Hungry for some Logical Truth Grab a

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Hungry for some Logical Truth!Grab a

• Leibniz Bar!
• And if you act now

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We might even send. . .

• Gottfried Wilhelm Leibniz Himself!!

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Objectives-

• Who was Leibniz? What are some of the details of
  his background?
• What were some of his major works?
• What were his major contributions to logic? Can
  you use them?

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Background/ Significance

• 17th Century German Philosopher (1646-1716)
• Rationalist, Mathematician who believed in the
  importance of the systematic organization of
  knowledge
• Most famous Work- Monadology

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Leibniz offers logical criteria towards finding
certainty

• There are two fundamental truths. . .

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1. Truths Known Through Principles of Logic

• The Law of Contradiction-
• A statement and its contradictory cannot be
  true.

• Law of the Excluded Middle-
• For any statement, either it is true or its
  contradictory is true.

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Based on each of the laws can you make two
statements that abide by the Law of Contradiction
and two that follow the Law of the Excluded
Middle.
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• "The same attribute cannot at the same time
  belong and not belong to the same subject in the
  same respect. (Aristotle)
• Conestoga really won the game. They outplayed
  their opponent even though the score was Radnor 4
  and Conestoga 2.
• Does this work?

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-Law of the Excluded Middle-Either a statement
or its opposite is true.

• Washington DC is on the East Coast.
• A proposition and its denial or negation cannot
  both be true.

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2. Truths of Fact

• Truths that cannot be certified by appeal to the
  laws of logic
• The apple is green
• In order to get to truths of fact, we must appeal
  to the Principle of Sufficient Reason

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Principle of Sufficient ReasonAn argument does
not have to be certain or true, but valid and
logical.

• Most of our knowledge is based on this principle

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Logic

• Deductive Reasoning and the syllogism
• A syllogism has
• Two premises
• And a conclusion
• Often has to do with membership in a group and
  uses the terms all, some, and none.

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Example 1 All men are mortal. Socrates is a
man. Socrates is mortal.

• It is valid if it confers to the rules of
  deduction.
• Valid or Invalid?
• Change this so that it would not be valid.
• Can you draw this scenario?

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• Does this work? Only in a closed system?

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Example 2 -No Rastafarians are Presbyterians.
-Tracy Saunders is not a Rastafarian. -Tracy
Saunders is Presbyterian.

• Explain how this works by drawing the scenario.

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• Does this work? You be the judge. . .

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For further help on logic, refer to page 62 in
your text, the handout from class, and the logic
resources from the class website.