Philosophy of Language Notes Part 1: Wittgenstein


Philosophy of Language

Notes on Wittgenstein, Kripke and the Nature of Truth

Jason's Pictures May 2009 - February 2010 283

Jason Zarri


(Based on my notes and papers for a philosophy of language class

taken in Spring 2008 at San Francisco State University)

(Also Available as a PDF)


~ Prelude ~

Why philosophers study language–

1) Philosophers have been accused of “making mistakes” based on language. Consider the sentences:

i) “Santa Claus does not exist.”

ii) “Santa Claus wears a red suit.”

a) “How can one talk about something”, philosophers sometimes ask, “and say something true or false about it, if it isn’t real or doesn’t ‘have being’ in some sense? In order for statements like (i) or (ii) to be true, they have to be about something—Santa Claus, in this case. Granted, in light of the fact that (i) is true, Santa Claus doesn’t exist, but nevertheless he is some kind of being and has properties—including the properties of being non-existent and wearing a red suit.” However, at least since Bertrand Russell published his famous article “On Denoting” in 1905, most philosophers think that arguments like this are based on linguistic confusions. It can be true that Santa Claus does not exist without Santa Claus being real in any sense.

b) From time to time philosophers also ask: Is there such a thing as “goodness”, or something like Plato’s “Form of the Good”? Able philosophers have thought so, but others–emotivists, in particular, such as A. J. Ayer, C. L. Stevenson, Richard Hare—have held that to call something good or bad, or to say that an action is right or wrong, is not to say that it objectively has some moral feature—“goodness”, “wrongness”, etc.—but to express how the speaker feels about the thing or action in question.  For example, on this view a sentence like “Lying is wrong” is neither true nor false; nor, when properly understood, is it purported to be. It merely evinces that the speaker who uttered the sentence disapproves of lying. It does not even say that the speaker disapproves of lying—that would be a sentence that is apt to be true or false; true if the speaker disapproves of lying and false if they do not. On the emotivists’ view, to say that lying is wrong is more like saying “Boo lying!”, “Screw lying!”, “Down with lying!”, or something of the sort.

(Personal note: Words like ‘good’ and ‘bad’, ‘right’ and ‘wrong’, may have an expressive function, but it doesn’t follow that they only have an expressive function. Sentences involving ‘good’ and ‘bad’ might sometimes attribute objective goodness or badness to some entity, and it may be that it is in virtue of one’s belief that the entity in question is objectively good that one can use the term ‘good’ or ‘goodness’ to express how one feels about it. For it may be that if one had no belief concerning the entity’s moral value, one might not have any feelings about it, whether positive or negative.)

2) What are the limits of human knowledge? What can we conceive? The “early” Ludwig Wittgenstein, for example, thought there was a connection between the limits of conception and the limits of what can be expressed in language:

The book will, therefore, draw a limit to thinking, or rather—not to thinking, but to the expression of thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought).

The limit can, therefore, only be drawn in language and what lies on the other side of the limit will be simply nonsense.—Tractatus Logico-Philosophicus, p. 3

3) Language is inherently interesting.

The class will focus on how words refer—how they come to stand for, or pick out, or point beyond themselves to things in the world.

There are three important assumptions shared by many philosophers of language prior to Wittgenstein’s Philosophical Investigations:

1) The Museum Model of reference:

The meanings of words—for nouns, at least—just are the things in the world that they “stand in for” or “pick out”. In modern philosophy, John Stuart Mill is the one who is most responsible for this model.  In the sentence “Barack Obama lives in the White House”, the meaning of ‘Barack Obama’ is a certain man, who as of this writing (August 2012) happens to be President of the United States, and the meaning of ‘the White House’ is a certain (very famous) house in Washington D.C. Furthermore, there is no more to the meaning of these terms than the individuals they stand in for. Notoriously, the name ‘Barack Obama’ elicits very positive feelings in some people and very negative feelings in others, but on this model the different feelings that different people have has nothing to do with the meaning of the name as they use it. As Mill would put it, these emotional associations are a matter of the name’s connotation rather than its denotation, the denotation being the individual to whom it refers.

