Fundamentals: Deductive Arguments

Hi! I'm Jeff Pynn, and I teach philosophy[br]at Northern Illinois University. In my earlier Introduction to Critical[br]Thinking video, I described the difference between deductive arguments and ampliative[br]arguments. In the next few videos, I'll talk a bit[br]more about each type of argument. Let's start with deductive arguments. An argument is a set of statements, called[br]its premises, that are meant to give you a reason to believe some further statement[br]called the argument's conclusion. In some arguments, the premises are meant[br]to guarantee that the conclusion is true. Arguments like this are called deductive[br]arguments. A good deductive argument can give you a[br]very good reason for believing its conclusion. After all, it guarantees that its [br]conclusion is true. But not all deductive arguments are good,[br]and so there are several things to think about when deciding whether to believe the[br]conclusion of a deductive argument. A good deductive argument really does[br]guarantee its conclusion. Part of what this means is that its[br]impossible for the premises to be true while the conclusion is false. When this is the case, we say that the[br]argument is valid. Now this is a special, technical use of[br]the word "valid." In ordinary life, we often use this word[br]to mean something like good, cogent, or reasonable. Like if you're disagreeing with someone[br]about something, and they respond to a claim you make by saying something that[br]seems pretty reasonable to you, you might say, "Well, I guess you have[br]a valid point." Though that's what the word often means[br]in ordinary life, it's not what the word means here. When philosophers say that an argument is[br]valid, they always mean this very specific thing: that if the premises are[br]true, the conclusion must also be true. There are several other Wi-Phi videos that[br]discuss this notion of validity in more detail. To say that an argument is valid is to say[br]something about the relationship between the premises and the conclusion. Namely, that if the premises are true, the[br]conclusion must also be true. But it's not to say that its premises or[br]conclusion are true. Consider, for example, this argument. Premise 1: Beyonce was born in Paris. Premise 2: Everybody who was born in Paris[br]loves cheese. Conclusion: Therefore, Beyonce loves[br]cheese. Those premises are false. Beyonce was born[br]in Houston, and I'm willing to bet that at least some people born in Paris hate[br]cheese. Still, it's a valid argument. If the premises were true, then the[br]conclusion would have to be true. But because the premises are false, this[br]argument doesn't give you a good reason to believe its conclusion, even though it's[br]valid. Philosophers call a valid argument with[br]true premises "sound." Like the word "valid," the word "sound" is[br]term with various meanings in ordinary life, and it can be used to describe some[br]claim as reasonable or compelling. But when philosophers describe an argument[br]as sound, they always mean this very specific thing: that it's valid, and that[br]its premises are in fact true. Here's a pretty boring sound argument. Premise 1: Beyonce was born in Houston. Premise 2: Everybody who was born in[br]Houston was born in Texas. Conclusion: Therefore, Beyonce was born in[br]Texas. For more discussion of the concept of a[br]sound argument, see Aaron Ancell's Wi-Phi video entitled[br]"Soundness." So, before deciding whether to believe the[br]conclusion of a deductive argument, you need to determine whether the argument[br]is sound. And this, in turn, requires determining[br]whether the argument is valid, and whether its premises are true. Well, how do you tell whether an argument[br]is valid? Sometimes, it's just obvious. But often,[br]it's not so obvious. One way to figure out whether an argument[br]is valid is to see if you can think of a[br]counterexample to it. A counterexample is a case, either real or[br]imaginary, where the argument's premises are true,[br]but the conclusion is false. So, for example, consider this argument. Premise 1: Classical musicians appreciate[br]opera. Premise 2: Beyonce is a pop star, not a[br]classical musician. Conclusion: Therefore, Beyonce doesn't[br]appreciate opera. Now, suppose that Beyonce's been listening[br]to opera since she was a little girl, and loves Mozart's Don Giovanni. Well, then she'd appreciate opera. The conclusion would be false, even though[br]the premises would still be true. It would still be true that classical[br]musicians appreciate opera, and that Beyonce is a pop star, not a[br]classical musician. This counterexample shows that the[br]argument isn't valid, and so that even if premises are true, the[br]argument doesn't provide you with a reason to believe its conclusion. There are other, more formal techniques[br]for figuring out whether an argument is valid, which we'll hopefully be able to[br]discuss in future videos. Now, if you don't know whether the[br]premises of an argument are true, then even if the argument really is sound,[br]it doesn't give you a good reason to believe its conclusion. When you know that an argument is valid,[br]but you don't know whether its premises are true, the argument gives you, at best,[br]a conditional reason to accept its conclusion. If you learn that its premises are true,[br]then you'll have to accept its conclusion. So, how do you tell whether an argument's[br]premises are true? Well, this isn't the kind of thing logic[br]or philosophy can give you much help with. To figure out whether an argument's[br]premises are true, you need to do some research. This is one reason why being a good[br]critical thinker requires more than just logical ability. It also takes a lot of real world,[br]empirical knowledge. Unless you know enough to know whether an[br]argument's premises are true, then even if you're a really brilliant logician and[br]know that the argument is valid, it doesn't give you reason to believe its[br]conclusion. The more you know, the better you'll be[br]able to evaluate deductive arguments. Subtitles by the Amara.org community