules of a game, have to the game.

Meaning, in our sense, is embodied in the explanation of meaning. By 'explanation of the meaning of a sign' we mean rules for use but above all definitions. The distinction between verbal definitions and ostensive definitions gives a rough division of these types of explanation. (PG i §§ 23-24, p. 60)

To explain the meaning of a sign = to give an account of the sign's grammar. It is also to give an account of what you know.

Note 1a: And if the umbrella is in the hallway, then where is the concept umbrella? The grammar of the word 'object' as we normally use that word: an object occupies space and has location and is in some way perceptible. But then what is an "abstract object" like the concept umbrella when it's at home? But compare: by the word 'concept' or 'essence' we mean: 'the rules for using a word in the language'. In contrast, what would we mean if we said that "a concept is the name of an abstract object" or "a concept is an abstract object"? A picture so nebulous as to be no picture at all.

Wittgenstein said that a serious philosophical work could be written entirely of jokes (Malcolm, Memoir p. 27-28; see e.g. PI § 250), that is, of grammatical jokes (ibid. § 111), as e.g. the questions 'How many dimensions does a point have?' and 'Where is the mind located?' and 'What color is the number 3?'

[Wittgenstein held several theories about the origins of philosophy, one of which was the analogy theory of the source of philosophical perplexity (i.e. conceptual muddles). And misleading "pictures" are formed that way, as e.g. that it follows from "All words are names of things" that just as visible things bear names, there are also invisible things that bear names.]

Lewis Carroll's examples of nonsense are examples of grammatical jokes. "No, no!" said the Red Queen. "Sentence first -- verdict afterwards" (Alice in Wonderland xii), but of course the verdict determines whether there will be a sentence or not. The rules of syntax nonetheless allow this nonsense. Little Bo-Peep can look for her lost sheep, but she cannot look for her lost temper (Through the Looking-Glass ix), although the rules of syntax would allow her to. [BACK]

Note 1b:

In Wittgenstein's jargon, grammar DEF.= (1) rules for using language, and (2) any description of the use of language according to rules.

The meaning of a word is to be defined by the rules for its use ... 'How is the word used?' and 'What is the grammar of the word?' I shall take as being the same question. (Wittgenstein's Lectures, Cambridge 1932-35, ed. Ambrose, i, 2)

That remark is dated 1932-1933 by the editor. The explanation of meaning of the word 'grammar' Wittgenstein gave Moore dates from 1932-1933 as well. [BACK]

Note 1c: It is "possible to be interested in a phenomenon in various ways" (PI § 108), but this way was Wittgenstein's. Why does Wittgenstein take the facts in plain view for granted? for do not Kant and maybe Goethe criticize doing that? The facts are the conceived facts: what are "the facts in plain view" is like knowledge: it belongs to the community rather than to the individual.

In Wittgenstein's logic of language the meaning of a word = a public rule for using that word. Were 'meaning' not defined that way, it would not be what we call 'objective' in contrast to 'subjective' (e.g. W.E. Johnson's assertion "If I say that a sentence has meaning for me, no one has the right to say it is senseless" does not make an objective distinction between sense and nonsense). This is the meaning of the word 'meaning' Wittgenstein selected out of the many in our language for his work in philosophy.

Trying to define words by examining one's state of mind

[Philosophers think] that the nature of such things as hoping and fearing, or intending, meaning and understanding [are to] be discovered through introspection ... Wittgenstein [changes] the whole approach by saying: what these words mean shows itself in the way they are used -- the nature of understanding reveals itself in grammar ... (F. Waismann, "How I See Philosophy")

Introspection can never lead to a definition. It can only lead to a psychological statement about the introspector. (RPP i § 212; cf. PI § 316)

The apparent experience that our body is a machine which is (more or less) ruled over by a mind has led philosophers to ask "if the body and mind or the mind alone is the essence of man", but before any metaphysical question is the question of grammar (Z § 458), of whether the part of speech of the word 'mind' is name-of-object. [BACK]

Note 1d: That "All nouns are names (if not of visible then of invisible things)" was a requirement philosophers imposed on their investigations; it was not the result of investigation (PI § 107). It was a metaphysical presumption, as was requiring common quality or essential definitions of words. [BACK]

Note 1e: Remember the Socratic standard: If we know anything we can explain what we know to other people, an explanation that can face the test of refutation in discussion. (Xenophon, Memorabilia iv, 6, 1) That is "discourse of reason". [BACK]

Facts that can explain 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)

Plato answers that indeed we ought. Plato's metaphysics of meaning is contrary to Wittgenstein's, and Wittgenstein's criticism of it -- "The idea that ... one had to find the common element ... has not only led to no result, but also made the philosopher dismiss as irrelevant the concrete cases, which alone could have helped him to understand ..." our language's logic, i.e. the actual rules of our language (BB p. 19-20) -- would be dismissed by Plato as irrelevant.

