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Intro to Logic

Intro to Logic

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Intro to Logic

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  1. Intro to Logic GLE 0701.5.5 Explore the concept of premises, including false premises.

  2. Validity • What is logic?

  3. Validity • What is logic? A science that evaluates arguments.

  4. Validity - True or False? All cats are mammals All mammals are animals  All cats are animals. All cats are mammals All mammals are feline  All cats are feline. All cats are mammals Circles are round  All cats are animals. All cats are mammals All mammals are animals  Circles are squares.

  5. Validity T All cats are mammals T All mammals are animals T  All cats are animals. T All cats are mammals F All mammals are feline T  All cats are feline. T All cats are mammals T Circles are round T  All cats are animals. T All cats are mammals T All mammals are animals F  Circles are squares.

  6. Validity T All cats are mammals T All mammals are animals T  All cats are animals. Good Argument T All cats are mammals F All mammals are feline T  All cats are feline. Bad Argument T All cats are mammals T Circles are round T  All cats are animals. Bad Argument T All cats are mammals T All mammals are animals F  Circles are squares. Bad Argument

  7. Validity Say it with me: Truth is not enough to make an argument good! Truth is not enough to make an argument good! Truth is not enough to make an argument good!

  8. Validity Truth Validity Good Argument

  9. Validity T All cats are mammals T All mammals are animals T  All cats are animals. Good Argument T All cats are mammals F All mammals are feline T  All cats are feline. Bad Argument T All cats are mammals T Circles are round T  All cats are animals. Bad Argument T All cats are mammals T All mammals are animals F  Circles are squares. Bad Argument

  10. Validity - Can you fill in the blanks? All A are B . All B are C .  All A are C . Good Argument All A are B . All B are C .  All A are C . Bad Argument All A are B . C are D .  All A are E . Bad Argument All A are B . All B are C .  D are E . Bad Argument

  11. Validity All A are B . All B are C .  All A are C . All A are B . All B are C .  All A are C . All A are B . C are D .  All A are E . All A are B . All B are C .  D are E .

  12. Validity All A are B . All B are C .  All A are C . All A are B . All B are C .  All A are C . T All cats are mammals T All mammals are animals T  All cats are animals. Good Argument T All cats are mammals F All mammals are feline T  All cats are feline. Bad Argument

  13. Validity All A are B . All B are C .  All A are C . Valid All A are B . All B are C .  All A are C . Valid T All cats are mammals T All mammals are animals T  All cats are animals. Good Argument T All cats are mammals F All mammals are feline T  All cats are feline. Bad Argument

  14. Validity T All cats are mammals T Circles are round T  All cats are animals. Bad Argument T All cats are mammals T All mammals are animals F  Circles are squares. Bad Argument All A are B . C are D .  All A are E . Invalid All A are B . All B are C .  D are E . Invalid

  15. Validity Truth Validity Good Argument

  16. Validity Truth Validity Sound Argument

  17. Validity Truth + Validity = Soundness (i.e. a good argument)

  18. Validity Is a valid argument a true argument?

  19. Validity Is a valid argument a true argument? No! A valid argument is one with a form that ensures if the premises are true, then the conclusion will be true. An argument where the conclusion follows from the premises.

  20. Validity An argument is valid if when the premises are true, the conclusion has to be true.

  21. Validity An argument is sound if it is valid, and the premises are true.

  22. Validity Validity Invalidity

  23. Validity Validity To show that it is impossible for an argument to have true premises and a false conclusion we have to Invalidity To show that it is possible for an argument to have true premises and a false conclusion we simply have to come up with an example where this occurs. construct a proof via the rules of logic. This is why the rules are how they are. Proof Counter-example

  24. Pop-quiz! Is a valid argument contain all truths? Is an argument that contains all truths a good argument? Can premises be valid? Can a valid argument have a false conclusion? Can an argument be true? How do you show invalidity?