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

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Presentation transcript:

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

Validity What is logic?

Validity What is logic? A science that evaluates arguments.

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.

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.

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

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

Validity TruthValidity Good Argument

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

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

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.

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

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

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

Validity TruthValidity Good Argument

Validity TruthValidity Sound Argument

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

Validity Is a valid argument a true argument?

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.

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

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

VALIDINVALID True Premises + True Conclusion True Premises + False Conclusion False Premises + True Conclusion False Premises + False Conclusion

VALIDINVALID True Premises + True Conclusion   True Premises + False Conclusion   False Premises + True Conclusion   False Premises + False Conclusion  

Validity Invalidity VALIDINVALID True Premises + True Conclusion   True Premises + False Conclusion   False Premises + True Conclusion   False Premises + False Conclusion  

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. VALIDINVALID True Premises + True Conclusion   True Premises + False Conclusion   False Premises + True Conclusion   False Premises + False Conclusion   construct a proof via the rules of logic. This is why the rules are how they are. ProofCounter-example

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?