Video Transcript: Venn validity for immediate categorical inferences

Hi, I'm David Feddes and this talk is about vend validity for immediate categorical inferences.  Don't you just love the sound of that? If you want to impress your friends today just say, well,  today I happen to be thinking about Venn validity for immediate categorical inferences. Well,  anyway, no, we don't need to go try to impress others with big, big words. But that's what this talk is about. And it's going to be based again on the writings of Dr. Mathew Van Cleave. If you 

have a hard time following what is said in this video, go read what Dr. Van Cleave wrote, If  you had kind of a hard time following what he wrote, watch the video a time or two. And  hopefully between the video and the reading, an understanding of this will sink in. In studying these things. We've seen four kinds of statements that are categorical statements. There's  the universal Affirmative, all S are P S, as subject, P is your predicate, all S are P and the Venn  diagram looks like this where the part of S is blacked out, except for what intersect with P.  There's also the universal negative, no S, are P, and then you black out the intersection  because the two categories don't intersect at all. The third kind is particular Affirmative, some S are P and you put a little asterisk or star in the intersection to show that something at least  is in the intersection of those two categories. And fourth, there is the particular negative,  some S are not P. And you put an asterisk in the part that is not intersecting with P to show  that there's at least something in that's not included in the category of P. Now, as we think  about immediate categorical inferences, what do we mean? Well, there are arguments with  one premise. And one conclusion pretty simple. So here's an example. Some mammals are  amphibians. Conclusion, therefore, some amphibious things are mammals. What do we do  with that? Well, we start by making a Venn diagram, we make a Venn of the premise. Some  mammals are amphibious. And here's what it looks like. When you have a some statement,  then you put the asterisk in the intersection when you say that some S are P, then you put  that asterisk in the intersection. That's what your Venn diagram looks like. Now, what is the  Venn for our conclusion look like? Some amphibious things are mammals. That's our  conclusion. And you make the Venn diagram, you have the two categories, and in the  intersection, you put the asterisk. Now, when you compare the two Venn diagrams, what do  you have? You have identical Venn diagrams. And so you know that it's a valid argument if the two events are identical. In fact, they don't quite have to be fully identical. The main condition to know that if it's valid, is if the conclusion Venn contains no information that's not already  found in the premise, then you actually could have a Venn diagram for a premise that contain  more info than you find any conclusion. But as long as there's no information in the  conclusion, that's not already contained in the Venn diagram for the premise, then it's a valid  argument. And certainly, it's a valid argument when you just look at the Venns, and they're  identical Venn diagrams. Now let's look at an example of an invalid argument. All cars are  vehicles. Conclusion, therefore, all vehicles are cars, to work out the Venns for that. Here's the Venn diagram for all cars are vehicles. You take that category of car, and you block out  everything that doesn't intersect with the category of vehicles that shows you there may be  some things that are vehicles that aren't cars, but there are no things that are cars that aren't also intersecting with the category of vehicles. Now, what is the Venn diagram for its  conclusion look like? Therefore, all vehicles are cars. The Venn diagram looks like this, where  you black out everything in the category vehicle, except what intersects with the category of  cars. So you would be saying that there is nothing that's a vehicle that's not also a car. And  what happens when you compare those two Venn diagrams, you see that they are not the  same. And that means it's an invalid argument, because the conclusion then has information  that isn't found in the permissive, then what information is that? Well, one piece of  information is the claim that there are things that are cars that are not in the category of  vehicle, that's what the conclusion is saying. But you can see in the premise that that whole  area of cars is blacked out. Another thing that's shown in the conclusion that's not shown in  the premise is You're blacking out everything in the category of vehicles, except for intersects with cars. But in the premise conclusion, you had things that could be vehicles that aren't  cars. And so in looking at the two Venn diagrams, you see that the conclusion van has  information that's not contained in the premise van. And that means that you have an invalid  argument. For an argument to be valid the Venn test of validity, we have to know that the  information in the conclusion doesn't contain anything beyond what's contained in the 

premises. Now, the untested validity can apply even if we don't know words from a sentence,  even if we know only the form of the argument, but not the actual categories that are  involved in the argument if we only have S and P, subject and predicate. For example, all S  are P. Therefore, no P are S. Let's try that one out. All S are P. That's our premise. And here's  what the Venn looks like your blackout. Everything else that's not in the intersection was T for  our conclusion, no SRP, you black out the intersection, because you're saying that nothing can intersect with what's in P. And when you compare those two Venn diagrams, you know, what's an invalid argument? The conclusion Venn has information that's not found in the premise. It  claims in the conclusion that there are some things in the category S that are not in the  category P, but when you look at the premise, you see that all of S is blacked out except the  intersection. It also claims that there's nothing in the intersection of those two categories in  the conclusion, whereas the premise said there is something in that intersection. So there's  two pieces of information in the conclusion then that are not in the premise, then. So overall,  when we think about Venn validity for arguments like this, an argument is valid. If there's no  information in the conclusion, then that's not also in the premise then, and the argument is  invalid. If the conclusion then has information that's not also in the premise then