In this video, I'm going to talk about some vocabulary. The three vocabulary words that I'm going to talk about are deductive reasoning, law of detachment, and law of syllogism. First off, I'm going to talk about deductive reasoning. Deductive reasoning is your basic ability of trying to draw a conclusion based on some predetermined properties or definitions or facts. So let's write that out.
Detective reasoning is drawing a conclusion based on facts, definitions, and properties. Okay, so these would be examples of if you knew a certain law, if you knew a certain definition or a property, you're able to draw a conclusion based on one of those definitions or properties. You're able to make a conclusion based on that.
Next off, we have the law of detachment. Next, we have the law of detachment. This is, you're going to have to understand a little bit of notation that we've used previously. If, we'll go over the definition first, if P then Q, so this little notation is what I was just talking about. This here is a conditional statement.
If you have a hypothesis and a conclusion, okay, if you have a hypothesis and conclusion, if you have what's called a conditional statement, if this conditional statement is true, then... The hypothesis P is true and Q, the conclusion, is true. If the hypothesis, if the conditional statement is in fact a true statement, then the pieces also have to be true.
Then P is true, P is true, and also Q is true. So if the entire... statement is true, that also means the pieces of that statement are going to be true. So here's a quick example. Here's a quick example of, get that out of the way, there we go.
Here's a quick example of what a law of detachment might use. So here we go. So if P then Q, so if I have a conditional statement, if that conditional statement is true.
So here we go. If I finish my chores, then I can go to the movies with my friends. That is a conditional statement. If, then statement.
So if. If both of those parts are true, say if I finish my chores, my parents say that I can go to the movies with my friends. If those hold true, then the individual pieces will also hold true. So if I did finish my chores, then I now go to the movies with my friends.
Both of those are going to be true. The individual pieces are going to be true. So that's an example of a law of detachment. Law of syllogism.
Law of syllogism, kind of a fun word to say, syllogism, in fact, uses some of the same notation, but is a little bit lengthier. If P then Q, if P then Q, so again, I have a conditional statement where I have if P then Q, and if Q then R, so I'm bringing in another conditional statement, but notice the pieces here. The first conditional statement, my conclusion, is the first part of my next statement, so that actually is the hypothesis here. Okay, so if P then Q, and if Q then R, okay, that's what the beginning of the law of syllogism is.
Then, then, then, oh, you know what, one thing that I forgot, one thing that I forgot, I'm always forgetting a few things here and there. One thing that I forgot is that we're talking about how true these statements are, if parts of these statements are true or false. So if P then Q and Q then R are true statements, then if P then R is also. True. So if I have two conditional statements where the conclusion of my first and the hypothesis of my second, if they're the same thing, and if they're both true statements, then I can say if P then R is also a true statement.
Now this is kind of confusing since we're just using definitions and we're using notation here. So let's see an actual example of this. So here's a very quick, very simple example. Bears are wild animals. Okay, so that's my first statement.
Bears are wild animals. Okay, so if an animal is a bear, then it is a wild animal. Okay, there's a conditional statement. And we have a second one.
If wild animals are dangerous. So if an animal is wild, then it is dangerous. There's my second conditional statement.
Both of these are true statements. Bears are wild animals, and wild animals are dangerous. Okay, we assume that all wild animals are dangerous for diseases or rabies or just in general.
I mean, animals are meant to survive out into the wild, and so they're not cuddly little creatures like we seem to think they are. Anyway, so if bears are wild animals, there's my first conditional. Wild animals are dangerous, there's my second conditional. They're both true statements.
Then I can also say that... Therefore, bears are dangerous. If bears are wild animals, and wild animals are dangerous, then bears can also be said to be dangerous.
See how we used the first part, very first bears, and then the very last part, they're dangerous. We brought that together saying bears are dangerous. So there's a very simple example of the law of syllogism.
Okay, that was a vocabulary review over deductive reasoning, law of detachment. and the law of syllogism.