intro to logic
DESCRIPTION
Intro to Logic. GLE 0701.5.5 Explore the concept of premises, including false premises. 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. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/1.jpg)
GLE 0701.5.5 Explore the concept of premises, including false
premises.
Intro to Logic
![Page 2: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/2.jpg)
ValidityWhat is logic?
![Page 3: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/3.jpg)
ValidityWhat is logic?
A science that evaluates arguments.
![Page 4: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/4.jpg)
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.
![Page 5: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/5.jpg)
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.
![Page 6: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/6.jpg)
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
![Page 7: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/7.jpg)
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!
![Page 8: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/8.jpg)
Validity Truth Validity
Good Argument
![Page 9: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/9.jpg)
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
![Page 10: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/10.jpg)
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
![Page 11: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/11.jpg)
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 .
![Page 12: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/12.jpg)
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
![Page 13: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/13.jpg)
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
![Page 14: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/14.jpg)
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
![Page 15: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/15.jpg)
Validity Truth Validity
Good Argument
![Page 16: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/16.jpg)
Validity Truth Validity
Sound Argument
![Page 17: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/17.jpg)
Validity
Truth + Validity = Soundness (i.e. a good
argument)
![Page 18: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/18.jpg)
Validity
Is a valid argument a true argument?
![Page 19: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/19.jpg)
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.
![Page 20: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/20.jpg)
Validity
An argument is valid if when the premises
are true, the conclusion has to be true.
![Page 21: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/21.jpg)
Validity
An argument is sound if it is valid, and the
premises are true.
![Page 22: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/22.jpg)
VALID INVALID
True Premises + True Conclusion
True Premises + False Conclusion
False Premises + True Conclusion
False Premises + False Conclusion
![Page 23: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/23.jpg)
VALID INVALID
True Premises + True Conclusion True Premises + False Conclusion False Premises + True Conclusion False Premises + False Conclusion
![Page 24: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/24.jpg)
ValidityValidity InvalidityVALID INVALID
True Premises + True Conclusion
True Premises + False Conclusion
False Premises + True Conclusion
False Premises + False Conclusion
![Page 25: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/25.jpg)
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
![Page 26: Intro to Logic](https://reader031.vdocuments.site/reader031/viewer/2022011718/56813029550346895d95b8cd/html5/thumbnails/26.jpg)
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?