Two-Dimensional (2D) Semantics is a big deal these days in Philosophy and has been for the last decade or two. This is a really cool way of thinking about certain words that have puzzled philosophers for a some time, like ‘I’ and ‘here’ and ‘now’. But to understand what is weird about those words and what 2D semantics is, we have to start at the beginning with 0-Dimensional Semantics and work our way up through 1-Dimensional Semantics.
Before we get into that stuff though, what is semantics? Semantics is basically the study of what words and sentences mean. There are different kinds of semantics and the type of Semantics we will be discussing here is called formal semantics. The purpose of formal semantic theories is to describe logical rules for deciding what words and sentences mean and why. So for instance, what does ‘banana’ mean? One semantic theory might say the the word ‘banana’ refers to an idea or concept of banana that you have in your head. Others might say that ‘banana’ refers to that fruit over there on the table. These theories are important in general because they help us understand how science and language interact* and why we can talk about things that don’t exist like unicorns and my dancing skills. But specifically for our purposes these theories are important because they help us understand why sentences are true or false. Semantic theories give us a way of deciding if a sentence is true or false by describing the rules for using words to say true things. For instance, if I say “the banana is yellow,” we know that this is true because we know the rules that govern what ‘the banana’ and ‘is yellow’ mean: ‘the banana’ refers to a banana and ‘is yellow’ refers to it’s color. We know immediately if the the sentence is true because we can look at the fruit and see whether or not it is actually (1) a banana and (2) yellow colored. If it is both a banana and yellow, then the sentence ‘the banana is yellow’ is true. Different semantic theories give different ways of understanding why sentences that are more tricky than that one are true or false, but that is a basic example of how a semantic analysis would work.
Now that we know what semantics is, let’s talk about some weird words that behave differently than most words. To begin, we have to understand the most basic rules that govern words, which are called 0-Dimensional (0D) semantics. This is the sort of basic semantics we use when we say that ‘banana’ refers to bananas. Basically, we are saying that every word has an extension and that if you know what the extension of every word in a sentence is, then you can understand what the sentence means. For instance, the extension of ‘the banana’ is a banana, and the extension of ‘the red ball I have in my hand’ is the red ball I have in my hand. Above, we saw that we can decide the truth or falsity of the sentence ‘the banana is yellow’ if we look at the extensions of the words ‘banana’ and ‘yellow’. That is essentially what 0-Dimensional semantics does. It simply takes a word and assigns it to an extension. We use it to teach babies words when we hold up an object, like a ball, and say “ball” to the baby. Things can get a little tricky when we take into account the fact that more than one word can have the same extension. For instance, the words ‘gas’ and ‘petrol’ and ‘fuel’ all have the same extension. This is very important for the next part. But for 0D semantics, that’s about as complex as it gets.
Let’s take it up a notch. Things get a bit more complicated when we look at 1-Dimensional (1D) semantics. That last point about different words with the same extension is crucial. At some point, the people working on semantic theories realized that different words or phrases that have the same extension don’t always play by the same rules regarding that extension. Some words or phrases always refer to the same extension while other words or phrases sometimes refer to different extensions depending on different possible ways things could be. Take for instance an extension with a few different words and phrases like Michael Jordan. To refer to Michael Jordan, we can say ‘the most famous basketball player of all time’ or ‘the Nike spokesman’ or simply ‘Michael Jordan’. The first two phrases could refer to different people. If Michael Jordan had become a musician instead of a basketball player, maybe the extension of ‘the most famous basketball player of all time’ would be Kobe Bryant or someone else. And the same is true for ‘the Nike spokesman’. If Nike had chosen a different athlete, like Shaq, maybe he would be ‘the Nike spokesman’. But the last phrase, ‘Michael Jordan,’ always refers to the man Michael Jordan no matter what. There’s something special about the phrase ‘Michael Jordan’ that makes it different from the other two phrases. No matter what the man Michael Jordan did with his life, he would always be the extension of the phrase ‘Michael Jordan’. For semantics, that means that some words and phrases (like ‘Michael Jordan’) always pick out the same extension, while other words and phrases don’t (like ‘the most famous basketball player of all time’). Specifically, this means that words and phrases have a dimension of possibility in their meanings: some words and phrases could have other possible extensions than the ones they have right now while other words and phrases can only have the one extension they always have.
Now we are ready for 2D semantics. Philosophers in the last decade or two have begun to pay more attention to words like I, here, and now. These words are special because their meanings change depending on their context. Philosophers call these words indexicals. in some sense indexicals act a bit like the words in 1D semantics that always necessarily pick out one object. For instance, if Michael Jordan says “I am the most famous basketball player of all time,” the ‘I’ means the same man as the word ‘Michael Jordan’ and the sentence is true. But obviously ‘I’ and ‘Michael Jordan’ aren’t synonyms. For instance, if Roger Clemens said “I am the most famous basketball play of all time” the sentence would be false because ‘I’ would then mean ‘Roger Clemens’. This is what makes indexicals distinctive is that they change meanings depending on their context of use. Another simple example: if I say, “I am here” and you say “I am here”, we have just said two different things with the same words because the meanings of the words ‘I’ and ‘here’ are different in these sentences.
So let’s recap. With 0D semantics, words and objects are paired 1 to 1. The word ‘Ball’ means ball, and the word ‘banana’ means banana. Simple. In 1D semantics, words and objects still pair 1 to 1, but now we introduce the dimension of possibility to meaning: the words ‘Michael Jordan’ always necessarily mean the same object, i.e. the man Michael Jordan, but the words ‘the most famous basketball player of all time’ don’t always necessarily pick out the same object; they could possibly pick out any number of players who could have been the most famous basketball player of all time if Michael Jordan had never played basketball. Finally, in 2D semantics, words and objects still pair 1 to 1, and some still could possibly have other meanings while others still necessarily mean one thing, but now we add in the dimension of context: indexicals, like I, here, now, there, you, it, this, etc. all point to different objects depending on the context in which they are used.
In another post, I’ll explain some interesting results of understanding language this way.
*for instance, what do chemists mean when they say they “discovered that water is H2O?” If water has always been H2O, then did the word ‘water’ always mean H2O? If not, then weren’t we referring to something other than H2O when we used the ‘water’ beforehand? After all, how could we have been referring to H2O when we said ‘water’ if we didn’t know about H2O at all? But then how could we be referring to something other than H2O if that’s what water is? And if so, then doesn’t this mean that they discovered something about the word ‘water’ too, namely that it has a meaning we didn’t know it had? And doesn’t that mean that we don’t always know what our own words mean? But how could we not know what own words mean?