Because concrete cases do not solve Plato's puzzle of the meaning of common names. Rather than solve Plato's puzzle, Wittgenstein rejects it (PI § 47) by pointing out that most common names do not have "meanings" -- i.e. do not in fact name common natures. Not, that is, if we describe our language as we normally use it (ibid. § 246).

But Plato will not accept that as a refutation, because Wittgenstein describes only the "appearances" (i.e. what is perceptible), not, as Plato believes, the reality behind those appearances (That is the meaning of 'meaning' that interests Plato, the metaphysical or "really real" meaning). [BACK]

Note 1f: Of course the facts in plain view do not answer philosophy's eternal questions, but it does not follow that there must be a different way of looking at language that will make those questions answerable, no more than it follows from Wittgenstein's later way of looking at language that those questions are absolute nonsense (i.e. mere undefined combinations of words), nor that man has no "need for metaphysics" (cf. Recollections p. 105). [BACK]

Theories not comparisons: Metaphysics vs. Logic

Note 1g: But when Wittgenstein says things like that the essence of metaphysics is that "the difference between factual and conceptual investigations is not clear to it" (RPP i § 949) and that philosophy's essence is to battle against "bewitchment by means of language" (PI § 109), and that the depth of philosophy is a "grammatical joke" (ibid. § 111), his claims are metaphysical. Because here Wittgenstein does not say that "essence belongs to grammar" (ibid. § 371) -- i.e. he is not explaining the meaning of the words 'philosophy' and 'metaphysics', but saying "what philosophy really is".

Now, that is not a comparison, nor is it an assigned meaning, nor a project in philosophy (It does not say what Wittgenstein wants philosophy to be rather than what it is). It is instead a generalized statement of fact -- i.e. an hypothesis. And therefore we can ask: Is the essence of philosophy really only conceptual muddles, a failure to understand the logic of our language? Because the generality of that claim is not justified by the very few examples Wittgenstein gives.

And if philosophy does suffer from conceptual confusion, does seeing that make its problems disappear, or does it only revise our understanding of them? Socratic ethics, mankind's eternal questions, and Plato's perplexity over the meaning of common names, as well as Plato's grammatical method in ethics -- are all these nothing more than self-mystification by means of language, and philosophy a "grammatical joke"? [BACK]

5. Types of Definition

Wittgenstein's logic of language gives methods for defining any sign [Note 2] -- by describing its use in the language ...

Wittgenstein and use

The explanation of the meaning explains the use of the word. The use of a word in the language is its meaning. (PG i § 23, p. 59, 60)

For a large class of cases ... the meaning of a word is its use in the language. (PI § 43. Another large class is names.)

What did Wittgenstein mean by the word 'use'? He used that word to make a simile: we use a sign like we use a tool, e.g. a saw to saw wood, a hammer to drive a nail, a ruler to measure, the word 'hello' to greet a friend, the sign 'Help!' to call for help, or the word 'meaning' to ask for an explanation of meaning. (ibid. §§ 11, 23; BB p. 67)

Look at the [sign] as an instrument, and at its sense as its employment. (PI § 421)

Words are deeds. (CV p. 46, a remark from about 1945)

Another simile Wittgenstein made was that: to ask for the meaning of a word is like asking for the rules for using -- e.g. moving -- a game-piece in chess.

A meaning of a word is a type of employment of it. Because it is this we learn when the word becomes part of our language.

This is where there is a connection between the concepts 'rule' and 'meaning'. (cf. OC § 61-2)

Isn't the question 'Have these words a meaning?' similar to 'Is that a tool?' ... (ibid. § 351)

To ask for the meaning of a sign (or tool or game-piece) is to ask what work the sign is used to do. Greeting, calling, asking, stating a fact are examples of this work.

A "grammatical account" (description of use in the language)

A description of the rules that are followed to use a sign is called the sign's 'grammar'. But if I am to make what Wittgenstein means by the sign 'grammar of a sign' clear -- and not much is made clear in logic except this way -- I have to give examples. This is because acquiring a concept (PI § 208), learning a word's meaning, is rarely about "grasping an essence", as most words don't have essential meanings (Most common names do not designate a defining quality that is common to all). This is why examples must be used in explanations of meaning (It is not for want of a better way -- as if there really were essences but we were unable to say what they are -- it is, rather, determined by the very nature of the concepts of our natural language).


