Testing Syllogisms with Venn Diagrams 2_hd.mp4 - Youtube.mp4

Mark: Okay, uh...let's do another Venn diagram. Why...because we can. Uh...this time, we'll take a look at an argument that appeals to things that don't exist. Um...there are some nut cases, I suppose, who believe unicorns exist. I wish mermaids existed, but I don't think that they do. If I'm having a conversation with somebody, I'm pretty sure they're gonna say these things don't exist. We can still argue about things that don't exist. Philosophers love doing that. We can actually get some interesting things discussed that way. But what do we do here? Well, again, I've got two universal premises, so it really doesn't matter which I do first. If one was particular, and one was universal, I'd do the universal one first. Um...what I think I will start by doing is I'm good at abbreviating. I like doin' that. Just so I can see the structure of the argument. No U are M. U for unicorns; M for mermaids. No mermaids are animals, and no unicorns...are animals. Your teacher may actually want you to do this. It seems pretty obvious, pretty straightforward, but sometimes people, um...still have a tough time seein' the structure of the argument. I kinda like having people do that. Let's label the argument. We've now, um...drawn our three circles, so we're gonna have two on the bottom, one at the top. We're, uh...we have the lower-left letter will be the lower-left circle. The lower-right letter will be the lower-right circle. And up above, we're gonna have one leftover. In this case, it'll be M for mermaids. Since these both are universal, it doesn't really matter which I do first. I'll arbitrarily start with the first one--no U are M. I know I'm gonna get shading, 'cause it's a universal statement. All and no statements will get shading. And it's gonna be somewhere in the U circle here. Somewhere in the U circle. What I'm thinking, again, in my mind, I'm looking at the U and the M circles. It's saying none of these Us are here, so I...and you shade where things are not. So I'd be shading this area. So I'm gonna shade right there. And that would be a picture of the first premise. Second premise-- no M are A. I'm focusing my attention on the M and A circles. I'm not gonna write it down every time. This is what I'm lookin' at-- the M and A circles. It says none of the Ms... none of these M things are in the A circle, so there's none... no Ms in here. You shade where things are not, so I'll shade that. So I ask myself, do these things exist-- unicorns and mermaids? They don't. Since they don't exist, we're done diagramming, and this would be a picture of the modern or Boolean standpoint. If these things did exist, I'd go, okay, then I'd be taking a look at the unicorn and the mermaid circles and see if there'd be a place to put an X. For instance, if mermaids existed, there's only one place for a mermaid to be, so I would put an X there. But mermaids don't exist, so no X. For unicorns, there's two quadrants here. I know unicorns... if unicorns existed, I'd be putting an X in here. Since I don't know if the X should go here or here, I would have an X on that line. But unicorns don't exist, so I'm done diagramming. So no existential Xs, if you will, for, uh...things that don't exist. So we now look at this and ask ourselves, is this enough information to guarantee that the conclusion's true? Well, for the conclusion to be true, the conclusion is about Us and As... again, this is what I'm doing in my head. I'm lookin' at the U and A circle. I would need to see this, because this is a picture of what the conclusion would be saying. Is it absolutely guaranteed this area's all shaded? No...this is shaded, but that isn't. I don't know what's going on. It might be full of things. It might be empty. I don't know. So there's not enough information in this picture to guarantee what the conclusion's saying, so this argument is invalid. If, um...this was completely shaded, then you could have valid arguments about unicorns. If this whole area was completely shaded, then it would be a valid argument.