The Limitations of Language

November 22, 2017

Introduction

Many would agree that humans can be distinguished from other mammals by the well-developed and incredibly useful capability to imagine and reflect on different scenarios, even ones that are yet to come or those who will never actually happen. We can’t help but feel like our way of communication differs from that of animals. Our intellect gives us the ability to have a theory of mind. From an evolutionary point of view, a natural interest in understanding what someone else is thinking and the ability to communicate played a crucial part in human survival. And we needed something, some sort of skill, that would allow us to communicate all these ideas we have inside our heads. Over time, we seem to have developed something we now call ‘language’.

Philosophers who acknowledge the importance of this skill we all seem to have cannot help but wonder, “What are languages?”. And there is more. “What are words?”, “What are sentences?”, “How do words get their meaning?”, “What does it take to understand an expression?”. We say, intuitively, that we understand an expression when we can grasp its meaning. But what exactly does it mean to mean something? And what is it precisely, we grasp?

It seems unlikely that language is capable of perfectly describing every possible situation and every possible idea or question one might have. The difficulty we have with trying to answer questions like “What does it mean to mean something?” is a good argument for thinking that language must at least have some limitations. Philosophers aim to communicate their ideas and theories as clear as possible. The limitations languages seem to have make it hard for them to describe their ideas the way they want to. This makes Philosophy of Language one of the most important and most complex topics in all of philosophy.

​ It is not surprising at all that many philosophers also happen to be mathematicians. We can use mathematic concepts, which are not even physical things we can study empirically, to make statements that we can validate or reject with complete certainty. Philosophers often dream of reaching this same level of certainty about all sorts of philosophical questions they come up with, so naturally, there have been attempts to say something systematic about language and meaning.

​ In this essay I will explore the work of Gottlob Frege (1848-1925), one of the first and most influential philosophers that explored this topic, and Ludwig Wittgenstein (1889-1951), who I think holds the most unique view of language. Wittgenstein’s work can be divided into two parts: his early work (when he wrote “the Tractatus” in 1922), and his later work (captured in “the Philosophical Investigations”, published in 1953). I will go over how Wittgenstein’s view on language has changed throughout his life and show in what aspects his work contrasts with that of Frege. I will also explain what I think makes Wittgenstein’s work unique.

Gottlob Frege

According to Frege, there are two ways to systemize language. You can either give an informal (intuitive) theory of meaning or a formal theory of meaning. (Miller, 2007: xi) And Frege has tried both.

“Frege’s work in the philosophy of language builds on what is usually regarded as his greatest achievement, the invention of the language of modern symbolic logic.” (Miller, 2)

In logic, arguments can be valid or invalid. An argument is valid, when it is impossible for the premises to be true and the conclusion to be false. Here is an example:

  • P → Q
P;
Therefore, Q

Frege examined the validity of arguments by translating sentences, as they appear in natural language, into a formal logical notation. (Miller, 2) The truth-value of a sentence is of crucial importance. The truth value of a sentence is either the true or the false, depending on whether the truth-conditions of that sentence are realized or not. We should not confuse the term ‘truth-value’ with the term ‘truth-condition’, for the latter is a condition that must obtain for the sentence to be true. The semantic value of a sentence is what it refers to. Frege says the truth-value of a sentence is its semantic value. I will give an example of how Frege reasons with sentences:

  • - “All men are mortal”
- “Socrates is a man”
- “Socrates is mortal”

According to the rules of logic, the sentence “Socrates is mortal” is true if the sentences “All men are mortal” and “Socrates is a man” are true.

It is worth mentioning that the premises do not necessarily have to be true; It is enough to say that if the premises were true, then the conclusion would also be true. For example:

- All flowers are red.

- Tulips are flowers.

- Tulips are red.

Here, the first premises is not true. We know that there exist flowers that are not red. But if all premises are true, then, as a matter of logic, the conclusion is also true.

Up to this point, Frege has looked into the semantic values of expressions, and used formal logic in attempt to give language structure. But in order to create a theory that accounts for all of language, more properties of language than solely semantic values should be involved. To complete his intuitive theory of meaning, Frege added the property of having a sense.

