Logic

1. Difference
between
Validity & Truth

2. Proposition
Sentence • Claims about the world
• True if the world is as claimed ;
otherwise, false.
• Expressed by sentences

3. Same Proposition or Different one?
Case I :
Andy : “I’m hungry.”
Mary : “I’m hungry.”
Different
Proposition

4. Same Proposition or Different one?
Case II:
Andy : “I’m hungry.”
Jack : “Andy is hungry.”
Same
Proposition

5. Same Proposition or Different one?
Case III:
Taiwanese : “It rains.”
Japanese : “It rains.”
Different
Proposition

6. Argument
Premise 1
Premise 2
…
Premise N
─────────
Conclusion
Lists of
Propositions
Argument

7. Argument I
Premise 1 : I’m a man.
Premise 2 : You’re a woman.
Conclusion: : I’m better than you.
Argument II
Premise 1 : You either passed or failed Calculus.
Premise 2 : You have not failed Calculus.
Conclusion: : I’m better than you.
Argument

8. Argument I
Premise 1 : I’m a man.
Premise 2 : You’re a woman.
Conclusion: : I’m better than you.
Bad Logical
Structure

9. Argument II
Premise 1 : You either passed or failed Calculus.
Premise 2 : You have not failed Calculus.
Conclusion: : I’m better than you.
Whether the
proposition is
really correct ?

10. Necessarily Truth-Preserving(NTP)
•True Premises → Truth Conclusion
•It is impossible that all premises are true and the
conclusion is false.
Is this argument a NTP ?
P1: John is Mary’s brother.
C: Mary is John’s sister.

11. Valid
Argument
NTP • If an argument is a NTP
because of its good structure.
→ This argument is valid.

12. Argument I
P1: Everyone will die.
C: John will die.
Argument II
P1: Everyone will die.
P2: John is human.
C: John will die.

13. Truth is the property of Propositions.
Validity is the property of Arguments.
One argument is valid doesn’t guarantee its
conclusion is true !
Only if in the case that its premises are all true.

14. [True or False]If an argument has all false premises
and a true conclusion, it must be invalid.
E.g. P1: All students in NCCU are men.
P2: Steve Curry is a student in NCCU.
C: Steve Curry is a man.