GLE 0701'5'5 Explore the concept of premises, including false premises'

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Intro to Logic

• GLE 0701.5.5 Explore the concept of premises,
  including false premises. 

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Validity

• What is logic?

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Validity

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

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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.

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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.

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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!

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Validity

• Truth

• Validity

Good Argument
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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

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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

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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 .

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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

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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

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Validity

• Truth

• Validity

Good Argument
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Validity

• Truth

• Validity

Sound Argument
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Validity

• Truth Validity Soundness
• (i.e. a good
  argument)

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Validity

• Is a valid argument a true argument?

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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.

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Validity

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

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Validity

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

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Validity

• Validity

• Invalidity

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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
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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?