Three types of definition

Grammatical rules are definitions (or parts of definitions). These fall into three broad categories.

Verbal versus Real Definitions

First, there are sign-for-sign substitution rules ("verbal definitions"): these take us from a sign that we do not know how to use to a sign that we have already learned how to use, just as synonyms do. Some misunderstandings "can be removed by substituting [or, replacing] one form of expression for another" (PI § 90).

Explanation of the meaning of the sign 'DEF.='

If I use two signs with one and the same meaning, I express this by putting between them the sign ' = ' (TLP 4.241, tr. Ogden). So ' a = b ' means that the sign ' b ' can be substituted for the sign ' a '. A definition is a rule dealing with signs. (ibid. tr. Pears, McGuinness) [Note 2a]

An Example of Real Definition of a Natural Phenomenon

Substitution rules are often found in dictionaries -- but only where dictionaries state no more than rules for using language signs. This is not always the case.

For example, (1) "Thunder is a sound that follows a flash of lightening" is indeed a rule for applying the word 'thunder', but (2) "Thunder is a sound caused by the sudden heating and expansion of air by an electrical discharge" is an hypothesis and does not belong to the grammar of the word 'thunder' -- it is not a definition of a word, but instead a "definition of a thing".

The distinction made by Aristotle

The above definition of 'thunder' and "definition of thunder" are from Webster's New World Dictionary (2nd edition). The distinction between these two types of definitions is made by Aristotle. The first type is often called a "verbal definition", the second a "real definition" --

one kind of definition will be a statement of the meaning of the name, or of an equivalent nominal formula [Anal. Post. 93b] ... a set of words signifying precisely what [the] name signifies [92b; -- e.g.:] thunder can be defined as noise in the clouds ... [94a]

Another kind of definition is a formula exhibiting the cause of a thing's existence. [A "definition is an expression indicating the essence of a thing" (Top. 154a; tr. Pickard-Cambridge), and "to know its essential nature is ... the same as to know the cause of a thing's existence" (Anal. Post. 93a)] [e.g.] the statement of what the nature of thunder is will be The noise of fire being quenched in the clouds. [Anal. Post. 93b-94a; tr. Mure]

A Verbal Definition is not a Theory (Grammar versus hypotheses)

Aristotle's "noise in the clouds", like World's "sound that follows a flash of lightening", is a possible definition of the word 'thunder'. It is a substitution rule for the word 'thunder', not an hypothesis about thunder. So that, Anaximander could speculate that thunder is the noise of air bursting out of clouds (cf. Aristophanes, The Clouds 394), or Anaxagoras that thunder is the noise of clouds colliding, or indeed Homer could speak of "Zeus, the thunderer" -- without thereby uttering something that was meaningless to Aristotle or to us. For although having different "real definitions" of (hypotheses about) thunder, we have the same "verbal definition" in common: the word 'thunder' means the same as the words 'noise in the clouds'. One sign, one grammar (not one sign, five grammars), but five different hypotheses about the phenomenon called 'thunder'.

In contrast, the above dictionary does for the expression 'will-o'-the-wisp' make the distinction between: (1) a definition of words and (2) an hypothesis about the nature of things, namely: (1) "a shifting, elusive light seen over marshes at night" (2) "believed to be caused by the combustion of gases arising from decaying organic matter". That is the distinction between (1) verbal and (2) real definitions.

Logic is about verbal definitions, never real definitions. [Note 3]


Grammatical rules, looked at as such, are not statements of fact; they are possible conventions. Of course, the sign 'The word 'thunder' means noise in the clouds' may be used to state a fact -- a fact about the English language that is, not as it were a fact about thunder.

Grammatical rules can be likened to commands. We can imagine a people who gave definitions this way: instead of saying "This [pointing] is called 'paper'", they say "Call this [pointing] 'paper'!" (This is noteworthy because a command does not have the form of a statement-of-fact, and so is unlikely to be mistaken for one.)

In logic of language (or, logic-philosophy), 'definition' = 'grammatical rule'.


Ostensive Definitions

The second category of grammatical rules is ostensive definitions: rules for the use of a sign that are given by pointing at things. We already have Wittgenstein's example above: when he points at a river to explain a meaning of the word 'flows'.

'King's College is on fire' ... How would we explain what this sentence means? [By] ostensive definitions. We would say e.g. 'this is King's College' (pointing to the building), 'this is a fire' (pointing to a fire). (cf. BB p. 37)

Note, however, that while the meaning of a name is often explained by pointing to the bearer of the name (PI § 43), the bearer of a name is not the meaning of the name. Also there are non-visual types of ostensive definitions, e.g. for 'the sound of a clarinet' and 'the scent of an orange'. And for some proper names Wittgenstein followed Russell's "Theory of Descriptions" (ibid. § 70); e.g. we don't define the name 'Socrates' by pointing to the bearer of that name (But Wittgenstein and Russell did not use the word 'grammar' the same way).


