How Do We Capture the Truth of Beliefs? Type Theory

How do we combine words to build full propositions? How do we account for what people believe, not just what's definitely true? In this week's episode, we talk about type theory: how we can define terms by how they relate to the world and each other, what the difference is between sense and reference, and how we can use possible worlds to work out what people believe.
This is Topic #83!
This week's tag language: Estonian!
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Last episode:
The Optimal Solution: Constraints on Sounds and Optimality Theory - • What Constraints Are T...
Other of our semantics and pragmatics videos:
Topic of Focus: How to Structure Information - • How Do We Signal What'...
Building Common Ground: Connecting in Conversation - • How Do We Create a Sha...
Scoping Out the Truth: Semantic Scope Ambiguities - • Semantic Scope Ambiguity
Our website also has extra content about this week's topic, discussing how kids learn how to rank their constraints, at: www.thelingspac...
(This link should be operating by Thursday evening.)
Find us on all the social media worlds:
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We also have forums to discuss this episode, and linguistics more generally.
Sources:
The three main sources for this episode:
Irene Heim & Angelica Kratzer's textbook, Semantics in Generative Grammar
Anders Schoubye's online lecture notes (schoubye.org/te...)
Kai von Fintel's Intensional Semantics online textbook/lecture notes (web.mit.edu/fin....
Looking forward to next time!

[@Pining_for_the_fjords]

I understood some of this but not all. I don't know if you mentioned this, but I've always found it interesting that the difference between the verbs 'believe' and 'know' doesn't depend on the person who believes or knows, and it doesn't depend on the thing they believe or know, but it depends on the belief of the speaker. For example you would say _"Sandra believes the earth is flat"_ if you were critical or neutral about her belief, but you would probably only say _"Sandra knows the earth is flat"_ if you also shared her belief. Yet both sentences say exactly the same thing about Sandra and the idea of the earth being flat, only the choice of whether it's referred to as knowledge, a belief or something else depends entirely on the speaker and their opinion of the clause in question.

[@oneheckofabanana2016]

I guess is this case "X knows Y" could be rephrased as "X believes Y and Y is true". With "X believes Y" we skip checking if Y is true and only care about whether X believes in Y. With "X knows Y" we do the same checks as with "X believes Y" but we do not skip checking whether Y is true. That's how I believe it works.

[@meanbeanmachine]

This is a fantastically lucid explanation. Subscribed. (Thanks to Steven Pinker for directing me here!)

[@thelingspace]

Thanks for watching! Glad you liked it. We've got some good stuff coming up, I think! And we're very grateful to Dr. Pinker for his support - he's really been a friend to the channel, and we really appreciate it. We did an interview with him last year, if you haven't seen it yet!

[@Abstract3030]

This is so important and interesting, I wish there was a series of videos about type theory and language. Great job.

[@ghofrant77]

You are amazing!! thanks a lot!! I had a course on this topic last semester in my masters, and you basically covered and explained almost everything in 10 minutes.

[@thelingspace]

Thanks! We tried our best for it. Glad you liked it! ^_^

[@TheAgoDuarte]

If the semantic type of believe is , how could we combine it with an entity ? Should we suppose that believe would be ?

[@Biped]

when exactly did this become a philosophy and mathematics channel? :D No, seriously. I'm stunned at how complex this everyday-thing is, everyone uses and takes for granted, the moment you look at it a little closer.

[@thelingspace]

Haha, well, I think that these are a couple of really cool things about language! First that it's such a broad field - like, really, theoretical semantics stuff basically is mathematics and philosophy stuff, and you can see the overlap there. But you also can find more psych and socio and anthro stuff in there, too. And second, yeah, there's so much stuff that goes into making it work that we don't even think about. Which is part of why it's so rich, and so interesting. Thanks for the comment. ^_^

[@Lucas_Simoni]

Seriously folks, the subject of this video puts bread on the table. lol I'm going down the rabbit hole of the idea of Domain-Driven Design (Eric Evans) approach to software development, and setting the proper vocabulary, semantics, etc, is part of the design of the system. It can be the difference between a garbage codebase that is bodged together and full of bugs, and one that can be expanded easily, and be as comprehensive as the domain is. See Also David Farley "Modern Software Engineering: Doing What Works to Build Better Software Faster", that's from where I got the recommendation.

[@cholten99]

Fascinating stuff I think we just got the tiniest insight into. Reminds me of predicate calculus for my undergrad days 20 years ago... Oh, nice Stranger Things theme btw folks :-).

[@thelingspace]

Thanks! And yeah, it's a challenge to fit everything in. We try to show something new and useful with it, but there's obviously a lot more to be said. ^_^

[@ucaneriste7497]

Yet another great topic to cover. Thank you very much. By the way, the beard suits you well. :)

[@thelingspace]

Thanks for watching! And thanks for the compliment, as well. ^_^

[@Edralis]

THE FACT THAT YOU DON'T HAVE TENS OF THOUSANDS OF VIEWS AND THOUSANDS OF LIKES FOR THE CONSISTENTLY AWESOME WORK THAT YOU ARE DOING ON THIS CHANNEL IS BEYOND COMPREHENSION

[@ouafaeslife123]

What semantic type has a trintransitive verb like „trade“? And what is the lexical entry ?? thanks

[@jacksonrosembachdeoliveira4281]

Nice presentation. Your examples helped a lot. I have been trying to understand the notations in Semantics, but they are a nightmare. I still don't get it why "students" is a type of "sentence".

[@anastasisstefas145]

Me neither!!!!! ahhahahaha

[@__WONTFIX__]

Hmmm, so basically we don't actually define intention, we just parameterize the type function so that we can notate that its there?

[@mohammedsalah2309]

I am a student whose major is English. I am an undergraduate student. I study Linguistics, Literature, and translation. Yesterday, I had the hardest linguistics' final exam ever. The course is Theoretical Linguistics . Damn, indeed it was the hardest exam ever.

[@nickel868]

At 4:03, why is there an extra set of brackets around the second "et"? Why is it not just , not ?

[@victorjauregui6721]

Going from what was said, I would've thought 'some' should be of type

[@brahimchouikha1412]

what should the type of the possessive morpheme 's be?

[@soupy4099]

hey! i loved that image on your shirt! i used to have it as a wallpaper, could i ask where you got it?

[@thelingspace]

Sure! I got it from Threadless, it's the Bad Memories design: www.threadless.com/product/2892

[@jahredtobin]

I spot the AD&D 2E Player's Handbook. HNNNGGGGG the nostalgia!

[@thelingspace]

That's our director Adele's! She provided her old D&D books for this one. Well spotted. ^_^

[@sg6091]

Good.make more videos

[@okuno54]

My question is (because I'm a sucker for meta), are these possible worlds given the 'entity' type, or do they have a different type? Since attitude verbs take their world from the subject rather than have them supplied explicitly, the world, and its type, are hidden in these example sentences. In sentences where possible worlds are manipulated explicitly, such as "I wish I lived in a world where unicorns were real," it looks on the surface like "a world where blah..." must be an entity. However, I would be surprised if this didn't lead to some serious foundational issues (along the lines of different speakers having different ideas about what worlds are/are not possible) which wouldn't be very good for a formal theory.

[@thelingspace]

A good question! Possible worlds are indeed treated as a different type (, confusingly). We have some discussion of this back on our website that addresses some of your points, but perhaps not the last one! Let me know what you think after you check it out: www.thelingspace.com/episode-83/

[@okuno54]

Ooooh, I had no idea there were extras! And the question you raise there about where to insert s into the types of words is interesting. I haven't looked at a variety of sentences, but first idea is to begin by making the complementizer obvious, as in "John believes that unicorns are real". Keeping as many of the types as naive as possible, what would the type of "that" be? If it is

[@qwertyTRiG]

What practical applications arise from this way of analysing language?

[@thelingspace]

Okay, so, if the question is just about why possible worlds semantics is useful, the idea helps to explain why certain verbs trigger presuppositions (e.g., why "believe" doesn't while "know" does), and it helps in talking about common ground - so, the knowledge that's shared between speakers. And, of course, the idea applies not just to the words we talked about in the episode, but to a whole range of attitudes that someone can have towards a sentence, like wishing that it were true, or even promising something. It's also hard to talk about the different kinds of modal verbs (may, must, might, can, should) without it, and it's useful in explaining certain kinds of ambiguities. More generally, intensional semantics covers all the factors that go into determining whether a sentence is true or false. Possible worlds are one tool, but whether sentences end up true or false also depends on when they're uttered, the context in which they're used, et cetera. So there are definitely plenty of topics for future semantics episodes!

[@andrewjonsson4400]

What practical applications Indeed. People tend to overlook the fact that Language (in general) and Semantics specifically are very good method of understanding human psychology and the working of the brain at a level that is not really possible using other avenues. Psychologist Steven Pinker has shown in several popular science works (and more academic studies, of course) that Linguistics as a disciple is just as correctly thought of and used as a branch of Psychology and Neuroscience is it a study of Communications and Sociology.

[@qwertyTRiG]

The Ling Space Thanks. I suppose that most of my reading in linguistics has been historical (language change) or sociolinguistics. This sort of stuff is quite alien to me, and I don't think I yet have enough context to appreciate it. I'll keep learning.

[@thelingspace]

Yeah, I think that this is really part of the thing about linguistics being so broad. You can really get into some parts of it, and only have a vague idea about the rest of it. I do know some about type theory, but I don't have the ability to write the script for this - that's why we have a team working on it. And if you've done a bunch on historical linguistics, you probably know more than me about it! The historical stuff we've done has also been by someone else. But I really enjoy getting to learn more about these different facets of it, too. Thanks for sticking with it. ^_^

[@qwertyTRiG]

I've not studied linguistics (yet! hoping to start in September). Got interested in etymological dictionaries as a kid, and have read a fair few of the "pop science" linguistics books out there directed to lay readers (which is mostly historical stuff). Have also read a couple of textbooks (An Introduction to Sociolinguistics, by Janet Holmes). My mother did Deaf Studies and Sign Language interpreting and I kept stealing her textbooks because they were so interesting.

[@harshtrivedi6605]

Hi ! Thanks a lot for all these videos. Would it be possible to cover CCG (en.wikipedia.org/wiki/Combinatory_categorial_grammar) in one of you videos? Thanks Again!

[@CoorDaLoor]

is this the same type theory that applies to programming languages

[@thelingspace]

Kind of, yeah! So, types are just ways of classifying different kinds of lambda expressions; they're syntactic categories, really. And to the extent that linguists and computer programmers alike use typed lambda calculi (untyped versions exist, too), we're talking about the same thing! Though, it's possible there's some special significance to the phrase "type theory" in computer science that we're not aware of. Thanks for the question!

[@justinward3679]

Leggo my eggo

[@thelingspace]

Our director took them home with her when she left, and I didn't get any! Sad.

[@rosenlogic]

stranger things references!

[@rashawnhoward564]

he got eggos in the corner