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Difference
between
Validity & Truth
Proposition
Sentence • Claims about the world
• True if the world is as claimed ;
otherwise, false.
• Expressed by sentences
Same Proposition or Different one?
Case I :
Andy : “I’m hungry.”
Mary : “I’m hungry.”
Different
Proposition
Same Proposition or Different one?
Case II:
Andy : “I’m hungry.”
Jack : “Andy is hungry.”
Same
Proposition
Same Proposition or Different one?
Case III:
Taiwanese : “It rains.”
Japanese : “It rains.”
Different
Proposition
Argument
Premise 1
Premise 2
…
Premise N
─────────
Conclusion
Lists of
Propositions
Argument
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
Argument I
Premise 1 : I’m a man.
Premise 2 : You’re a woman.
Conclusion: : I’m better than you.
Bad Logical
Structure
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 ?
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.
Valid
Argument
NTP • If an argument is a NTP
because of its good structure.
→ This argument is valid.
Argument I
P1: Everyone will die.
C: John will die.
Argument II
P1: Everyone will die.
P2: John is human.
C: John will die.
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.
[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.

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第一週學習單:教學用Ppt

  • 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.