1. Deductive and Inductive Reasoning
Mimi Opkins
CECS 100
Fall 2011

2. 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.

3. 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.

4. Examples of Inductive Reasoning
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.

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

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

7. Inductive or Deductive Reasoning?
Geometry example…

11. Deductive Reasoning
This method of reasoning produces results that are certain within the logical system being developed.
It involves reaching a conclusion by using a formal structure based on a set of undefined terms and a set of accepted unproved axioms or premises.
The conclusions are said to be proved and are called theorems.

12. 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.

13. Deductive Reasoning
Syllogism: An argument composed of two statements or premises (the major and minor premises), followed by a conclusion.
For any given set of premises, if the conclusion is guaranteed, the arguments is said to be valid.
If the conclusion is not guaranteed (at least one instance in which the conclusion does not follow), the argument is said to be invalid.
BE CARFEUL, DO NOT CONFUSE TRUTH WITH VALIDITY!

14. Deductive Reasoning Examples: All students eat pizza.
Claire is a student at CSULB.
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.

15. Deductive Reasoning Examples: All students eat pizza.
Claire is a student at CSULB.
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.

16. Deductive Reasoning 3. All math teachers are over 7 feet tall.
Mr. D. is a math teacher.
Therefore, Mr. D is over 7 feet tall.
The argument is valid, but is certainly not true.
The above examples are of the form
If p, then q. (major premise)
x is p. (minor premise)
Therefore, x is q. (conclusion)

17. Venn Diagrams
Venn Diagram: A diagram consisting of various overlapping figures contained in a rectangle called the universe U
This is an example of all A are B. (If A, then B.) B A

18. Venn Diagrams This is an example of some A are B.
(At least one A is B.)
The yellow oval is A, the blue oval is B.

19. Example
Construct a Venn Diagram to determine the validity of the given argument.
#14 All smiling cats talk.
The Cheshire Cat smiles.
Therefore, the Cheshire Cat talks.
VALID OR INVALID???

20. Example Valid argument; x is Cheshire Cat
Things
that talk
Smiling cats x

21. Examples #6 No one who can afford health insurance is unemployed.
All politicians can afford health insurance.
Therefore, no politician is unemployed.
VALID OR INVALID?????

22. Examples X=politician. The argument is valid. Politicians X
People who can afford
Health Care.
Politicians X
Unemployed

23. Example #16 Some professors wear glasses. Mr. Einstein wears glasses.
Therefore, Mr. Einstein is a professor.
Let the yellow oval be professors, and the blue oval be glass wearers. Then x (Mr. Einstein) is in the blue oval, but not in the overlapping region. The argument is invalid. x

24. 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.

25. 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 3 (31 days in a month).
The next number could be 4 (30 day month)
Or it could be 5 (29 day month – Feb. Leap year)
Or even 6 (28 day month – Feb.)

26. More Examples

27. All mammals are warm-blooded. So, all bats are warm-blooded.
All bats are mammals.
All mammals are warm-blooded.
So, all bats are warm-blooded.
All arguments are deductive or inductive.
Deductive arguments are arguments in which the conclusion is claimed or intended to follow necessarily from the premises.
Inductive arguments are arguments in which the conclusion is claimed or intended to follow probably from the premises.
Is the argument above deductive or inductive?

28. All mammals are warm-blooded. So, all bats are warm-blooded.
All bats are mammals.
All mammals are warm-blooded.
So, all bats are warm-blooded.
Deductive.
If the premises are true, the conclusion, logically, must also be true.

29. There are four tests that can be used to determine whether an argument is deductive or inductive:
·      the indicator word test
·      the strict necessity test
·      the common pattern test
·      the principle of charity test

30. 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.

31. 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.

32. 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.

33. 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.

34. Tess: Are there any good Italian restaurants in town?
Don: Yeah, Luigi's is pretty good. I've had their Neapolitan rigatoni, their lasagne col pesto, and their mushroom ravioli. I don't think you can go wrong with any of their pasta dishes.
Based on what you've learned, is this argument deductive or inductive? How can you tell?

