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Frege and Semantics

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I think it makes sense to mention Descartes + Hobbes + Wittgenstein before talking about Frege and his idea about sense & reference. In the context of Cartesianism, language was analyzed subjectively. Frege thought this was misguided, and tried analyzing language objectively. He was no doubt motivated by his mathematical background, and in fact he originally became interested in what the signs of mathematics meant, then developed a broader interest in semantic theory later.

Recall that Descartes raised serious doubts about whether we can know about other minds. Our own mind is the thing we know the best. Descartes' contemporary, Hobbes took this view and thought that language's most important function was to organize our own thoughts, communication with others is an accident.

For no man is able to remember ... colors without sensible and present patterns, nor number without the names of numbers disposed in order and learned by heart ... From which it follows that, for the acquiring of philosophy, some sensible moniments are necessary, by which our past thoughts may not only be reduced, but registered every one in its own order. These moniments I call marks ... The nature of a name consists principally in this, that it is a mark taken for memory's sake; but it serves by accident to signify and make known to others what we remember ourselves.

Essentially he's saying we need 'sensible moniments' in order to recall our own thoughts. He seems pretty extreme here, asserting that we can't even remember colors or quantities of objects without marks. Additionally, marks principally serve our thoughts, whereas it is an accident that marks are capable of making known to others what we remember ourselves.

For Hobbes, the meaning of words/marks is the thought associated with that word. Private language is possible in this way, because it is a simple process to assign a kind of ostensive definition to words by associating thoughts and feelings with memories.

However, Wittgenstein was critical of private languages. He attempted to show that private languages are meaningless, because without a method to check whether or not someone is using a system of language correctly, then private language is arbitrary.

Let us imagine the following case. I want to keep a diary about the recurrence of a certain sensation. To this end I associate it with the sign "S" and write this sign in a calendar for every day on which I have the sensation.--I will remark first of all that a definition of the sign cannot be formulated.--But still I can give myself a kind of ostensive definition.--How? Can I point to the sensation? Not in the ordinary sense. But I speak, or write the sign down, and at the same time I concentrate my attention on the sensation--and so, as it were, point to it inwardly.--But what is this ceremony for? for that is all it sems to be! A definition surely serves to establish the meaning of a sign.--Well, that is done precisely by the concentrating of my attention; for in this way I impress on myself the connection between the sign and the sensation.--But "I impress it on myself" can only mean: this process brings it about that I remember the connection right in the future. But in the present case I have no crterion of correctness. 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."

Essentially he's saying that Hobbes' method of ostensive definition is inherently contradictory. Hobbes says that we primarily use marks in order to recall thoughts, therefore he recognizes that our memory is fallible. If our memory is fallible, how can we know that we are using marks correctly? The answer is we don't. We need a 'criterion of correctness' as Wittgenstein calls it.

Personally, I'm not convinced by this argument. I'm not sure entirely sure where Wittgenstein is going with his private language argument. He wants to show that private languages are meaningless because without a criterion of correctness, it's arbitrary. But what bugs me is that a criterion of correctness is also arbitrary. You can devise an infinite number of ways to describe a pattern of associations within a language. He seems to be ignoring the fact that at its core, human language is entirely made up, whether you are discussing anything both within and without the mind.

He does have another example of a beetle in a box. Maybe that will help elucidate what he's saying. In this example, he is showing why we believe we are able to name sensations, such as 'pain', as if pain were a private object. But we are wrong, there is no such thing as me having a pain (me, and the pain, 2 objects), only the state of me-having-a-pain.

Now someone tells me that he knows what pain is only from his own case.--Suppose everyone had a box with something in it: we call it a "beetle." No one can look into anyone else's box, and everyone says he knows what a beetle is only by looking at his beetle.--Here it would be quite possible for everyone to have something different in his box. One might even imagine such a thing constantly changing.--But suppose the word "beetle" had a use in these people's language?--If so, it would not be used as the name of a thing. The thing in the box has no place in the language-game at all; not even as a something: for the box might even be empty.--No one can "divide through" by the thing in the box; it cancels out, whatever it is.