Frege’s notion of sense

What I did not mention in the section above, is that Frege’s incomplete theory stumbled upon a few issues. I will briefly explain these issues and how the notion of sense solves these.

  1. 1. The problem of informativeness: Let’s say the semantic value of a name is the object it refers to and we can only understand a sentence when we know its semantic value. Then two expressions referring to the same object should have the same meaning. But this is not true, Frege showed. The expressions “the Evening Star” and “the Morning Star” both refer to the same object: the planet Venus. To someone who is familiar with the two expressions, but does not know they both refer to the same object, the expression “the Evening Star is the Morning Star” is informative, while “the Evening Star is the Evening Star” is not. How is it possible to understand a sentence without knowing its semantic (truth) value?

  2. 2. The problem of bearerless names: If the semantic value of a name is the object it refers to, then names of fictional characters have no semantic value since they cannot refer to anything in the real world. The expression would be meaningless, but we can understand it, and distinguish it from gibberish. So there must be some other semantic property to fictional names in addition to its reference. I will explain how sense offers a solution.

  3. 3. The problem of substitution into belief contexts: Sometimes, substitution of a part of a sentence with another that has the same semantic value will not change the truth value of the sentence. But substituting within belief context fails. When two sentences “x” and “y” are true, they have the same semantic value. We can often substitute y for x in sentences, and the truth value remains unchanged. “It is true that x” has the same truth value as “It is true that y”. But if John knows that x is true, but does not know that y is true, you cannot perform the substitution. “John believes x is true” has not the same truth value as “John believes that y is true”.

These three problems show us that it is unlikely that meaning of an expression is nothing but its semantic value. Frege introduces the notion of sense: a semantic property that determines the semantic value of a sentence. Names now have references (the objects they stand for) and a sense, which is “some condition which an object has to satisfy in order to count as the reference of the name”. (Miller, 28) This provides a solution to the three problems above:

  1. 1) Both the sense and the semantic value of an expression seem to be responsible for determining the truth or falsity of a sentence. Since is possible to know the sense of an expression without being sure what the reference is, it is also possible to understand a sentence without knowing its truth value. The key difference between these the two notions is that the sense of an expression is what someone who understands the expression grasps. The semantic value, which is determined by sense, of that expression is no part of what this person grasps. (Miller, 35) This makes it possible to understand a sentence without knowing its truth value. This solves the problem of informativeness.

  2. 2) We can give fictional names some descriptive condition in such a way that someone can understand what kind of person a fictional name refers to, even though this name has no object in the real world it can refer to. This makes it possible for an expression to have a sense (are not necessarily meaningless) even if it lacks a semantic value (reference). (Miller, 30) This solves the problem of bearerless names.

  3. 3) If you substitute part of a sentence by something with the same truth value, the truth value of the whole sentence should remain the same. In belief context, this posed a problem. However, according to Frege, embedded sentences, used in belief contexts, refer to their senses (He calls this the indirect reference), not their references. The semantic value (truth-value) of these embedded sentences are, within belief context, their senses. Substituting a part of a sentence with another that has the same sense, leaves the sense of the whole sentence the same. This makes substitution possible, and solves the problem of substitution into belief contexts.

But it also gives rise to yet another problem… The sense of a proper name is easy to understand, because we can give a descriptive explanation that anyone can grasp. But what is the sense of a sentence?

Frege says the sense of a sentence is a thought. This thought is objective, because it specifies the necessary and sufficient conditions for the sentence to be true. It seems like substituting a sentence with another that expresses the same thought leaves the truth-value unchanged: London is south of Glasgow” seems to expresses the same thought as “Glasgow is north of London, but the linguistic meaning is different. (Miller, 33)

Wittgenstein

Frege's theory is about applying logic to language. He strives for a theory where all statements/sentences, in the form such that there is a function and a place for an argument, can be explained with logic and the aid of the notions of sense and reference. Wittgenstein on the other hand found that the language of logic works in a totally different way from natural language.

