1.1.notebook
August 29, 2016
1.1 "Deductive" vs "Inductive" Logic
Definition of "Deductive" in the book: "The application of a general rule to a specific instance."
1. All men are mortal
2. Socretes is a man
Therefore, Socretes is mortal
Example 6 from the book:
1. No snake is warm­blooded
2. All mammals are warm­blooded
Therefore, snakes are not mammals
Better definition: Deductive reasoning narrows the scope. It works inward from things that are assumed to be true, and draws an internal conclusion. It "cuts something out".
Definition of "Inductive" from the book: "Going from a series of specific cases to a general statement."
1. All swans in England are white
2. All swans in France are white
Therefore, all swans are white
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1.1.notebook
August 29, 2016
"Valid" vs "Sound"
Definition of "Valid":
Valid Arguments
Definition of "Sound":
Sound Arguments
Definition of "True":
1. All politicians are really reptilian shapechangers
2. My professor is a politician
Therefore, my professor is a reptilian shapechanger!
1. All professors of Math 101 are required to teach the chapter on Logic
2. Mr. Adams is a professor of Math 101
Therefore, Mr. Adams is required to teach the chapter on Logic
1. All mammals have some kind of fur
2. A moose has fur
Therefore, a moose is a mammal
"Syllogism"
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1.1.notebook
August 29, 2016
Proving Invalidity (Often Requires a Counterexample)
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1. All forest rangers are environmentalists
2. All forest rangers are storytellers
Therefore, all environmentalists are storytellers
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counterexample
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1. Some professors wear glasses
2. Mr. Einstein wears glasses
Therefore, Mr. Einstein is a professor
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1.1.notebook
August 29, 2016
For next time (Wednesday, August 31), quiz #1 will be the following question:
Of the following four choices, which chapter should be included in this class?
a) Chapter 2 (Sets, Counting, and Infinity)
b) Chapter 7 (Number Systems and Number Theory)
c) Chapter 8 (Geometry)
d) Chapter 13 (Calculus)
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