Play-acted (or demonstrative) Definitions

The third category is similar to the second. These rules of grammar can be called play-acted definitions (cf. PI II, ix, p. 188m); actors could perform them on stage. They may be comparatively simple, as e.g. when I sit down in a chair to explain the meaning of the phrase 'to sit down in a chair' (BB p. 24).

But these rules may also be very complicated indeed. And some emotions, dispositions and moods may be more challenging to play-act than others. Imagine e.g. what would be involved in play-acting sorrow or sadness. It would require quite a stage-set, quite a number of circumstances; e.g. there might be a history or background of the sorrow, an object of sorrow (e.g. the death of a friend), then the behavior of sorrow (e.g. the sad face, tears) [Note 4] ... Think of just how very complicated -- and varied -- the circumstances in which a child learns to use a word like 'sorrow' or 'sadness'. Or the word 'hope' are.

Caroline was expecting some one, and with anxious eagerness; for she walked up and down the room, started at every sound, looked out from the window, glanced at the clock, tried, but in vain, to work with her needle, and could hardly bear the voices of her children in their play. [Note 5]

Psychological-words are defined by patterns of behavior

And yet all these and similar circumstances belong to the grammar of the particular category of words (psychological-word), because all these circumstances would belong to a description of the 'meaning' = 'use in the language' of these words.

A psychological-word (e.g. 'hope', 'sorrow' or 'sadness', 'anger', 'fear', 'love', 'joy') names a pattern of behavior without necessarily a defining common nature ("names", I say, because its definition belongs to the second category identified by Wittgenstein: words defined by pointing to or in the presence of their bearer, in this case not an object but a phenomenon).


The meaning of this language seems unexplainable (hopelessly nebulous)

Wittgenstein's logic (i.e. describing rules) makes the meaning clear. It says what to look for. Learning what to look for. In this context, to remind = to make aware of what we know [have learned] (but do not realize that we know [have learned]).

In logic we make for ourselves grammatical reminders

But in philosophical logic we ordinarily have to talk only about a language we speak fluently: English e.g. is our mother tongue. So that in order to make grammatical remarks -- i.e. give explanations of meaning -- we have only to remind ourselves of some ways we normally use our language. But we do have to remind ourselves: a child learns to use a word, e.g. 'sorrow', in particular circumstances, but the child is not taught to describe the circumstances it learns to use the word in (Z § 114).

We want to understand something that is already in plain view. For this is what we seem in some sense not to understand ...

Confessions: quid est ergo tempus? si nemo ex me quaerat, scio; si quaerenti explicare velim, nescio. [What then is time? If no one asks me about it, I know. But if someone asks me to explain it to him, I do not know. (xi, 17)]

Something that we know when no one asks us, but no longer know when we are asked to give an account of what we know to others, is something we need to remind ourselves of. (cf. PI § 89)

The work of the philosopher consists in assembling reminders for a particular purpose. (ibid. § 127)

Note 2: Wittgenstein, significantly, never made this claim. Nor did he ever claim to have invented a logic.

I don't believe I have ever invented a line of thinking. I have always taken one over from someone else ... for my work of clarification. (CV p. 19, a remark from 1931)

We are always more dogmatic, things are always more "settled" for us than they ever were for the philosopher himself.

[Are there meaningful signs without grammars? and Socrates' logic of language have instances where Wittgenstein's logic may not "give methods for defining every sign".]


Note 2a: In Russell's "Theory of Descriptions", when he says that the author of Waverley is identical with Scott (a is identical with b), he is not defining either the word 'Scott' or the phrase 'the author of Waverley'.

'Scott is the author of Waverley' is not an example of a sign-for-sign substitution rule, although Russell says that because Scott and the author of Waverley are identical, 'Scott is the author of Waverley' is identical to 'Scott is Scott' (If a is identical to b, then a can replace b).

But there is a difference between saying that the persons named are identical and saying that 'Scott' and 'the author of Waverley' are identical in meaning (Russell titled his paper "On Denoting"), which they would have to be if the one can replace the other.

In Russell's example, the proposition 'Scott is the author of Waverley' is a statement of fact, not a rule of grammar. In this instance the Theory of Descriptions is not concerned with defining words, which is the use Wittgenstein's makes of it in PI § 79. [BACK]

Note 3: That mixing up these two types of definition (these two meanings of the word 'definition'), failing to distinguish between definitions of linguistic-signs and metaphysical hypotheses ("real definitions") about phenomena, as a source of confusion in philosophy was recognized by Blaise Pascal when criticizing the Scholastic philosophers. [Pascal uses the word 'nominal' rather than the word 'verbal', but there is a fundamental problem with nominalism.]