That is to say: if we construe the grammar of the expression of sensation on the model of "object and designation" the object drops out of consideration as irrelevant.

In all of this discussion, we're trying to get a grasp on language as it relates to inner subjective experience. Frege wanted to take this in a direction by thinking about language as it relates to the outer objective world. By reframing our analysis from subjective to objective we can solve 2 problems.

1. What would Hobbes say if you asked him what a sentence means? If marks are labels for memory, then the meaning of a sentence are the thoughts held by the speaker. However, the problem of other minds makes it impossible to know about the thoughts of another person, therefore it is impossible to know the meaning of a sentence.

2. When I say "chair", I'm not talking about the particular and variable psychology of a person who utters "chair", I am referring to the actual object in objective reality, not the conception in a person's mind when they utter chair.

One major idea he had was that words on their own don't meaning anything. The meaning of a word depends on the sentence it is within.

The thing that a word refers to is called its 'reference'. However, just knowing the reference of a word is not enough to understand it, here's the example Frege gives.

- The Morning Star is the Evening Star.

If the meaning of Morning Star was just its reference, then this sentence isn't informative at all. It would be equivalent to saying, "The Morning Star is the Morning Star."

We can find out whether 2 words have the same meaning by using compositionality in this way

- If two words or phases have the same meaning, then we can substitute one of them with the other in any sentence, S, without changing the meaning of S.

If we compare the following two sentences:

1. The Morning Star is the Evening Star.

2. The Morning Star is the Morning Star.

Clearly these have 2 different meanings, even though they both share the same referent. Frege explained that the Morning Star and the Evening Star differ in their mode of presentation, what he called 'sense'. Sense is a way of identifying the referent.

Now we can apply this to a whole sentence and ask what the meaning of a sentence is.

We now ask after the sense of reference of a whole assertoric sentence. Such a sentence contains a thought. Is this thought now to be regarded as its sense or its reference? Let us suppose for the moment that the sentence has a reference! Now replace a word in that sentence with another word with the same reference, but a different sense; then this can have no influence on the reference of the sentence. But now we see that the thought is in fact altered in such a case; because, for example, the thought of the sentence "The Morning Star is a body illuminated by the sun" is different from that in the sentence "The Evening Star is a body illuminated by the sun." Someone who didn't know that the Evening Star is the Morning Star could take one of these thoughts to be true and the other to be false. The thought then cannot be the reference of the sentence; we will do better to interpret it as its sense.

First, when he says thought he's talking about the objective content of the sentence, not thoughts in people's heads. Next, he says that the reference of a sentence is determined by its component references, and altering its senses will have no influence on the component references, and therefore alteration of sense has no influence on the reference of the sentence. Finally, we see that the thought of a sentence is altered by its sense.

The 'truth value' of a sentence is the same when we substitute co-referential words in the sentence. If the reference of a sentence is its truth value, then the sense of a sentence is the mode of presentation of a truth value, or its 'truth conditions'. If we know what determines whether a sentence is true or false, we know its truth conditions.

In simple statements, we have a subject and a predicate. In the sentence, "Michio is in Texas." 'Michio' is the subject, and 'is in Texas' is the predicate.

What can we say about the reference of the predicate (the 'extension') 'is in Texas'? If we take the statement 'X is in Texas', the reference of 'is in Texas' would be the class of objects that can be substituted in X and preserve the truth value.

What can we say about the sense of the predicate (the 'intension') 'is in Texas'? If we take the statement 'X is in Texas', and substitute 'is in the 2nd largest state in the U.S.' we get the same class of objects for X.

