1. Deductive Arguments

2. Arguments
An argument is a set of claims put forward as reasons to believe some statement.

3. Arguments
An argument is a set of claims put forward as reasons to believe some statement.
The reasons are given in the premisses
The statement they support is the conclusion

4. Arguments
An argument is a set of claims put forward as reasons to believe some statement.
The reasons are given in the premisses
The statement they support is the conclusion
An argument
If children like ice-cream, and Bob is a child, then Bob likes ice-cream

5. Arguments
An argument is a set of claims put forward as reasons to believe some statement.
The reasons are given in the premisses
The statement they support is the conclusion
An argument in standard form
P1 Children like ice-cream
P2 Bob is a child
C Bob likes ice-cream

6. Arguments Two kinds of arguments
Deductive - conclusion doesn’t tell us more about the world than the premisses

7. Arguments Two kinds of arguments
Deductive - conclusion doesn’t tell us more about the world than the premisses
Inductive – does claim to tell us more

8. Arguments Two kinds of arguments
Deductive - conclusion doesn’t tell us more about the world than the premisses
If children like ice-cream, and Bob is a child, then Bob likes ice-cream
Inductive – does claim to tell us more

9. Arguments Two kinds of arguments
Deductive - conclusion doesn’t tell us more about the world than the premisses
If children like ice-cream, and Bob is a child, then Bob likes ice-cream
Inductive – does claim to tell us more
All the swans I have seen are black. Therefore all swans are black

10. Deductive Arguments Validity
If the premisses are true then the conclusion must be true

11. Deductive Arguments Validity
If the premisses are true then the conclusion must be true
All men are mortal
Socrates is a man
Socrates is mortal

12. Deductive Arguments Validity
If the premisses are true then the conclusion must be true
Note: if the premisses are false then the conclusion may be false

13. Deductive Arguments Validity
If the premisses are true then the conclusion must be true
Note: if the premisses are false then the conclusion may be false
All men are turtles
Socrates is a man
Socrates is a turtle

14. Deductive Arguments Validity Invalid:
If the premisses are true then the conclusion must be true
Note: if the premisses are false then the conclusion may be false
Invalid:
Even if the premisses are true the conclusion may be false

15. Deductive Arguments Validity Soundness
If the premisses are true then the conclusion must be true
Note: if the premisses are false then the conclusion may be false
Soundness
The argument is valid and the premisses are true
Note: the conclusion must be true

16. Deductive Arguments Logic
Some arguments are valid just because of their form
All men are mortal
Socrates is a man
Socrates is mortal

17. Deductive Arguments Logic
Some arguments are valid just because of their form
All men are mortal All A are B
Socrates is a man C is an A
Socrates is mortal C is B

18. Deductive Arguments Logic
Some arguments are valid just because of their form
All men are mortal All A are B
Socrates is a man C is an A
Socrates is mortal C is B
These are Formally Valid

19. Deductive Arguments Not Logic
Some arguments are not valid just because of their form
Socrates is a bachelor
Socrates is unmarried.

20. Deductive Arguments Not Logic
Some arguments are not valid just because of their form
Socrates is a bachelor A is a B
Socrates is unmarried A is C
Not much to say about these sorts of arguments

21. Logical Arguments Propositional logic Syllogistic
The logic of sentences and connectives
Syllogistic
The logic of categories

22. Propositional Logic Propositional Connectives Disjunction ‘… or …’
‘Grass is green or snow is white’ is true if ‘grass is green’ is true or ‘snow is white is true’

23. Propositional Logic Propositional Connectives Conjunction ‘… and …’
‘Grass is green and snow is white’ is true if ‘grass is green’ is true and ‘snow is white is true’

24. Propositional Logic Propositional Connectives Negation ‘not …’
‘Grass is not green’ is true if ‘grass is green’ is not true

25. Propositional Logic Propositional Connectives
Implication ‘if … then …’
‘If grass is green then snow is white’ is true if in any case that ‘grass is green’ is true it is also the case that ‘snow is white is true’

26. Truth Tables
Negation
A                not A
T                  F
F                  T

27. Truth Tables
Disjunction
A                B                A or B
T                T                  T
T                F                   T
F                T                  T
F                F                   F

28. Truth Tables
Conjunction
A                B                A and B
T                T                  T
T                F                   F
F                T                  F
F                F                   F

29. Truth Tables
Implication
A                B                A and B
T                T                  T
T                F                   F
F                T                  T
F                F                   T

