A Closer Look at Inductive vs. Deductive Reasoning

Deductive vs. Inductive Reasoning The difference: inductive reasoning uses patterns to arrive at a conclusion (conjecture) deductive reasoning uses facts, rules, definitions or properties to arrive at a conclusion.

Inductive reasoning - Think of it like a We start with specifics and move to generalities Deductive reasoning – think of it like a We start with generalities and move to specifics.

Examples of Inductive Reasoning Some examples Every quiz has been easy. Therefore, the test will be easy. The teacher used PowerPoint in the last few classes. Therefore, the teacher will use PowerPoint tomorrow. Every fall there have been hurricanes in the tropics. Therefore, there will be hurricanes in the tropics this coming fall.

Deductive Reasoning An Example: The catalog states that all entering freshmen must take a mathematics placement test. You are an entering freshman. Conclusion: You will have to take a mathematics placement test.

Inductive or Deductive Reasoning? Geometry example… 60◦ x What is the measure of angle x? Triangle sum property - the sum of the angles of any triangle is always 180 degrees. Therefore, angle x = 30°

Inductive or Deductive Reasoning? Geometry example… What is the next shape in the sequence?

All humans have 2 ears. Joe is human, therefore Joe has two ears. DEDUCTIVE

INDUCTIVE You are a good student. You get all A’s Therefore your friends must get all A’s too INDUCTIVE

DEDUCTIVE All oranges are fruits. All fruits grow on trees Therefore, all oranges grow on trees DEDUCTIVE

Mikhail hails from Russia and Russians are tall, therefore Mikhail is tall INDUCTIVE

Kristin is a law student. Most law students own laptops. So, probably Kristin owns a laptop. The indicator word test asks whether there are any indicator words that provide clues whether a deductive or inductive argument is being offered. Common deduction indicator words include words or phrases like necessarily, logically, it must be the case that, and this proves that. Common induction indicator words include words or phrases like probably, likely, it is plausible to suppose that, it is reasonable to think that, and it's a good bet that. In the example above, the word probably shows that the argument is inductive.   Go to next slide

No Texans are architects. No architects are Democrats. So, no Texans are Democrats. The strict necessity test asks whether the conclusion follows from the premises with strict logical necessity. If it does, then the argument is deductive.   In this example, the conclusion does follow from the premises with strict logical necessity. Although the premises are both false, the conclusion does follow logically from the premises, because if the premises were true, then the conclusion would be true as well. Go to next slide

Either Kurt voted in the last election, or he didn't. Only citizens can vote. Kurt is not, and has never been, a citizen. So, Kurt didn't vote in the last election. The common pattern test asks whether the argument exhibits a pattern of reasoning that is characteristically deductive or inductive. If the argument exhibits a pattern of reasoning that is characteristically deductive, then the argument is probably deductive. If the argument exhibits a pattern of reasoning that is characteristically inductive, then the argument is probably inductive. In the example above, the argument exhibits a pattern of reasoning called "argument by elimination." Arguments by elimination are arguments that seek to logically rule out various possibilities until only a single possibility remains. Arguments of this type are always deductive. Go to next slide

Arnie: Harry told me his grandmother recently climbed Mt. Everest.   Sam: Well, Harry must be pulling your leg. Harry's grandmother is over 90 years old and walks with a cane. In this passage, there are no clear indications whether Sam's argument should be regarded as deductive or inductive. For arguments like these, we fall back on the principle of charity test. According to the principle of charity test, we should always interpret an unclear argument or passage as generously as possible. We could interpret Sam's argument as deductive. But this would be uncharitable, since the conclusion clearly doesn't follow from the premises with strict logical necessity. (It is logically possible--although highly unlikely--that a 90-year-old woman who walks with a cane could climb Mt. Everest.) Thus, the principle of charity test tells us to treat the argument as inductive.   Go to next slide

Guided Questions Inductive vs Deductive reasoning What is deductive reasoning? What is inductive reasoning? What kind of reasoning in the comic? What are the 4 tests you can use to determine if an argument is deductive or inductive? Explain each test and give an example Go to the 2nd powerpoint on January 16th on the website and answer the scenarios with the guided questions into your ISN