2) The meanings of words are derived from corresponding mental imagery:

On this view, the meaning of a word—‘red’, for example—is based on a mental image that one has when imagining something. If someone says that something is red, one cannot understand them unless one can imagine a red object. (This can be called the Empiricist Assumption.) Thus, someone who is blind from birth cannot understand what the word ‘red’ means, though they could perhaps come to learn about the neuroscience of color perception. Perhaps the most famous exponent of this view of meaning was David Hume. It was inherited by the Vienna Circle, the group which was primarily responsible for the rise of Logical Positivism, a highly influential radical empiricist movement that flourished in the early Twentieth Century.

3) Mathematization of language:

To eliminate the vagueness and ambiguity inherent in natural languages—non-mathematical languages, such as English, French, German, Spanish, Italian, etc.—they should be translated into what is essentially a mathematical language which is based on formal logic. (If you would like to know what formal logic is, check out my “A Primer on Logic” series here.)

~ Part One: Wittgenstein ~

Language Games—

1) According to Wittgenstein, there is no single thing that all that we call ‘language’ has in common. Nevertheless, one can give a rough explanation: A language game is a use of language for a particular purpose. What that purpose may be can vary from case to case, and there may be cases where the only “purpose” of the language game is the activity of playing that very game. This definition is very broad and vague, but so is the phenomenon it is trying to capture. The important thing to note is that, as the term ‘game’ implies, language games are at bottom a type of activity. In section 7 of the Philosophical Investigations, Wittgenstein says “I shall also call the whole, consisting of language and the actions into which it is woven, the ‘language game’.” (Philosophical Investigations, p. 5)

2) One example of a language game is the language of the builders in section 2. One builder, A,  calls out names for different building materials, like blocks, pillars, slabs, and beams; and another builder, B, brings the right materials to A. Wittgenstein tries to make the point that one of the functions of language is to get people to do things. The purpose of this particular “game” is that a command such as “Slab!”  is to get B to act in a certain way—namely, bringing a slab—on hearing the call. But this is not the only purpose a language game may have.  Wittgenstein also describes the following as language games: “primitive” languages, the uses of language through which a child learns to speak, naming things, repeating words after someone, and games such as “ring-a-ring-a-roses.” Also, in section 23 Wittgenstein gives such diverse examples of language games as giving and obeying orders, measuring an object, telling jokes, and doing math problems.

3) These examples all seem very different at first sight, but they have at least one thing in common: They are all uses of language which don’t necessarily involve the communication of thoughts or ideas. In other words, they are not descriptive; they are not—at least, not primarily—activities whose aim is to state facts. Instead, their purpose may be to help someone learn a skill, to teach someone to respond to something (like a builder’s call “Slab!”) in a certain way, or simply to have fun. Wittgenstein, it seems, believes these examples show that language has more than one function. Language games are fundamentally bound up with various kinds of action that are commonly thought—by philosophers, anyway—to be “external” to language proper.

4) What, then, is the significance of the concept of a language game? I think there are two main points: First, language is primarily social—it involves activities which are bound up with our day-to-day lives. Language is primarily for communication and interacting with others. Second, the various language games do not have too much in common. Language is not all about stating facts, even though many philosophers have thought it was, and so diversity is a major point. Stating facts may be one point, yet it remains but one point among many.


Words and Tools

1) In various places Wittgenstein compares words to tools. I think Wittgenstein’s point in those sections is that, like tools, words have a plurality of functions. Like the various levers in a train cabin they all look similar, but this is only because they are all intended to be used by us, but the uses we put them to are quite different. Because they all look similar, we tend to think they must all function the same way, but that assumption is mistaken. Words do not all “stand for objects”, even though many philosophers seem to assume this. Words like ‘bread’, ‘table’, stone, etc., may; but what about ‘perhaps,’ ‘very’, ‘ouch’, ‘no’, and so on.   Such words have a use in our language, and so are meaningful according to Wittgenstein, but it seems obvious that they don’t refer to anything. To think that they all have the same sort of use, he would say, is like saying that a hammer, a glue pot, and a ruler all serve to “modify something”, (Philosophical Investigations, section 14, p. 7). We might gerrymander a sense of “modify” in which this is true—a hammer modifies the position of a nail, the glue pot modifies the temperature of the glue, and a ruler modifies our knowledge of a thing’s length—but such assimilation of different expressions only produces confusion (Philosophical Investigations, section 14, p. 7).

