Are we living in the same world?

One of the first unanswered questions that children tend to come up with goes something like "Are the colours you see the same as the colours I see?" In philosophy, this is known as the problem of inverted qualia. It goes roughly like this:

We have words for some subjective stimuli, like colour. For instance, the sky above us is blue (unless you're in California, in which case there's a reasonable chance it's orange). We can call lots of things blue, like the ocean, blueberries, and most of the flag of Iceland. People tend to agree on what is blue and what isn't. But we have no guarantee that when you and I look at the sky, we are having the same visual experience. Perhaps when you look at the sky, you perceive the colour I call "yellow", or some unique colour that I can't even perceive at all. How could we tell the difference? We might try to ask questions like "are blue and green similar colours?" but that doesn't ensure that we have the same subjective experiences, only that the experiences we assign the label "blue" to are similar to the experiences we assign the label "green" to. Your blue might be my yellow and your green my red.

So we can't directly compare sensory experiences. We only talk about how labels for experiences relate to each other. Our colour concepts are coherent, we can talk about how they relate to each other and we assign the same colour words to the same things, but they could represent different underlying realities and we would have no way of detecting them. That's fun to think about, but I'm far more interested in how a weaker version of this plays out. While the inverted qualia argument claims that there might be behaviourally undetectable differences in the subjective experiences we associate with the same terms, I think we have different understandings of virtually all concepts which are behaviourally very hard to detect.

We often use the same words to mean different things. This can cause confusion. For instance, if I say "The rational indicator function is integrable" you might be confused and say "no it's not!" We might go back and forth for a while before eventually discovering that I interpreted integrable to mean Lebesgue integrable while you interpreted it to mean Riemann integrable. There was no underlying mathematical disagreement, we just used the same word for different things.

That difference is easy to correct in math, where terms have clear definitions. In 99% of conversations, we're using ill-defined terms to describe the world around us as well as we can. I wonder how many arguments could have been avoided if both participants stated their definitions at the outset.

I'm not even sure whether "stating your definitions" is possible in the vast majority of cases, though. Many of the categories we talk about are clusters: they don't have clear rules defining whether something is in or out of the category, but any two of its members share some similarities. For instance, consider the category "game." How might we define "game?" Well, maybe games need to involve competition between more than one agent. But Solitaire is a game. You could say that games need to be fun, but the military does war games. Perhaps we could try to define games as interactive processes with fail states. But what about puzzles? A puzzle doesn't have a fail state, only a success state and a lot of intermediate states, yet people tend to agree that those are "games."

Wittgenstein labelled this "family resemblance." There's no clear definition of the category "game", but any two members of the category will share a number of features. There's another dimension along which our categories can differ, though. People often perceive membership in a category not as a boolean {in, out}, but some continuous value. For instance, you might agree that a dog is a pet and a goldfish is a pet, but a dog probably feels more pet-like to you. If you'd like to try to capture this intuition in words, feel free to give it a try, but I've never seen anyone successfully do it.

So it's really hard to directly compare categories. We can only talk about how the labels for categories relate to each other.

Suppose you wanted to discern how similar representations are to each other. One way to do this might be to get people to make judgements about how closely concepts are related to each other (Marti et al., 2019). Give people a set of phrases and ask them to rate a word or its opposite better applies to the phrase. For instance, you might be given a phrase like "making murder illegal" and asked to respond whether the term "freedom" or "prohibition" applied more closely to that situation. From those judgements, you can do some math to figure out how many unique concepts are represented by a word like "freedom." It can't necessarily give you a succinct definition of the different concepts of freedom, but it can tell you that people tend to be using it in (say) four different ways. We can look at the phrases to which each of these concepts applies to get a rough sense for what the definitions are.

More generally, I think that using similarity judgements to learn about the concepts people are using could be really useful. Suppose if, before getting into an argument about whether some idea would expand or constrict liberty, you first had to make a number of judgements about what is and isn't liberty. Then you might get a notification saying "just so you know, the person you are arguing with uses 'liberty' to refer to fairly different concepts than you do." Perhaps they use liberty #3 and #5, while you mostly use liberty #2. In general, asking people to rate how similar concepts are in conversation might be a useful and under-valued way to clear up misunderstandings.

This comes back to the classic phrase in lexical semantics, "tell me who  your friends are and I'll tell you who you are." I've never been able to find the source of this phrase, but I've heard it a lot and I think it captures a valuable way to learn about concepts. A concept such as liberty wouldn't make sense without other concepts, such as those of "person" and "choice." Maybe many concepts simply are their relationships to other concepts, and all we need to do to understand others' representations is inquire about how they relate to each other.

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