Early Wittgenstein (Tractatus)

Wittgenstein holds that sentences are the perceptible form of our thoughts. There are three kinds of sentences:

  1. 1. meaningful sentences, which are expressions of thoughts

  2. 2. meaningless sentences, which have a logical form but lack meaning (also called ‘the logical sentences’)

  3. 3. nonsensical sentences, which do not have a logical form or meaning. (Rombout, 2011: 49)

The structure of a sentence is similar to the structure of the thought, which is what the sentence represents. (Rombout, 49) This is similar to what Frege says about sentences: the sentence is perceived as a function of its parts. (Tractatus, 3.318) But according to Wittgenstein, these names are nothing more than the linguistic counterparts of whatever they represent, so we do not need to give them a definition or try to describe their meaning. In the Tractatus Wittgenstein writes:

3.3 Only propositions have sense; only in the context of a proposition has a name meaning”.

What he means by that is that names only have meaning (refer to objects) in the context of a sentence. (Rombout, 50)

In the Tractatus, sentences are compared to pictures. Sentences represent situations in a similar way as pictures do. The sentence as a whole pictures a state of affairs or situation in the real world. Meaningful sentences relate to the world, even though it often does not seem like it. When we see the sheet music of “Für Elise” we also do not hear the music Mozart plays. Yet is does represent it. The meaning of a sentence is, according to Wittgenstein, the state of affairs it depicts. Only meaningful sentences can be true or false, and we can understand a sentence without knowing it’s truth value. Wittgenstein defines truth in the Tractatus:

2.222 In the agreement or disagreement of its meaning with reality, its truth or falsity consists.

So if the picture looks like the state of affairs in the real world, it is true. If it does not look like it, it is false. And these states of affairs cannot be explained through language. It can only be shown.

4.1212 What can be shown, cannot be said.

4.121 A sentence cannot depict logical form: logical form is mirrored in it. What mirrors itself in language, language cannot depict. What expresses itself in language, we cannot express by means of language. A sentence shows the logical form of reality. It displays it.

Wittgenstein says here, is that a sentence shows its logical form. This is the form underlying the structure of the names. Why can we not describe the logical form of a sentence? According to Wittgenstein, in order to describe the logical form of a sentence, or explain what it is, we have to step outside of the realm of the expressible. This cannot be done. Language, Wittgenstein concludes, is not the right tool for the job.

Similarly, the sentence shows its meaning (Tractatus, 4.022). The names in it represent objects, and the structure of the sentence shows how these objects are related to one another. The only thing a sentence says, is that the situation/state of affairs it depicts is, in fact, the case. There is nothing else it can say. Everything else that can be said about sentences, languages, and logics falls in the category called ‘meta-expressions’, and those are all meaningless because they are not pictures of facts of the world. (Rombout, 53)

3.02 The thought contains the possibility of the state of affairs which it thinks. What is thinkable is also possible.

So we have sentences, that belong to language. We have a state of affairs, that belongs to the real world. And now we have a third property, thought, that contains the possibility of a state of affairs. All meaningful sentences together capture every possible situation that may or may not be the case in the world. This determines the limit of our capability to express our thoughts.

Meaningless sentences are sentences that do not picture a (possible) state of affairs in the world. Their truth-value does not depend on what the world is like. The logical sentences (contradictions and tautologies) fall in this category. They do not represent facts in the world, so they have no meaning. Sentences can only have a truth-value, if we can tell whether the meaning can be realized or not, so meaningless (including logical-) sentences have none. Logical sentences are not nonsense, they are all just analytical sentences that belong to symbolism and serve a purpose in logics. (Tractatus, 6.11) They say nothing, but they do show something. They can, for example, show that they are tautologies.

In the Tractatus, Wittgenstein tried to capture language’s capability to represent the world. Sentences would be like pictures of what the world could possibly look like. In the Philosophical Investigations, Wittgenstein’s later work, he reconsidered having a theory about language at all. His main point being, when we try to come up with a theory, we inevitably simplify and abstract the complexity of language.

Late Wittgenstein (Philosophical Investigations)

The Philosophical Investigations begins with quoting Augustine:

Augustine says in the Confessions "quid est ergo tempus? si nemo ex me quaerat scio; si quaerenti explicare velim, nescio" [1] […] Something that we know when no one asks us, but no longer know when we are supposed to give an account of it, is something that we need to remind ourselves of.