2) In more contemporary terms, the following analogy may make the same point in a more familiar way. Words can be compared to the various keys of a computer keyboard. Many of the keys serve to make symbols appear in a window on your computer monitor. Such is the function of ‘a’, ‘b’, ‘c’, and other letter keys; and the same goes for punctuation keys. Yet someone who supposed that all the keys on the keyboard made symbols appear on the screen would have a very confused notion of how a keyboard works. What of the spacebar, the shift key, the backspace key and the enter key? The spacebar serves to separate symbols, and the backspace key to erase them.  The enter key makes a paragraph break, and the shift key only works in conjunction with other keys. Someone who thought that every key on the keyboard makes a symbol appear would have trouble if they had to use a computer to write something, and it is only when they discard this prejudice that they could use it properly. The same is true, according to Wittgenstein, with the philosopher who assimilates the use of all words to the use of nouns.

Meaning and Reference—

1) Wittgenstein puts forward the view that the meaning of a term is its use in the language of which it is a part. It must be noted that Wittgenstein is not asserting the rather trivial thesis that a term—if one could even call it a term—would not be meaningful if no one ever spoke it or wrote it down or in any way employed it in communication. Nor is he maintaining the equally trivial thesis that a term’s meaning depends on the particular way it is used, so that it would have meant something different if it had been used differently. These theses are true of course, but Wittgenstein is making the stronger claim that the meaning of a term is determined by the way it is used to communicate and to shape behavior.

2) Wittgenstein distinguishes the meaning of a name from the bearer of a name. The bearer of a name is the individual to whom it refers, while the meaning of a name is the set of rules which determine whether or not a name has been correctly applied to this individual. Wittgenstein thinks that the bearers of proper names have little to do with their names’ meaning because a proper name can be meaningful even when its bearer has died or ceased to exist. According to Wittgenstein, naming is preparatory for actual use. Names can refer to things, but they can do so only in the context of a language game: “Naming is so far not a move in the language-game—any more than putting a piece in its place on the board is a move in chess. We may say: nothing has so far been done, when a thing has been named. It has not even got a name except in the language game.” (Philosophical Investigations, section 49, p. 24) For Wittgenstein, then, naming—and hence reference—play but a minor role in the mechanics of language.

Gettier Problems—

1) What does it mean to say that we have knowledge? A Gettier case is a “counterexample” to the classical (in Analytic philosophy, anyway) analysis of knowledge as Justified True Belief™.  In order for you to know something, what you know must be justified. I might form the belief that you’re going to have corn flakes for breakfast tomorrow morning and be right, but if my belief is based on nothing—if you don’t have a habit of eating corn flakes for breakfast, if you don’t tell me that you will, and so on—I don’t really know that you will, I’ve just made a lucky guess. Furthermore, what you know must be true. No one knows that the Earth is flat, because it isn’t. Members of the Flat Earth Society might think they know it, but they’re wrong. Finally, to know something you must believe it—that is, you must think that it is true. If there is life elsewhere in the universe, I can’t count as knowing that there is if I don’t think there is—even if I’m in possession of evidence which strongly indicates that there is, but which I discount for some reason.

2) Gettier cases are supposed to show that the above three criteria are not jointly sufficient for knowing something–they might be necessary for knowing something in they sense that one can’t know something if they aren’t met, but something more is required. Gettier cases originated with Edmund Gettier’s article “Is Justified True Belief Knowledge?”,[1] which is one of the most famous articles on epistemology in the Twentieth Century.  Here is one example of a Gettier case: Suppose I’m driving by a field and I see, from a great distance, some piles of shorn wool which I take to be sheep. Given that I already know there are a lot of sheep in the area, this belief is perfectly reasonable and would seem to be justified. Let’s also suppose that there really are sheep in the field, though as it turns out I never see them. In this case, I have a Justified True Belief™ that there are sheep in the field, but it sounds wrong (to Analytic philosophers, anyway) to say that I know that there are sheep in the field. Wittgenstein, by contrast, would say there is no “essence of knowledge,” and that the answer to the question of whether Gettier cases are really cases of knowledge can be determined by convention—in much the same way that whether one gives measurements in feet or in meters is determined by convention.