... let's not forget that a word hasn't got a meaning given to it, as it were, by a power independent of us, so that there could be a kind of scientific investigation into what the word really means. A word has the meaning someone has given to it. (BB p. 28; cf. Z § 467)

Presuming that words have meaning in themselves belongs to the background of this confusion, which is related to the picture that words are the names of things and the meaning of word is the thing the word names, and therefore that to investigate the meaning of word is to investigate the nature of the "independent phenomenon" the word names. [BACK]

Note 4: To describe a language game is to describe a form of life (PI § 19). [BACK]

Note 5: Charles Dickens, A Christmas Carol, Stave iv. [Dickens may have meant the word 'stave' in the sense of 'rung of a ladder'.] [BACK]

6. 'Grammatical Remarks'

Wittgenstein called these reminders 'grammatical remarks'. And whether they take a form we would naturally call a 'rule' or not, these remarks do the work of rules, and so they are rules -- regardless of their form. In logic tools (i.e. signs) are defined by the work they are used to do.

To "look at language as a collection of tools" is a statement of Wittgenstein's method in philosophy, and a statement of method is neither true nor false, although statements about the limit of its application are. And so 'Language is a collection of tools' is not a statement of fact, although that is its form.

The Logic of Comparison

Actually what Wittgenstein said was that language is like a collection of tools: "I have often compared language to a tool chest" (That was his simile). The command 'Look at language as if it were a collection of tools' is clearly not a statement of fact but a suggestion to make that comparison, as is 'Language is like a collection of tools'. Because anything can be compared to anything else in some way or another. That belongs to the grammar of the word 'comparison'. And that remark is an example of a grammatical remark (reminder), as is this:

After all, everything resembles everything else up to a point. There is a sense in which white resembles black, and hard soft, and so on ... (Plato, Protagoras 331d-e, tr. Guthrie)

A 'comparison' says that A is like B in some specified way, not that A is identical to B (much less that A really is B rather than A itself).

Comparisons are made. A = using language is like B = playing games in the ways D and C, where C = played according to rules (cf. used by following conventions), and D = game-pieces (cf. language signs). But A is unlike (not like) B in that most, indeed almost all games are played according to strict rules; if there were constant disputes about the rules, people would fall out with one another and quit playing (trying to play) the game.

Language users are, in some contexts, much more tolerant of unclarity. (And sometimes we tolerate nonsense, e.g. at school in geometry and at university in philosophy. Life can teach you the value of understanding the logic of our language.)

Limit of the comparison to tools

There is an important way in which words ("signs") are not like tools, because a hammer cannot be used to saw wood, but any given word can be assigned almost (language consists of conventions, but not of mere conventions) any job that can be done with language. If A is like B, then A is also unlike B. And that too is an example of a grammatical remark. That is the logic of comparison.

The expression "the eye of God" is a metaphor, but the comparison isn't to a face with nose and eyebrows (LC p. 71). It is true that a cat is like a dog because it has paws, but it is false that a cat is like a dog because it barks.

As signposts when lost

'Grammatical remarks' are 'reminders of some of a sign's grammar, made for the sake of clarification'. We would not naturally call them 'definitions'; perhaps we want to call them "partial definitions". But when is a definition complete? How much explanation of meaning do we need in a particular case before we are able to go forward on our own (PI § 151) to use a sign correctly? A grammatical remark,

an explanation [of meaning,] serves to remove or to avert a misunderstanding -- one, that is, that would occur but for the explanation; not every one that I can think of.

The sign-post is in order -- if, under normal circumstances, it fulfills its purpose. (ibid. § 87)

Our aim isn't to define words, except to resolve philosophical problems (ibid. § 109); our interest is philosophy rather than lexicography. Note that, if generally we don't use words according to strict rules (BB p. 25), then words don't have strict definitions, and this is reflected in dictionary definitions of common words which tend to give only very general orientation, as e.g. my definition "Philosophy is investigations in logic, ethics, and metaphysics by the natural light of reason alone", or Plato's definitions "Piety is correct conduct towards the gods (or towards God), as justice is correct conduct towards men" (Gorgias 507b).

A grammatical remark, a rule of grammar, is a sign-post: it tells us how to go on. (ibid. §§ 151, 123) [A sign-post may also warn us how not to go on.]

Next chapter:

7. The Rules of the Game

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