Bellwork 81607

1
Bellwork 8/16/07

• Give a single sentence definition of the
  following laws
• The Law of Identity
• The Law of Non-Contradiction
• The Law of Excluded Middle
• What are the 3 elements of an argument?

2
Todays Objective

• You will be able to create
• Deductive arguments
• Inductive arguments
• Valid arguments
• True arguments
• Sound arguments

3
Deduction vs. Induction
4
Deduction vs. Induction

• Deduction
• From general to particular
• Conclusion follows logically from the premises
• Arguments are valid or invalid

• Induction
• From particular observations to general
  conclusion
• Conclusion is only probable, not necessary
• Arguments are judged on degree of probability

5
Deduction

• From the general to the particular
• Ex All Vail High School students are
  well-behaved
• Shawn is a Vail High School student.
• Therefore, Shawn is well-behaved.

6
Deduction

• Lets look at another example
• Ex All philosophy students do better on tests.
• Billy is a philosophy student
• Therefore, Billy does better on tests.

7
Deduction

• Conclusions follow logically from the premises
• Nothing is added in that cannot be found in
  premises or in the inference
• It is not a guess or a generalization
• The conclusion (if valid) is derived from and
  supported by the premises

8
Deduction

• Valid or Invalid
• All about form structure
• Various forms are naturally valid
• Other forms are naturally invalid
• Has nothing to do with truth
• A valid argument can have false premises,
  a false conclusion, or both!!
• Validity only applies to deductive arguments

9
Induction

• From particular observations to a general
  conclusion
• Ex Ernie is a goof off a Vail High School
  student
• Susan is a goof-off a Vail High School student
• Robert is a goof-off a Vail High School
  student
• Therefore, all Vail High School students are
  goof-offs.

10
Induction

• Cont
• Phil is a philosophy student and does well on
  tests
• Susan is a philosophy student and does well on
  tests.
• It is likely that all philosophy students do
  well on the test
• Lets take a close look at the difference

11
Lets Compare

• Induction
• Phil is a philosophy student and does well on
  tests.
• Susan is a philosophy student and does well on
  tests.
• It is likely that all philosophy students do well
  on the test.

• Deduction
• All philosophy students do well on tests.
• Billy is a philosophy student.
• Therefore, Billy will do well on the test.

12
Induction

• Its all about making a generalization based on
  observations

13
Induction

• Conclusion is only probable,
• not necessary
• This is due to the fact that it is a
  generalization, not created by the premises
• Can be exceptions to the observations
• Exceptions may seem unusual or unlikely, but they
  can still exist

14
Induction

• Ex The sun rose this morning.
• The sun rose yesterday morning.
• The sun has risen every morning since
• the beginning of recorded history.
• The sun will rise tomorrow morning.
• This is an inductive argument

15
Induction

• Be careful!!
• If there are no indicators of probability
  (i.e., all vs. most, etc.), an argument could be
  twisted either way (deductive or inductive)
• People who own Jaguars are rich.
• Joey owns a Jaguar.
• Joey must be rich.

16
Induction

• Deductive
• All people who own Jaguars are rich.
• Joey owns a Jaguar
• Joey is rich.

• Inductive
• Most people who own Jaguars are rich
• Joey owns a Jaguar
• Joey is rich.

17
Induction

• Arguments are judged on degree of probability
• Has nothing to do with validity
• Has everything to do with probability
• Strength of premises create a probable or
  unlikely conclusion (either true or false)
• Big question Is this conclusion certain based
  upon the premises or only likely?

18
Induction

• Final note
• Correlation does not mean causation
• Ex I get up every morning when the sun rises.
• The sun rising causes me to get up.
• Most people who drink diet soda tend to work out.
• Drinking diet soda creates the urge to work out.

19
Deduction vs. Induction

• Deduction
• From general to particular
• Conclusion follows logically from the premises
• Arguments are valid or invalid

• Induction
• From observations to conclusion
• Conclusion is only probable, not necessary
• Arguments are judged on degree of probability
• Correlation does not mean causation.

20
Practice

• On your slate
• Write a deductive argument
• Write a inductive argument
• Now write an argument of your choice
• Be prepare to share with the class and see if we
  can guess which it is
• (deductive or inductive)
• Hint
• Watch your statements
• Watch your descriptors

21
Validity, Truth, and Soundness
22
Validity vs. Truth

• Validity
• Is it logically sound?
• Example
• 2
• 2
• 4
• The conclusion is logically inferred from the
  premises.

• Truth
• Is it true or false?
• Example
• All boys are mortal
• Caitlyn is a boy
• Caitlyn is mortal
• The conclusion can be logically inferred from the
  premises, but can be false.

23
Examples of Valid Arguments

• All mammals have lungs
• This bear is a mammal
• This bear has lungs
• No mammals have gills
• This bear is a mammal
• This bear does not have gills

• If you run the race, you will win the trophy
• You ran the race
• You won the trophy
• All men are mortal
• Socrates is a man
• Socrates is mortal

24
Examples of Invalid Arguments

• All mammals have lungs
• This bear is a mammal
• This bear has feet
• No mammals have gills
• This bear is a mammal
• This bear has gills

• If you run the race, you will win the trophy
• You ran the race
• You are tired
• All men are mortal
• Socrates is a man
• Socrates could not die

25
Examples of Valid, but False, Arguments

• All mammals have lungs
• This fish is a mammal
• This fish has lungs
• All humans have gills
• This bear is a human
• This bear has gills

• If you win the race, you will win the trophy
• You flew on your wings to win the race
• You won trophy
• All men are immortal
• Socrates is a man
• Socrates is immortal

26
Practice

• Which is the following? Valid or Invalid?
• True or False?
• All men have an X chromosome
• This teacher is a man
• This teacher has an X chromosome

27

• Valid True

28
Practice

• Which is the following? Valid or Invalid?
• True or False?
• All fish are immortal
• Otto is a fish
• Otto is immortal

29

• Valid but False

30
Practice

• Which is the following? Valid or Invalid?
• True or False?
• No students have jobs
• This boy is a student
• This boy has money

31

• Invalid False

32
Practice

• Which is the following? Valid or Invalid?
• True or False?
• Some students have jobs
• This boy is a student
• This boy has some money

33

• Invalid True

34
Practice

• Which is the following? Valid or Invalid?
• True or False?
• The sun rose yesterday
• The sun rose today
• The sun will rise tomorrow
• The sun will rise on Saturday
• Tonight it will be dark

35

• Invalid True?

36
Sound arguments

• A sound argument is BOTH
• Valid
• True
• These are the best arguments!!

37
Example 1

• All men are mortal
• Socrates is a man
• Socrates is mortal

38
Example 2

• All men have an X chromosome
• This teacher is a man
• This teacher has an X chromosome

39
Practice

• On your slate, write a
• Valid True argument
• Valid but False argument
• Invalid but True argument
• Invalid False argument
• Sound argument

40
Independent Practice

• On a piece of paper, create 5 arguments
• 2 Valid False
• 1 Invalid True
• 1 Invalid False
• 1 Sound
• Label the arguments
• Be prepared to share to with the group and well
  see if we can correctly guess which it is
• Put your name on the paper turn it in

41
Closure

• Deductive
• Inductive
• Valid
• Invalid
• True
• False
• Sound

42
Homework

• Worksheet, problems 9-17
• Answer them on a separate sheet of paper
• Staple the two together
• Due tomorrow 8/17