Wittgenstein on Rules—

1) Poker:

i) What do we do if someone dies, or runs away from the game? If the second obtains, and we later come across them, do we give them back what they started with, or what they’ve won so far, or…?

ii) To some extent, then, we make up the rules as we go along.

2) Writing ‘color’ vs. ‘colour’: Which spelling is ultimately correct, independent of where one lives? Most suppose there is no uniquely correct answer to this question, and Wittgenstein thinks the same is true of many philosophical problems.

3) For Wittgenstein, rules are essentially public, which means roughly that whether or not someone is following a rule “correctly” can be checked by other people. That rules are public can be seen by attending to the “grammar” of the word ‘rule’; that is, the way we actually use the word ‘rule’ in our everyday language. In his examination of rule following, Wittgenstein focuses primarily on cases where people say things like “…then it came to me in a flash, and I knew how to continue”, or “Now I understand it” and then work out the rest of a series. Wittgenstein finds such expressions problematic—or perhaps more accurately, he finds the way in which philosophers tend to (mis)understand such expressions problematic.

4) Suppose that someone has learned the series of natural numbers up to 1,000 and that I then give them the order to start with zero and add 2 until I tell them to stop. Up until they reach 1,000 everything goes smoothly, but once they reach 1,000 they continue the series like this:

1,000; 1,004; 1,008; 1,012…

Now, did I really mean that they should write 1,002 after 1,000, 1,004 after 1002, and 1006 after 1004? Did I also mean that they should write 1,056 after 1,054, and so on? In short, how can we mean an infinite number of things if our minds are finite? Could an infinite sequence of numbers come before one’s mind in an instant? It seems that it couldn’t, but how else are we to explain someone’s suddenly being able to go on?

(Personal Note: What if, instead of talking about a person writing down an indefinitely long series, we suppose that someone has a disposition to obey a rule in any particular case, since one can arguably have an infinite number of dispositions. For example, if I ask someone who disbelieves in elves, “Is there one elf?”, they would respond “no”. If I asked them “Are there two elves?”, they would also respond “no”, and if I asked them “Are there three elves?”, they would still respond “no”, …and so on, for every natural number. This seems to show that one can have an infinite number of dispositions. Could one then be said to follow a rule in virtue of having an infinite number of dispositions?)

5) Wittgenstein attacks the notion that a flash of insight could uniquely determine how I follow a rule. In working through a numerical series, it may happen that at a certain point I find myself unable to go on. Should we say that I suddenly forgot what I grasped in a flash, or should we rather say that my feeling of having grasped the rule in a flash was mistaken? In the first case, the flash of insight was not causally sufficient for my correctly continuing the series, and in the second case, my understanding cannot consist in what goes on in me during that flash. Either way, the flash cannot serve as an infallible guide as to how I am to follow a rule. It cannot be the whole explanation of how I go on as I do, even if it is an important part of it.