35. Don: Yeah, Luigi's is pretty good
Don: Yeah, Luigi's is pretty good. I've had their Neapolitan rigatoni, their lasagne col pesto, and their mushroom ravioli. I don't think you can go wrong with any of their pasta dishes.
Inductive.
The argument is an inductive generalization, which is a common pattern of inductive reasoning. Also, the conclusion does not follow with strict necessity from the premises.

36. Is this argument deductive or inductive? How can you tell?
I wonder if I have enough cash to buy my psychology textbook as well as my biology and history textbooks. Let's see, I have $200. My biology textbook costs $65 and my history textbook costs $52. My psychology textbook costs $60. With taxes, that should come to about $190. Yep, I have enough.
Is this argument deductive or inductive? How can you tell?

37. I wonder if I have enough cash to buy my psychology textbook as well as my biology and history textbooks. Let's see, I have $200. My biology textbook costs $65 and my history textbook costs $52. My psychology textbook costs $60. With taxes, that should come to about $190. Yep, I have enough.
Deductive.
This argument is an argument based on mathematics, which is a common pattern of deductive reasoning. Plus, the conclusion follows necessarily from the premises.

38. Is the father's argument deductive or inductive? How can you tell?
Mother: Don't give Billy that brownie. It contains walnuts, and I think Billy is allergic to walnuts. Last week he ate some oatmeal cookies with walnuts and he broke out in a severe rash.
Father: Billy isn't allergic to walnuts. Don't you remember he ate some walnut fudge ice cream at Melissa's birthday party last spring? He didn't have any allergic reaction then.
Is the father's argument deductive or inductive? How can you tell?

39. Mother: Don't give Billy that brownie
Mother: Don't give Billy that brownie. It contains walnuts, and I think Billy is allergic to walnuts. Last week he ate some oatmeal cookies with walnuts, and he broke out in a severe rash.
Father: Billy isn't allergic to walnuts. Don't you remember he ate some walnut fudge ice cream at Melissa's birthday party last spring? He didn't have any allergic reaction then.
Inductive.
The father's argument is a causal argument, which is a common pattern of inductive reasoning. Also, the conclusion does not follow necessarily from the premises. (Billy might have developed an allergic reaction to walnuts since last spring.)

40. John is a Luddite. It follows that he doesn't believe in technology.
Is this argument deductive or inductive? How can you tell?

41. John is a Luddite. It follows that he doesn't believe in technology.
Deductive.
This argument is an argument by definition, which is a common pattern of deductive inference. Also, the phrase "it necessarily follows that" is a deduction indicator phrase. Also, the conclusion follows from the premises.

42. Larry: Do you think Representative Porkmeister will be re-elected?
Norman: I doubt it. Porkmeister's district has become more conservative in recent years. Porkmeister is a liberal Democrat, and 63% of the registered voters in his district are now Republicans.
Is this argument deductive or inductive? How can you tell?

43. Larry: Do you think Representative Porkmeister will be re-elected?
Norman: I doubt it. Porkmeister's district has become more conservative in recent years. Porkmeister is a liberal Democrat, and 63% of the registered voters in his district are now Republicans.
Inductive.   
This argument is both a statistical argument and a predictive argument, which are two common patterns of inductive reasoning. Also, the conclusion does not follow necessarily from the premises.

44. Is this argument deductive or inductive? How can you tell?
If Buster walked to the game, then he didn't drive to the game. Buster didn't drive to the game. Therefore, Buster walked to the game.
Is this argument deductive or inductive? How can you tell?

45. If Buster walked to the game, then he didn't drive to the game
If Buster walked to the game, then he didn't drive to the game. Buster didn't drive to the game. Therefore, Buster walked to the game.
Deductive.
This argument is a hypothetical syllogism, which is a common pattern of deductive reasoning.
Note, however, that the conclusion does not follow logically from the premises. (Maybe Buster rode his bike to the game, for example.) The argument commits the fallacy of "affirming the consequent."