Venn Diagrams_aristotelian Vs Boolean Assumptions_hd.mp4 - Youtube - 1 - .mp4

Okay, if we're gonna be doing, uh...categorical logic with Venn diagrams, there's a little bit of a problem we gotta take a look at. There's no way of gettin' around it. When we're dealing with universal statements-- like all S are P, no S are P-- they're ambiguous. It took a long time for people to figure this out. We actually can mean two different things. There's no problem with the existential or particular statements-- some S are P, some S are not P. I'm only talkin' the all or no statements. Imagine we're at some bar or what not, and we're havin' some drinks. We're having a perfectly normal conversation. You're intelligent; I'm intelligent. We've had some college background. And, uh...I start bemoaning my lot in life, and I tell you this. I give you this A statement. I say the following, "All the dogs in my neighborhood are barkers." Okay, now...and I sigh just a little bit. What do you think I'm sayin'? What do you think I mean? I'm a normal person, you're a normal person, we're having a normal conversation. What I mean-- and you know what I mean-- is there's dogs in my neighborhood, and they'll bark. They're keeping me awake. That's why I'm kind of bleary-eyed right now. So you take pity upon me and buy the next round of beer. So when I say all S are P, you... I'm actually making two claims. This...the Ss exist, and every single one of them is a P. That's a very normal thing to say. All cats are animals, cats exist, and every single one of them's an animal. Uh...all Fords are...cars or vehicles. And what you're saying is, okay, Fords exist, and they're all vehicles. The conversation continues on a bit. Uh...we started remembering classes we took in college. I remember this Greek mythology class I took, and I want to say the following. I can tell you about unicorns. All unicorns are white animals. All unicorns are white animals. Well, what do you think I mean? I'm a perfectly normal, thoughtful, moderately educated guy. Do you think I believe in unicorns? No, I'm not nuts. I don't believe in unicorns. When I say all unicorns exist, what I mean is, if there were any unicorns, they would all be white animals. I also believe that all vampires are bloodsuckers, but I don't believe that vampires exist. And when I say all vampires are bloodsuckers, what I mean is, if there were any vampires-- and I don't say there are-- then they'd all be bloodsuckers. All leprechauns are little green Irish guys. I don't believe in leprechauns, but...maybe I believe that if you were a leprechaun, you'd be a little green Irish guy-- or maybe a little Irish... little green Irish gal. All mermaids are fishy-smelling creatures. I don't believe in mermaids, but I'm saying, if there were any mermaids, they'd all be fishy-smelling creatures. The second interpretation is called a modern-- or the Boolean--standpoint. George Boole kinda came up with the notion in the 19th century, so it's sometimes named after him. The modern, um...interpretation-- the Boolean interpretation. The other one--the first one's called a traditional-- or the Aristotelian interpretation. Aristotle invented a lot of this logic. He just was figuring we'd be talking about things that existed. So if somebody was to offer an S... or a statement like all S are P, they'd be meaning there's Ss in the world. They exist, and they're all Ps. Well, we gotta make this distinction. I make the following suggestion. If we see an argument, we look at the premises, and if the argument is about mermaids and unicorns, let's just use the Boolean standpoint-- or the modern standpoint. We won't assume they exist. We'll just assume the arguer is saying, if there were any unicorns, they'd all be white animals. If the arguments are about dogs, cats, rats, things that actually exist-- like raindrops-- uh...then we'll take the traditional standpoint-- or the Aristotelian standpoint. We'll assume, like in a perfectly normal conversation, that the person actually believes raindrops or dogs exist, and every single one of them is a pain in the neck, or whatever we might be saying. We'll come back to this when we start lookin' at the Venn diagrams. We'll want to make a decision as to whether the things exist or not. If they exist, we'll take the Aristotelian-- the traditional--standpoint. If the things don't exist, then we'll take the modern. What if we don't agree? What if it's angels? Then, we might wanna look at both interpretations and see what happens. If the argument's good both ways, it really doesn't matter. If the argument's bad both ways, it does matter. Um...well, it wouldn't matter. If the argument's good one way but bad the other, then it looks like the strength of the argument-- the validity of the argument-- is gonna depend upon how we understand that, uh...the premise. Let's keep it simple, and we'll take a look at some Venn diagrams. We'll deal with things that clearly exist or clearly don't exist, and we'll know how to handle the difference between the traditional and modern standpoints.