When we ask ourselves misleading questions like “What is the meaning of meaning?”, we feel a desire to understand them more clearly. Wittgenstein believes that framing these questions like this, makes us approach them in the wrong way. He holds that such questions should not have been asked in the first place, because they suggest that we have to explain something. And explaining involves using language, and language simply cannot cover it.

Wittgenstein had in mind to investigate language at its roots. So his Investigations start with Augustine, who describes an naïve theory about language acquisition. According to Augustine, humans are born with thoughts and wishes, but are not yet capable of expressing them. In Augustine’s theory, it is assumed that the human baby is already cognitively capable enough to realize that, when people point to objects and utter a word, they mean that the object pointed to has that word attached to it. Understanding is when the appropriate connection is made between a sound and the object it signifies. (McGinn, 2002: 38)

According to Wittgenstein, this is the first move toward the abstraction of language because the theoretical attitude tends toward an over-simplified (idealized) theory of language. By introducing to us the concept of a 'language-game', Wittgenstein tries to compel us to look at language where it actually functions. He actually gives examples of (simple) language situations to make the reader realize that language is much richer and complex when it is used in everyday life. Language is not a means of communicating our thoughts and wishes, it is rather a tool within the activity speakers are engaging in.

Furthermore, Wittgenstein says that “everything that we need to understand the essence of language ‘already lies open to view’” (PI 126). When we ask questions like “What do the words of this language signify?”, we are led to abstract language and create a false picture of how it functions. Such questions are answered by looking at how that person goes on using it in the upcoming language games. When someone uses the words of a language in the right way, this shows that he knows what the words mean.

Wittgenstein’s critique of other people’s theories of language does not suggest that we should try to classify different expressions, for such distinctions only become clear when we look at when those expressions are being used in real life. That is what’s so brilliant and unique about his Investigations: it only describes concrete cases/examples that show how language is used, without putting his findings in an abstract theory. He stays away from generalizing different cases, and provides us with a new way of looking at language.

[1] Augustine says here that he cannot explain what “time” is, when someone asks him to define it. But before it was asked, he really felt like he knew what time was.

Frege vs Wittgenstein

Wittgenstein studied Frege's work. He admires him publicly at the beginning of one of his major philosophical works, the Tractatus. He recommends anyone who is interested in the philosophy of language to study his work. Still, there are a few points where and Wittgenstein clearly differ. I will now address them.

Identity Relations

Both Wittgenstein and Frege have thought about identity relations. In the Tractatus, Wittgenstein writes there is no such thing:

5.5303 […] to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing.

Frege also finds it difficult to explain identity as a relation. In ‘Sense and Reference’ he writes:

“Equality gives rise to challenging questions which are not altogether easy to answer. Is it a relation?"

Wittgenstein’s Tractatus is usually held to propound a correspondence rather than Frege’s identity theory of truth: a sentence is true, only if there is an appropriate relation of correspondence between sentence and state of affairs. But some might argue that Wittgenstein’s work in the Tractatus is using a theory similar to the identity theory of truth, the only difference being that he simply discarded the notion of sense, so that there are only levels of language and reference left, with nothing like “sense” in between those levels.

Judgement stroke

One more problematic notion of Frege is that of the judgement stroke. A judgement stroke represents the act of judgement. Frege thus holds an epistemological understanding of logic: he says one needs to establish a consequence relation between sentences in order for it to exist. (Rombout, 57) Wittgenstein says in the Tractatus that the judgement stroke is ‘logically altogether quite meaningless’. According to Wittgenstein, there is no need for a subject, let alone the acknowledgement of the truth of a sentence. The truth of a meaningful sentence is already ‘out there’: it is only dependent on the situation it depicts. There is no need for inference rules because the logical consequence between sentences exist as soon as the sentences themselves exist. I assume that Wittgenstein holds an ontological understanding of logic here, since he holds that there is no need to justify conclusions through laws of inference.

4.064 proposition must already have a sense; assertion cannot give it a sense, for what it asserts is the sense itself. And the same holds of denial, etc.

It seems like Frege attaches the truth value later on, where Wittgenstein thinks it is already imbedded in the meaningful sentence from the moment the sentence exists. In his later works, where much of his views have changed, Wittgenstein still holds on to this critique of Frege:

PI 22 It is only a mistake if one thinks that the assertion consists of two actions, entertaining and asserting (assigning the truth-value, or something of the kind)

Also, sentences cannot be used for acknowledging their own truth. It would require them to take a meta-position, outside the realm of what’s expressible and this cannot be done.

