 In addition to being able to use the rules of inference, it's almost as important to be able to identify logical fallacies, and these occur as follows. Sometimes we wish that a statement has a certain truth value. A logical fallacy occurs when we conclude a statement has the truth value even when it might have the opposite truth value. For example, suppose the conditional if A then B is true and A is false. Let's explain why concluding B is false is a logical fallacy. In other words, you know the antecedent is false and the conditional is true. And so the question is, are you willing to put $20 on the claim that the consequent is false? Well, that would probably be a bad idea to see why let's set up a truth table. And since we know the conditional is true and A is false, we know that we're in one of these two cases. So from our truth table, we saw that B could be true or false. So if we claim it's false, it could have been true and that's a $20 lesson on logical fallacies. So deciding that B must be false is a fallacy since it could be true. And it's worth pointing out it won't help us if we claim that B is true because it could actually be false. And if we make that claim, that also is a fallacy and it'll cost us another $20. And this fallacy is so common it actually has its own name. Claiming the consequent false because the antecedent is false is a logical fallacy known as denying the antecedent. So for example, suppose if this is Tuesday, this must be Belgium. If it's Monday, why can't we conclude that it's not Belgium? So again, suppose is math speak for let's assume this is true. We're assuming the conditional if this is Tuesday, then this must be Belgium. That's if A, then B. And if it's Monday, that's the same as saying it's not Tuesday. That's the negation of A. But if we conclude it's not Belgium, the negation of B, we're denying the antecedent. That's our logical fallacy. How about another one? Suppose if A, then B is true and B is true. Let's explain why concluding A is true is a logical fallacy. So again, our Hexter guarantees that B is true and the conditional if A, then B is also true. Are you willing to put $20 to say that A is true? And we can set up a truth table. We know the conditional is true and the consequent is true, which puts us in one of these two cases. And there's no way of knowing which case we're in. And since A could be true or false, then concluding that A is true is a fallacy. And we're likely to lose our $20. And again, this logical fallacy is so common that it has its own name claiming the antecedent true because the consequent is true is a logical fallacy known as affirming the consequent. So assume that if it's raining, I'm carrying an umbrella and that I'm carrying an umbrella. Can you conclude that it's raining? So we're assuming the conditional, if it's raining, then I'm carrying an umbrella. We're also assuming that I'm carrying an umbrella. But if we conclude it's raining, we're affirming the consequent, a logical fallacy. The third common logical fallacy emerges as follows. Suppose the disjunction A or B is true and we also know that A is true. Explain why concluding that B is false is a fallacy. So again, our Huckster sets up the table and guarantees that both A is true as well as A or B is true. So are we willing to put $20 down on the claim that B is false? Well, let's set up our truth table. So we see that A or B is true and A is true could be in one of these two lines. So B could be true or false. So if we claim it's false, that's a fallacy and we'll lose our $20. So again, this is a common enough fallacy that it has its own name, requiring only one term of a disjunction to be true is the fallacy of affirming a disjunct. So you can have cake or ice cream. If you have cake, are you unable to have ice cream? So we're assuming the disjunction, you can have cake or you can have ice cream. We're also assuming that you have cake. But if we conclude you can't have ice cream, that's the negation of B we're affirming a disjunct, which is a logical fallacy. And in particular, you can have both cake as well as ice cream.