This week we're going to be studying propositional logic, which is the rules that determine the validity of an argument based on the propositional connectives that are used in that argument. Now I've said a little bit about propositional connectives, but in order to say more about what propositional connectives are, in particular, in order to give the definition of propositional connectives, I have to start out by giving a definition of propositions. So what are propositions? A proposition is the kind of thing that can be true or false and that can be the premise or the conclusion of an argument. Let me give you some examples to illustrate that definition. See these binoculars? These binoculars are not a proposition. They can't be true or false, and they can't be the premise or the conclusion of an argument. See this hand? This hand is not a proposition. This hand cannot be true or false, and it can't be the premise or the conclusion of an argument. But now suppose I say the binoculars are in my hand. Now what I just said, that the binoculars are in my hand, that is the kind of thing that can be true or false. For instance, right now it's true, and right now it's false. It's also the kind of thing that could be the premise or the conclusion of an argument. For instance, I could say the binoculars are in my hand. Therefore, my hand is not free to shake yours. Or I could say, you just gave me the binoculars and I haven't let go of them. Therefore, the binoculars are in my hand. >> See? So that the binoculars are in my hand, that's a proposition. That's the kind of thing that can be true or false, and that can be the premise or the conclusion of an argument. Now, now that we know what propositions are, what's a propositional connective? A propositional connective is something that takes propositions and connects them to create new propositions. For instance, sometimes, in English, the word and can work as a propositional connective. So let me give you an example of how, in English, the word and can sometimes function as a propositional connective. So consider the proposition I'm holding the binoculars. That's a proposition. It's the kind of thing that can be true or false, and it's the kind of thing that can be the premise or the conclusion of an argument. Well, there's also the proposition I'm looking through the binoculars, right? That's the kind of thing that can be true or false, and it's the kind of thing that can be the premise or the conclusion of an argument. Well, you could use the word and to connect up those two propositions to make a new proposition. The new proposition would be I'm holding the binoculars and looking through them. See, now that's a proposition. It's the kind of thing that can be true or false, and it's also the kind of thing that could be the premise or the conclusion of an argument. For instance, right now it's true that I'm holding the binoculars and looking through them, whereas right now it's false that I'm holding the binoculars and looking through them. I could say, what you're seeing right now is really happening. Therefore, I'm holding the binoculars and looking through them. Or I could say, I'm holding the binoculars and looking through them. Therefore, I should not be driving a car right now. You see? So that I'm holding the binoculars and looking through them is also a proposition. It's the kind of thing that can be true or false, and it's the kind of thing that can be the premise or the conclusion of an argument. But it's a proposition that we created by combining two other propositions, namely the proposition I'm holding the binoculars and the proposition I'm looking through the binoculars, by combining those two propositions with the word and. So that's an example of how the word and, in English, can work as a propositional connective, connecting two propositions into a third proposition.