4.022 The proposition shows how things stand, if it is true. And it says, they do so stand.

To proof whether a (meaningful) sentence is true, it should be shown that this is in fact the case.

Locke’s private ideas

To compare Frege and Wittgenstein in their standpoints concerning private ideas, we turn to the philosopher John Locke. Locke holds that a speaker grasps the sense a word ‘if and only if he is disposed to have a mental image of this word whenever he hears or utters the word’. (Miller, 38) But Locke’s theory poses a problem: How can we communicate private ideas? Do we have common senses that we attach to our language? Frege attacks Locke’s idea of private ideas, and reasons as follows:

Inner items have no role to play in explaining the practical success of language in facilitating communication between two speakers, and given that the crucial role of sense is to explain how linguistic communication is possible, grasping a sense cannot consist in the possession of some inner, private item. (Miller, 39)

So according to Frege, who does not agree with Locke’s view, sense is objective: grasping a sense is not a matter of having ideas, mental images, or private psychological items. (Miller, 42) Frege and Wittgenstein both oppose this view of having mental images or any other associated ideas, but they have different counterarguments. Frege says that instead, we should not confuse the sense of an expression with any associated ideas that come with it. Wittgenstein says language is not something that happens inside one’s mind, but that it is instead embedded in our daily lives.

Conclusion

Frege has been one the first philosopher who applied logics to language, and his theory has been successful and paved the way for many future philosophers. Any philosopher who wants to say something about language should start by looking into Frege’s work.

Philosophers have attempted and failed to give a full account of the essence of meaning, asserting and language. This failure, Wittgenstein believes, is due to the fact that the real distinctions and complexities are only revealed when we practice language. And they all took it out of that essential context.

The Tractatus is about understanding how language functions, and has no examples of situations where language is used in our everyday life. He focusses on getting the main point across, which was his claim that sentences picture possible states of affairs.

The Philosophical Investigations does not oppose specific theories in the Tractatus, but rather the whole style of thought. The Philosophical Investigations opposes any theory (including Augustine’s, Frege’s, and his own old theory of the Tractatus) that studies language in isolation, and not where it functions.

Frege and Wittgenstein have some specific, individual differences. Wittgenstein seems to hold a correspondence theory of truth, where Frege holds an identity theory of truth. Frege he says one needs to establish a consequence relation between sentences in order for it to exist, so he holds an epistemological understanding of logic. Wittgenstein seems to hold an ontological understanding of logic, claiming the truth of a meaningful sentence is already ‘out there’ and there is no need for a subject. Even though they both attack Locke’s view of having mental images, they clearly differ in the way they oppose his views.

References/Bibliography

- St Augustine (1961), Confessions. Harmondsworth: Penguin.

- Frege, G (1892), On sense and Reference: ‘Über Sinn und Bedeutung’, translated as ‘On Sense and Reference’ by M. Black in Translations from the Philosophical Writings of Gottlob Frege, P. Geach and M. Black (eds. and trans.) third edition (1980). Oxford: Blackwell

- McGinn, M. (2002), Routledge Philosophy GuideBook to Wittgenstein and the Philosophical, Routledge: Taylor & Francis e-Library

- Miller, A. (2007), Philosophy of Language (Second Edition), Routledge: Taylor & Francis e-Library

- Rombout, F. (2011), ‘Frege, Russell and Wittgenstein on the Judgment Stroke’. MSc Thesis: Universiteit van Amsterdam

- Validity and Soundness, Internet Encyclopedia of Philosophy http://www.iep.utm.edu/val-snd/, accessed on 27 October 2017

- Wittgenstein, L. (1958) Philosophical Investigations, Translated by G. E. M. ANSCOMBE. Oxford: Basil Blackwell Ltd

- Wittgenstein, L. (2017), Tractatus Logico-Philosophicus, side-by-side edition. London: Kegan Paul

Further Reading:

- David Bell – Frege’s theory of Judgement

- Charles Travis – Thought’s Footing