intro to logic

GLE 0701.5.5 Explore the concept of premises, including false

premises. 

Intro to Logic

ValidityWhat is logic?

ValidityWhat 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.

ValidityT All cats are mammalsT All mammals are

animalsT All cats are animals.

T All cats are mammalsF All mammals are felineT All cats are feline.

T All cats are mammalsT Circles are roundT All cats are animals.

T All cats are mammalsT All mammals are

animalsF Circles are squares.

ValidityT All cats are mammalsT All mammals are

animalsT All cats are animals.

Good Argument

T All cats are mammalsF All mammals are felineT All cats are feline.

Bad Argument

T All cats are mammalsT Circles are roundT All cats are animals.

Bad Argument

T All cats are mammalsT All mammals are

animalsF Circles are squares.

Bad Argument

ValiditySay 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!

Validity Truth Validity

Good Argument

ValidityT All cats are mammalsT All mammals are

animalsT All cats are animals.

Good Argument

T All cats are mammalsF All mammals are felineT All cats are feline.

Bad Argument

T All cats are mammalsT Circles are roundT All cats are animals.

Bad Argument

T All cats are mammalsT All mammals are

animalsF 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 mammalsT All mammals are

animalsT All cats are animals.

Good Argument

T All cats are mammalsF All mammals are felineT 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 mammalsT All mammals are

animalsT All cats are animals.

Good Argument

T All cats are mammalsF All mammals are felineT All cats are feline.

Bad Argument

ValidityT All cats are mammalsT Circles are roundT All cats are animals.

Bad Argument

T All cats are mammalsT All mammals are

animalsF 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 Truth Validity

Good Argument

Validity Truth Validity

Sound Argument

Validity

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

argument)

Validity

Is a valid argument a true argument?

ValidityIs 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.

VALID INVALID

True Premises + True Conclusion

True Premises + False Conclusion

False Premises + True Conclusion

False Premises + False Conclusion

VALID INVALID

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

ValidityValidity InvalidityVALID INVALID

True Premises + True Conclusion

True Premises + False Conclusion

False Premises + True Conclusion

False Premises + False Conclusion

ValidityValidityTo show that it is impossible for an argumentto have true premises and a false conclusion we have

to

InvalidityTo show that itis possible foran argumentto have true

premises anda false conclusion we simply

haveto come up with an example

where this occurs.

VALID INVALID

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.

Proof Counter-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?