6) But if knowing how to go on—that is, how to follow a rule correctly—does not consist in a flash of insight, what does it consist in? The answer will become clear if we remember Wittgenstein’s account of meaning, which is that the meaning of a word or sentence consists in the use we make of it. If meaning is use, and if to understand an expression is to grasp its meaning, it follows that to understand an expression is to be able to use it correctly. So how does it come about that we understand words, sentences, and rules? The answer is through training. Ostensive definitions—definitions by pointing something out, e.g., that is called ‘red’—can always be misunderstood—someone who is still learning English may think that I mean that that particular red ball I’m pointing at is called ‘Red’ (as if the word ‘red’ was the name of the ball), or perhaps that I mean that only that particular shade of red is called ‘red’. However, definitions of words by means of more words either bottom out in undefined expressions or loop around in a circle. In training someone, though, we can correct them if they misunderstand, and we can avoid undefined terms and circular definitions because what we are ultimately doing is getting them to behave in a certain way, to react to these stimuli with these responses. This, however, is possible only because we can all observe each other’s behavior. If we couldn’t do that, we would have no means of demonstrating things to each other or correcting each other’s mistakes. Without other people to correct one’s mistakes—or, at least, without the possibility of such correction—there would be no criteria for one’s having grasped a rule correctly or not. One cannot check one’s own understanding, for that is all one has to go on—there is nothing else to compare it with. This is why understanding is public—that it is something that can be checked by other people. This is also why grasping a rule is something public, and why following a rule is a social practice.

7) For Wittgenstein, the rules governing language simply describe what we do. (We should simply look at what people do with rules, not think about it.)

Wittgenstein on Private Language—

1) One of the most significant themes running through Wittgenstein’s Philosophical Investigations can be found in a chain of related aphorisms collectively known as the Private Language Argument.  This argument aims to show that the notion of a private language—a language whose terms are intelligible only to its speaker—is incoherent. The main thrust of Wittgenstein’s arguments concerning the possibility of a private language is that a would-be private linguist has no means of telling whether they are using a sign which purportedly picks out one of their private sensations correctly or not. For a private linguist to use a sign for one of their sensations meaningfully there must be a distinction between correct and incorrect usage. But what could this distinction consist in for a term of a private language? Not in its agreement or disagreement with how the term is used by others in the private linguist’s community, for by hypothesis the meaning of the term is not determined by and cannot be inferred from anything that is publicly observable, including the private linguist’s behavior. Nor can its correctness consist in its conformity with the private linguist’s judgments regarding whether they are having the same sensation or a different one, for then the distinction between correct and incorrect usage would evaporate. For what we are after here are not merely the conditions under which, as a matter of fact, the term is correctly or incorrectly used, but rather what it is for the term to be used correctly or incorrectly.

2) The issue at stake in the Private Language Argument is not the skeptical one of whether, given that there are private sensations, we can be sure that for the most part we are applying our sensation words to them correctly. The issue is instead whether talk of such things as private sensations is meaningful at all. So when Wittgenstein demands criteria for the correct use of words, what he wants is simply some means of distinguishing correct from incorrect use; how often our use is correct is immaterial. Now, if the criterion for the correct use of a term in a private language is its accordance with the judgments of the private linguist, it will be nonsense to speak of any possibility of error. As Wittgenstein puts it, “One would like to say: whatever is going to seem right to me is right. And that only means that here we can’t talk about ‘right’.” (Philosophical Investigations, Section 258, p. 92) Yet if the correct or incorrect application of the term is established neither by public use nor private judgment, what else could establish it?

3) Given Wittgenstein’s account of meaning and reference sketched above, it is easy to understand why Wittgenstein, in attacking the notion of a private language, focuses his arguments on the notion of a “private ostensive definition”—on how the connection between the private linguist’s sign and the private linguist’s sensation is set up. In section 244 of the Philosophical Investigations Wittgenstein asks, “How do words refer to sensations?—There doesn’t seem to be any problem here; don’t we talk about sensations every day, and give them names? But how is the connexion between the name and the thing named set up? This question is the same as: how does a human being learn the meaning of the names of sensations?—of the word “pain” for example.” (Philosophical Investigations p. 89) Wittgenstein here identifies the question of how sensation words come to refer with that of how one learns their meaning.



Gettier, Edmund. “Is Justified True Belief Knowledge?”, Analysis, 23: 121–123, 1963 [Available online here].

Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. Translated by C. K. Ogden. Barnes  & Noble Books 2003, First Published 1922 [Available online here].

Wittgenstein, Ludwig. Philosophical Investigations, 3rd Edition. Trans. G.E.M. Anscombe. Engelwood Cliffs, New Jersey: Prentice Hall, 1958.


(Also Available as a PDF)

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[1] “Is Justified True Belief Knowledge?”, Analysis, 23: 121–123


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