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### It’s Logical

Deductive and Inductive Reasoning

What is Logic?

- 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

- 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

- 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.

Deductive reasoning

- 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.

Deductive reasoning

- 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

- 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

- 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.

Inductive REasoning

- 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?

Which is it?

- 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.

Which is it?

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.

Which is it?

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-reasoninghttp://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:

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