And share the screen.

I think that's about all.

So we were talking about philosophy of science essentially.

How can we find out anything about the meaning of language in a scientific way?

And we converged on this idea that we want to make theories,

theory sets of hypotheses from which as many as possible observable phenomena can follow

and non-scientific are falsifiable as well.

We basically ended up with this notion of a meaning theory.

And I won't do that. We're not going to look at foundational theories.

Much too hard and possibly uninteresting.

We looked at a couple for singular terms.

One of the meaning theories that you should know about is this idea of sense and reference.

That you need these two kind of parts.

And we ended up with the most certain principle which gave rise to this idea of meaning.

Right, so in practice what actually happens is truth to the truth is we tell the story.

We describe situations in which the sentence that we're looking at that exhibits a phenomenon here

that John chased the gangster in the red Ford's car in his attachment ambiguity.

We tell little stories.

We describe the worlds that make various readings true.

Importantly, these three are not equivalent.

We describe different dots which means that we have three readings.

Well, like these, we would probably be honest enough to say at least three.

There might be more.

But of course, syntactic theories typically tell us that we only have three syntactic structures.

So apart if gangster or lexical ambiguity for gangster sports car,

we should be relatively safe.

Okay, I also tried to convince you a little bit about this phenomenon of compositionality.

But just something I would like you to keep an eye on

because it's an important principle that is kind of so built into

computer science that we tend not to notice it anymore.

Essentially, if all of our processes are compositional, then the world is good.

If they're non compositional, the world is bad.

So the compositionality and the congruence principle really give us the chance to go from

truth to the truth, which only tells us about sentences.

We can actually maneuver things by having sentences that only differ in the things

we are interested in. We can use that. We can use the truth conditions and find out about smaller things.

The problem here is that this doesn't always work. We have to be careful. The embedding should enjoy its influence.

If it doesn't, like propositional attitudes we talked about, then we have a problem.

But that's not in and of itself. We just have to be careful in what we embed.

We can't use propositional attitudes or other withoutities.

So, and now what we want to do in this course mostly, and we've already started

in the lab, we want to use logic to deal with the truth conditions. Logic is something where we can

make all of these phenomena explicit. And we have a well understood way of dealing with truth and logic.

So basically what we're doing is we are defining a logical language model to be a logical system.

Remember a logical system has a formal language or formulae. We have a class of models and we have a satisfaction relation.

We basically say that this logical system models a natural language faithfully if the truth conditions are always met.

That's our test. And so really the truth conditions are something that human speakers have to

formulate. They're essentially the conjecture in physics, where you basically make predictions and you say,

well, if Kepler's theory is correct, then Mars should be somewhere over there at nine o'clock tonight.

And then you can look whether Mars is over there indeed, and if it's wrong, bye-bye Kepler.