STATISTICAL GENERALIZATIONS
One classic example of an inductive argument is an opinion poll. Suppose a candidate wants to know how popular she is with voters. Because it would be practically impossible to survey all voters, she takes a sample of voting opinion and then infers that the opinions of those sampled indicate the over- all opinion of voters. Thus, if 60 percent of the voters sampled say that they will vote for her, she concludes that she will get around 60 percent of the vote in the actual election. As we shall see later, inferences of this kind often
1. The sun is coming out, so the rain will probably stop soon.
2. It’s going to rain tomorrow, so it will either rain or be clear tomorrow.
3. No woman has ever been elected president. Therefore, no woman will ever be elected president.
4. Diet cola never keeps me awake at night. I know because I drank it just last night without any problems.
5. The house is a mess, so Jeff must be home from college.
6. If Harold were innocent, he would not go into hiding. Since he is hiding, he must not be innocent.
7. Nobody in Paris seems to understand me, so either my French is rotten or Parisians are unfriendly.
8. Because both of our yards are near rivers in Tennessee, and my yard has lots of mosquitoes, there must also be lots of mosquitoes in your yard.
9. Most likely, her new husband speaks English with an accent, because he comes from Germany, and most Germans speak English with an accent.
10. There is no even number smaller than 2, so 1 is not an even number.
1. The following arguments are not clearly inductive and also not clearly deductive. Explain why.
a. All humans are mortal, and Socrates is a human, so Socrates is likely to be mortal also.
b. We checked every continent there is, and every raven in every continent was observed to be black, so every raven is black.
c. If there’s radon in your basement, this monitor will go off. The monitor is going off, so there must be radon in your basement. (Said by an engi- neer while running the monitor in your basement.)
2. In mathematics, proofs are sometimes employed using the method of mathematical induction. If you are familiar with this procedure, determine whether these proofs are deductive or inductive in character.