Intensionality has a problem though. Consider two sentences,

1. I believe that the Morning Star is Venus.

2. I believe that the Evening Star is Venus.

Frege realized, "one can only justifiably conclude that the Morning Star doesn't not always refer to the planet Venus." However, this is not a counterexample of compositionality for references, because we can give an explanation of both when and when not, why and why not, it refers to Venus.

Consider the open sentence,

1. ________ is the Morning Star.

A sentence such as this has the same truth value when we substitute in an expression with the same reference called the 'extensional context'.

If you consider this open sentence,

1. I believe that _______ is Venus.

we have to substitute terms with the same sense called the 'intensional context'.

In short, some terms require an extensional context, other terms require an intensional context.

1. The Morning Star is Venus. -- In this sentence, 'The Morning Star' is refers to its reference.

2. I believe that the Morning Star is Venus. -- In this sentence, 'the Morning Star' refers to its sense.

It's quite hard to get a grasp on all of this. We've only been looking at rather simple statements, and trying to apply these concepts to more complex expressions quickly gets out of hand.

Frege is attempting to explain the meaning of language in an objective context, partly because of prior failed attempts to explain the meaning of language in a subjective one beginning with Hobbes. He went beginning words and tried to assert that words and terms have meaning depending on the sentence it is used in. I find this awkward because although he asserts the primacy of the sentence, it's still difficult to analyze the meanings of sentences on their own.

Frege spoke German, and on top of that, was a mathematician, I feel that his approach to natural language is far too rigorous.

1. Hard division between sense and reference

2. Centering around sentences

First, I don't like this idea of "this is the reference" and "this is the sense". Let's use his example.

- The Morning Star is Venus.

We can change the sense,

- The Morning Star is the planet that appears at dawn and dusk.

We can just keep changing the sense an arbitrary number of times. There are an infinite number of senses we could substitute. In addition to that, I'm skeptical about whether 2 individuals can agree on what a reference is.

If I point at a chair that's right in front of me and you and say, "That's a chair." and you say, "Yep, that's a chair." It seems obvious that there is no question what the reference is here. We can both look at the chair, touch it, see it, and confirm that is indeed a chair, but this assumes that both of us are having a similar experience of the chair. My experience of the chair can potentially be quite different from your experience. Not only is there still the problem of other minds and the question of whether our phenomenological experiences are identical, but there are many different ways of looking at this chair. If I turn off the lights, we can see the chair in a dark room, and it now looks quite different. If I became a dog, and looked at the chair (which is perhaps colorful), it would look quite different. If I look at the chair by sticking my face in it versus looking at it from 20 feet away, the chair has seemingly taken on a very different reality. What is the true reference of "That" in "That is a chair."? Can we even know about it? Is the objective reality arbitrarily defined? If so, why is it even useful to discuss references if they are arbitrary and therefore meaningless?

I guess I'm uncomfortable with how Frege wants to apply mathematical rigidity to language, which is inherently slippery and turbulent. Not only that, but we've been limiting ourselves to actual words, what about body language and tone of voice? I would argue that all language is inherently meaningless, but, while meaningless, it also extremely useful.

Think about when the first human language developed. Perhaps in the beginning, someone made some sort of gesture with their body or made a sound with their voice while doing a behavior X. Over time, other people picked up on this and realized this was a useful behavior and began to expand the range of expressions and abstracted it until they were able to discuss a broad range of concepts and feelings. The only reason language began was because it was useful, not because it was meaningful.

I argue that language is useful to us because: Language is the manifestation of the human will to impose order on a world that is constantly trying to kill us. I grunt once at my friends to signal that this food is good to eat, and I grunt twice to signal that it is not good to eat. This is a useful behavior, but entirely arbitrary and inherently meaningless. As soon as this system of behavior becomes not useful, it becomes pointless. There no use for it even existing, and even if I used it, it would be an arbitrary act, among infinite possibilities of expression.

You can apply this to any language act. Anytime, anyone, anywhere expresses themselves through language, they are attempting to impose something on the world. They are attempting to acquire something, inspire thoughts and feelings in another, fulfill a physical, mental, or emotional desire etc.

