DEDUCTIVE vs. INDUCTIVE REASONING Section 1.1

Problem Solving Logic – The science of correct reasoning. Reasoning – The drawing of inferences or conclusions from known or assumed facts. When solving a problem, one must understand the question, gather all pertinent facts, analyze the problem i.e. compare with previous problems (note similarities and differences), perhaps use pictures or formulas to solve the problem.

Scientific Observations Scientific observations can be made directly with our own senses or may be made indirectly through the use of tools. In science, observations are used as evidence to help us figure out which of our explanations are correct.  MISCONCEPTION: Scientists' observations directly tell them how things work (i.e., knowledge is "read off" nature, not built). Correction: Scientists build knowledge through a complex process that involves coming up with ideas about how things work and then seeing if observations back those explanations up

Scientific Inferences Inferences are explanations or interpretations of what you are observing. They are statements that explain what you are observing. Process of Inferring Observe an object, event, or situation. Gather information through experimentation or observation. Think about what you already know and what you find. Look at your results and compare them to what you previously thought.

At five feet six and a hundred and ten pounds, Queenie Volupides was a sight to behold and to clasp. When she tore out of the house after a tiff with her husband, Arthur, she went to the country club where there was a party going on. She left the club shortly before one in the morning and invited a few friends to follow her home and have one more drink. They got to the Volupides house about ten minutes after Queenie, who met them at the door and said, “Something terrible happened. Arthur slipped and fell on the stairs. He was coming down for another drink—he still had the glass in his hand— and I think he’s dead. Oh, my God—what shall I do?” The autopsy conducted later concluded that Arthur had died from a wound on the head and confirmed that he’d been drunk.

Slip or Trip?

Inductive Reasoning Inductive Reasoning, involves going from a series of specific cases to a general statement. The conclusion in an inductive argument is never guaranteed. Example: What is the next number in the sequence 6, 13, 20, 27,… There is more than one correct answer.

Inductive Research Approach Inductive reasoning works the other way, moving from specific observations to broader generalizations and theories Informally, sometimes we call this a “bottom up” approach. Conclusion is likely based on premises Involves a degree of uncertainty

Inductive Reasoning Here’s the sequence again 6, 13, 20, 27,… Look at the difference of each term. 13 – 6 = 7, 20 – 13 = 7, 27 – 20 = 7 Thus the next term is 34, because 34 – 27 = 7. However what if the sequence represents the dates. Then the next number could be 4 (31 days in a month).

Deductive Reasoning Deductive Reasoning – A type of logic in which one goes from a general statement to a specific instance. The classic example All men are mortal. (major premise) Socrates is a man. (minor premise) Therefore, Socrates is mortal. (conclusion) The above is an example of a syllogism.

Deductive Research Approach Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a"top-down" approach.. Conclusion follows logically from premises (available facts)

Deductive Reasoning Examples: All students eat pizza. Claire is a student at Medaille. Therefore, Claire eats pizza. 2. All athletes work out in the gym. Barry Bonds is an athlete. Therefore, Barry Bonds works out in the gym.

Deduction Vs. Induction commonly associated with “formal logic.” involves reasoning from known premises, or premises presumed to be true, to a certain conclusion. the conclusions reached are certain, inevitable, inescapable. Induction commonly known as “informal logic,” or “everyday argument” involves drawing uncertain inferences, based on probabalistic reasoning. the conclusions reached are probable, reasonable, plausible, believable.

Sample Deductive and Inductive Arguments Example of Deduction major premise: All tortoises are vegetarians minor premise: Bessie is a tortoise conclusion: Therefore, Bessie is a vegetarian Example of Induction Boss to employee: “Mark has a tattoo of an anchor on his arm. He probably served in the Navy.”

Other types of deductive arguments Suppose the following statements are all true: Person L is shorter than person X Person Y is shorter than person L Person M is shorter than person Y What additional piece of information would be required to conclude that “Person Y is shorter than Person J”? Person L is taller than J Person X is taller than J Person J is taller than L Person J is taller than M Person M is taller than Y Solution: Answer C M < Y < L < X So, if J is taller than L, Y must be shorter than J

Other types of deductive arguments A mother wants to order one large pizza, with exactly 5 toppings for her three picky children. She can choose from 7 toppings; cheese, mushrooms, olives, ham, sausage, onions, and pineapple. Fifi says there has to be pineapple Mona says there cannot be any olives Rex says that if there is going to be sausage, then there has to be ham too. Which combination of toppings should she select if she is to satisfy all three children’s combined demands? pineapple, onions, cheese, mushrooms, sausage cheese, sausage, ham, olives, pineapple cheese, mushrooms, ham, onions, pineapple sausage, mushrooms, onions, cheese, and ham.

the five topping solution cheese mushroom olive ham sausage onion pineapple Fifi Yes Mona No Rex then ham if sausage Note: the statement “if sausage, then ham” doesn’t imply “If ham then sausage.” The obverse doesn’t necessarily follow.