30. Conditional Statements
‘if P then Q’ is a Conditional Statement.
P is the Antecedent
Q is the Consequent

31. Conditional Statements
‘if P then Q’ is a Conditional Statement.
P is the Antecedent
Q is the Consequent
The conditional ‘if P then Q’ can be drawn as

32. Conditional Statements
‘if P then Q’ is a Conditional Statement.
P is a sufficient condition for Q
Q is a necessary condition for P
If P is a necessary and sufficient condition for Q then Q is also a sufficient and necessary condition for P.  
                If P then Q and if Q then P.
This is a biconditional.
  P if and only if Q

33. Valid Arguments in PL Modus Ponens: If P then Q P Q
If you are English then you like fish and chips.
You are English.
So, you like fish and chips.

34. Valid Arguments in PL Modus Tollens: If P then Q not Q not P
If you are English then you like fish and chips
You don’t like fish and chips
So, you are not English

35. Formal Fallacies in PL Affirming the Consequent: If P then Q Q P
If you are English then you like fish and chips.
You like fish and chips.
So, you are English.

36. Valid Arguments in PL Denying the Antecedent: If P then Q not P not Q
If you are English then you like fish and chips
You are not English
So, you don’t like fish and chips

37. Syllogistic Categorical Propositions
All S are P Universal Affirmative A
No S are P Universal Negative E
Some S are P Particular Affirmative I
Some S are not P Particular Negative O

38. Syllogistic Sample Arguments No G are H All F are G No F are H
No men are perfect
All Greeks are men
No Greeks are perfect

39. Syllogistic Sample Arguments No G are H Some F are G Some F are not H
No philosophers are wicked
Some Greeks are philosophers
Some Greeks are not wicked

40. Euler Diagrams
Universal Affirmative
All S are P

41. Euler Diagrams
Universal Negative
No S are P

42. Euler Diagrams
Particular Affirmative
Some S are P

43. Euler Diagrams
Particular Negative
Some S are not P

44. Euler Diagrams
Sample Arguments
No G are H                            
All F are G                            
No F are H

45. Euler Diagrams Sample Arguments No G are H Some F are G
Some F are not H

46. Testing Arguments Disproving Validity
Method 1 — The Counterexample Method

47. Deductive Arguments Disproving Validity
Method 1 — The Counterexample Method
Determine the pattern of the argument to be criticised

48. Deductive Arguments Disproving Validity
Method 1 — The Counterexample Method
Determine the pattern of the argument to be criticised
Construct a new argument with:
(a) the same pattern
(b) obviously true premises; and
(c) an obviously false conclusion.

49. Deductive Arguments Disproving Validity
Method 1 — The Counterexample Method
Example
If God created the universe then the theory of evolution is wrong
The theory of evolution is wrong
God created the universe

50. Deductive Arguments Disproving Validity
Method 1 — The Counterexample Method
Example
If A then B B A

51. Deductive Arguments Disproving Validity
Method 1 — The Counterexample Method
Example
If Stephen is a wombat then Stephen is a mammal T
Stephen is a mammal T
Stephen is a wombat F !

52. Deductive Arguments Disproving Validity
Method 2 — Invalidating Possible Situations

53. Deductive Arguments Disproving Validity
Method 2 — Invalidating Possible Situations
Describe a possible situation in which the premises are obviously true and the conclusion is obviously false

54. Deductive Arguments Disproving Validity
Method 2 — Invalidating Possible Situations
Example (Fallacy of Affirming the Consequent)
If my car is out of fuel it won’t start
My car won’t start
My car is out of fuel

55. Deductive Arguments Disproving Validity
Method 2 — Invalidating Possible Situations
Example (Fallacy of Affirming the Consequent)
My car will indeed not start without fuel (it is a fuel-driven car) and the electrical system needed to start the car has been taken out for repairs (so it won't start). Yet the car has a full tank of petrol.

56. Deductive Arguments Disproving Validity
Method 2 — Invalidating Possible Situations
Example (Fallacy of Denying the Antecedent)
If the committee addresses wilderness values it must address naturalness
It will not address wilderness values
It need not address naturalness

57. Deductive Arguments Disproving Validity
Method 2 — Invalidating Possible Situations
Example (Fallacy of Denying the Antecedent)
Wilderness value involves, amongst other things, naturalness (Federal legislation actually defines 'wilderness value' this way). Moreover, the Committee's terms of reference do not include consideration of wilderness value (so it won't address it). Yet the Committee is explicitly formed to consider naturalness (to feed their findings into those of other Committees, so that a joint finding can be made regarding wilderness values)