For example, "That is a chair." For all practical purposes, this language act serves us well. Perhaps someone was looking for a chair. I found one, they haven't, so I point to a chair and say, "That is a chair." Great, now they can carry the chair or use it in some way. That language act was useful. Was it inherently meaningful? No, for the reasons I explained earlier (it's questionable what the reference is, we can define an infinite number of senses). However, between me and the target audience, we have an implicit agreement. Neither of us necessarily knows the rules of the language act, nor we do care, because our participation in it continues insofar as it remains useful.

There is a will within me, so I employ a tool known as language to impose this will upon the world. My voicebox vibrates, the atmosphere shudders, the listener receives the communication into their ear, which is processed by byzantine circuitry, and the world changes.

If this indentical situation occurred in another country, or the audience did not understand English, and I said, "That is a chair." they may not understand me, it may cause confusion, it wouldn't be useful. I may try a different language act, I may try to teach the other person, the other person may try to learn my language, I might go get the chair myself. It all depends on quite a lot of factors.

Focusing on the sentence as the determiner of meaning is not enough. I would go beyond the primacy of the sentence and discuss context and the universe itself as the determiner of "meaning". I use the word 'meaning' here a little loosely, in the sense that, we can narrow down the sense and reference of language acts, such that applying the language act is a benefit. For example in the chair example above, neither participant in the language act necessarily cares about some sort of metaphysical meaning of language. Although we often talk about understanding and expressing oneself clearly, both understanding and expression can be viewed as useful tools to survive in the world, and not as mutual agreements of meaning.

Now, Frege was German and a mathematician, it's no surprise he stopped at sentences. Germanic languages are not as reliant on context (but still metaphysically relevant) as other languages, they are fairly explicit. Japanese for example relies on context to determine the meaning of a statement quite a lot.

Many people like to say that the word order of Japanese is <subject> <object> <verb>. But the truth is, word order is very fluid in Japanese. There is a general word order that is often followed, but it is not strictly required. Next, a complete statement in Japanese only requires <verb>. That's it, just a verb. How is this possible?

Take the verb 'iku'. It's the plain form/dictionary form of "go". If you look it up in the dictionary, it will be iku. However, iku can mean to go, goes, will go, he goes, she goes, they go, possibly going and maybe even went and so on. Some meanings more common than others. How do you know what it means? With context. iku on its own doesn't mean much, but it can mean a wide variety of things depending on context.

This isn't an extreme example either, this is very common in Japanese, and omission of the topic/subject and even objects from the sentence, perhaps even no verb will occur. How can we even discuss statements, much less the reference and sense of a "sentence" when it's not even explicitly stated?

Finally, I'd like to make an analogy to clouds, I think language is similar to a cloudy sky. When you look up on an average day, there's probably some clouds up there. We often talk about the shapes of clouds, as if they have a well-defined geometry, but if we take a time-lapse video of clouds, we see that the skies are very turbulent. We've been biased by our own cognition to discuss the shape of something that is boiling and transient. Language is similarly turbulent, and yet we write dictionaries and grammar books. Even further than that, we often use language that breaks the rules of our grammar books, because there are no inherent rules or meanings, we are the playful inventors of language. We make the rules, and we will break them if it suits us.

Everyone has a different vocabulary size, enjoys a different choice of expressions, a different tone of voice, subtle differences in body language, an unique will that wishes to spill out into the world in a variety of ways in an increasingly complex civilization, unique experiences and personalities that affect their expression ...

An inability to define an objective referent, an infinite number of senses to hone in a referent, arbitrary and changing language rules, meaning that fluctuates with an arbitrarily broad context, misunderstandings in every day communication...

I'm having trouble accepting that language has any kind of inherent meaning at all. It seems like an imaginary toy, but a very useful one.

Edited by Michio

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