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It’s Logical

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It’s Logical

Deductive and Inductive Reasoning

- Logic – The science of correct reasoning.
- Reasoning– The drawing of inferences or conclusions from known or assumed facts.
- There are two main types of reasoning:
- Deductive
- Inductive

- Deductive reasoning is a method of drawing conclusions from premises based upon fact.
- The conclusions reached are mostlycertain, inevitable, inescapable as long as it is within logical bounds.

- Goes from a general statement to a specific instance.
- The structure of a deductive argument is very important to prove its validity. This is called a syllogism.
- Standard Structure: Ifthe premises are true, thenthe conclusion is necessarily true.

- Deductive reasoning does not grant new knowledge, but clarifies concepts that we already know about.
- It aims to produce true, valid conclusions but is dependent on experience with and prior knowledge of the premises.

- Examples:
- All men are mortal. (general) FACTSocrates is a man. (specific) FACTTherefore, Socrates is mortal. (conclusion)
- All high school students are teenagers. Claire is a high school student.Therefore, Claire is a teenager.

- Are there any other conclusions you could possibly come to given this information?
- What about this one?
- Some dogs are ill-behaved.Dogs are animals.Therefore, animals are ill-behaved.

- Athletes work out.Michael Jordan is an athlete.Therefore, _______________________________.
- Musicians are crazy.Madonna is a musician.Therefore, _______________________________.
- You create one!
- You create one!

- Inductive reasoning is a method of drawing conclusions based upon limited information.
- The conclusions reached are probable, reasonable, plausible, believable.
- Analogies and statistics are the basic forms of this type of argument.

- Goes from a series of specific cases to a general statement.
- Is a sophisticated replacement for the word “guessing”!

- Inductive reasoning is useful for gaining knowledge by understanding statistical patterns and identifying causes and effects.
- The terms valid and invalid cannot be accurately applied to inductive reasoning—only likely and unlikely.
- Inductive arguments cannot guarantee true conclusions even if the premises are true.

- Examples:
- Some horses are big.All horses have tails.Therefore everything that has a tail is big.
- What number comes next in this sequence? 2, 4, 6, 8, 10
- John just bought a car. His favorite color is blue. What color is John’s car?

- Do you KNOW the answers or do you ASSUME the answers?

- Tell whether the following arguments use inductive or deductive reasoning:
- All turtles eat vegetables. Betsy is a turtle. Betsy eats vegetables.
- Biff has a tattoo of an anchor on his arm. It is known that Sailors often get nautical tattoos.He probably served in the Navy.
- January has always been cold here in Siberia. Today is January 14, so it is going to be another cold day here.
- I knew the soccer game was on either Thursday or Friday. I just found out that it was not on Thursday, so the game must have been on Friday.
- All 15 of Ty’s cats like to play with yarn. He just adopted a new kitten and he is sure that she will definitely enjoy playing with yarn.

A sample of fifty drivers who were stopped by at a sobriety checkpoint on a Saturday at midnight revealed that one in four drivers were either uninsured, intoxicated, or both. Thus, if you get involved in an accident on the freeway there is a 25% chance the other motorist will be drunk or uninsured.

The local branch of Wachovia Bank was robbed yesterday. Jenny needed money to pay off her gambling debts. She just bought a gun two days ago, and I saw her hanging around the local Wachovia Bank yesterday morning. Today the bookie’s goons stopped looking for Jenny. So Jenny definitely robbed Wachovia Bank yesterday.

- http://factchecked.org/2007/lesson-plans/house-and-holmes-a-guide-to-deductive-and-inductive-reasoning/
- 5 Minute Mysteries:
- http://factchecked.org/Downloads/LessonPlans/DeductionInduction/student.handout.2.where.theres.a.will.pdf
- http://factchecked.org/Downloads/LessonPlans/DeductionInduction/student.handout.3.menagerie.murder.pdf
- http://factchecked.org/Downloads/LessonPlans/DeductionInduction/student.handout.4.fragment.serpentine.marble.pdf

- 5 Minute Mysteries: