A brief introduction to logic and argumentation. Revised edition.

1. Logic
reasons and reasoning
George Matthews
Fall 2015

2. theoretical reasons

3. theoretical reasons
reasons to believe
! My senses may tell me that the sun moves across
the sky.
! But what is really going on here – what should I
believe?

4. theoretical reasons
reasons to believe
! My senses may tell me that the sun moves across
the sky.
! But what is really going on here – what should I
believe?
! Whatever is based on the best available evidence.

5. practical reasons

6. practical reasons
reasons to act
! My impulses tell me to scream at that jerk.
! But is that really the best thing to do – what
should I do?

7. practical reasons
reasons to act
! My impulses tell me to scream at that jerk.
! But is that really the best thing to do – what
should I do?
! Whatever course of action is supported by the best
reasons.

8. the structure of an argument

9. the structure of an argument
an argument in standard form
Whatever is illegal is immoral.
Murder is illegal.
Thus murder is immoral.
premises
conclusion
! Premises are the given information we start with – our
reasons in support of the conclusion.
! The conclusion is what we are trying to establish.

10. Indicator words

11. Indicator words
premises
! Since . . .
! Because of . . .
! Assume for the sake of argument that . . .
! We all know that . . .

12. Indicator words
premises
! Since . . .
! Because of . . .
! Assume for the sake of argument that . . .
! We all know that . . .
conclusions
! Therefore . . .
! Thus . . .
! So we can see that . . .
! It follows that . . .

13. Identify Premises and Conclusion

14. Identify Premises and Conclusion
We know for a fact that my client was not at the scene of
the crime. Furthermore, the chief prosecution witness is a
known perjurer. Thus my client is not guilty.

15. Identify Premises and Conclusion
We know for a fact that my client was not at the scene of
the crime. Furthermore, the chief prosecution witness is a
known perjurer. Thus my client is not guilty.
in standard form
My client was not at the scene of the crime.
The chief prosecution witness is a known perjurer.
My client is not guilty.

16. Identify Premises and Conclusion

17. Identify Premises and Conclusion
Christopher Columbus was a criminal. This is because
whoever steals land or gold, enslaves people or kills
innocent people is a criminal and he did all of the these
things.

18. Identify Premises and Conclusion
Christopher Columbus was a criminal. This is because
whoever steals land or gold, enslaves people or kills
innocent people is a criminal and he did all of the these
things.
in standard form
Whoever steals land or gold, enslaves people or kills
innocent people is a criminal.
Christopher Columbus did all of the these things.
Christopher Columbus was a criminal.

19. What makes a good argument?

20. What makes a good argument?
! The best, most persuasive arguments are both valid and
sound.
definition: In a valid argument, if the premises are true,
the conclusion must be true.
definition: A sound argument is a valid argument with
premises that are really true.

21. Valid or invalid?

22. Valid or invalid?
All human beings are mortal.
Socrates is a human being.
Whoever is going to die worries about dying occasionally.
Socrates worries about dying occasionally.
If the premises are true must the conclusion also be true?

23. Valid or invalid?
All human beings are mortal.
Socrates is a human being.
Whoever is going to die worries about dying occasionally.
Socrates worries about dying occasionally.
If the premises are true must the conclusion also be true?
YES, this argument is VALID.

24. Valid or invalid?

25. Valid or invalid?
All human beings are animals.
Plato is an animal.
Plato is a human being.
If the premises are true must the conclusion also be true?

26. Valid or invalid?
All human beings are animals.
Plato is an animal.
Plato is a human being.
If the premises are true must the conclusion also be true?
NO, this argument is INVALID.

27. Valid or invalid?

28. Valid or invalid?
If abortion is wrong it should be illegal.
Abortion is wrong.
Abortion should be illegal.
Can the premises both be true and the conclusion be false?

29. Valid or invalid?
If abortion is wrong it should be illegal.
Abortion is wrong.
Abortion should be illegal.
Can the premises both be true and the conclusion be false?
No. The only way for the conclusion to be false is if at least
one of the premises were false, so this argument is VALID.

30. Valid or invalid?
If abortion is wrong it should be illegal.
Abortion is wrong.
Abortion should be illegal.
Can the premises both be true and the conclusion be false?
No. The only way for the conclusion to be false is if at least
one of the premises were false, so this argument is VALID.
But is it sound?

31. Sound or unsound?

32. Sound or unsound?
Poor people do not have much money.
It costs a lot of money to buy first class airline tickets.
So poor people do not fly first class except in unusual
circumstances.
This argument is VALID.

33. Sound or unsound?
Poor people do not have much money.
It costs a lot of money to buy first class airline tickets.
So poor people do not fly first class except in unusual
circumstances.
This argument is VALID.
The first premise is true by definition, the second is true in
fact.

34. Sound or unsound?
Poor people do not have much money.
It costs a lot of money to buy first class airline tickets.
So poor people do not fly first class except in unusual
circumstances.
This argument is VALID.
The first premise is true by definition, the second is true in
fact.
Thus this argument is SOUND, the conclusion is really true.

35. Sound or unsound?

36. Sound or unsound?
Poor people do not have much money.
If you do not have something, you must not want it.
So poor people are poor of their own free will, because they
want to be poor.
Are both premises of this argument true?

37. Sound or unsound?
Poor people do not have much money.
If you do not have something, you must not want it.
So poor people are poor of their own free will, because they
want to be poor.
Are both premises of this argument true?
The first premise is true by definition.

38. Sound or unsound?
Poor people do not have much money.
If you do not have something, you must not want it.
So poor people are poor of their own free will, because they
want to be poor.
Are both premises of this argument true?
The first premise is true by definition.
The second premise is false – so this argument is UNSOUND,
even though it is VALID.

39. Sound or unsound?

40. Sound or unsound?
If abortion is wrong it should be illegal.
Abortion is wrong.
Abortion should be illegal.
This is a VALID argument, but are the premises really true?

41. Sound or unsound?
If abortion is wrong it should be illegal.
Abortion is wrong.
Abortion should be illegal.
This is a VALID argument, but are the premises really true?
The second premise might be true but needs more support.

42. Sound or unsound?
If abortion is wrong it should be illegal.
Abortion is wrong.
Abortion should be illegal.
This is a VALID argument, but are the premises really true?
The second premise might be true but needs more support.
The first premise is false – not all that is wrong should be
illegal, can you think of an example?

43. Sound or unsound?
If abortion is wrong it should be illegal.
Abortion is wrong.
Abortion should be illegal.
This is a VALID argument, but are the premises really true?
The second premise might be true but needs more support.
The first premise is false – not all that is wrong should be
illegal, can you think of an example?
This argument is UNSOUND.

44. Summary: analyzing arguments

45. Summary: analyzing arguments
identify
argument

46. Summary: analyzing arguments
identify
argument
Is it
valid?

47. Summary: analyzing arguments
identify
argument
Is it
valid?
INVALID
discard

48. Summary: analyzing arguments
identify
argument
Is it
valid?
INVALID
discard
VALID

49. Summary: analyzing arguments
identify
argument
Is it
valid?
INVALID
discard
VALID
Are
premises
true?

50. Summary: analyzing arguments
identify
argument
Is it
valid?
INVALID
discard
VALID
Are
premises
true?
no: UNSOUND
discard

51. Summary: analyzing arguments
identify
argument
Is it
valid?
INVALID
discard
VALID
Are
premises
true?
no: UNSOUND
discard
yes: SOUND
accept