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1

Logic

The science and art of reasoning well.

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3 Laws of Thought

1. Law of Excluded Middle - T or F
2. Law of Identity - If T, then T
3. Law of Noncontradiction - Not both T and F

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Formal Logic

Deals with proper modes of reasoning

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Informal Logic

Deals with operation of thinking that are indirectly related to reasoning

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Induction

Reasoning with probability from examples or experience to general rules

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Deduction

Reasoning with certainty from premises to conclusions

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Term

A concept expressed precisely in words

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Definition

A statement that gives the meaning of a term

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Five Types of Definitions

Lexical definition - from a dictionary
Precising definition - reduces vagueness
Stipulative definition - increases vocabulary
Theoretical definition - explains concepts theoretically
Persuasive definition - influences attitudes

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Genus and Species

Genus - more broad or general
Species - more specific

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Extension and Intension

Increasing Extension - becomes more broad
Decreasing Extension - becomes more specific

Increasing Intension - becomes more specific
Decreasing Intension - becomes more broad

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The Three Methods of Defining

Defining by Synonym - similar words
Defining by Example - give an example (picture, story, object, etc.)
Defining by Genus and Difference - genus is bag, difference is backpack

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The Rules for Defining by Genus and Difference

A definition should...
1. state the essential attributes of the term
2. not be circular
3. not be too broad or too narrow
4. not be unclear or figurative
5. be stated positively, if possible
6. be of the same part of speech as the term

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Statement

A sentence that is either true of false

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Self-Supporting Statements

A statement whose truth value can be determined from the statement itself.
1. Self -reports
2. T of F by logical structure
3. T or F by definition

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Supported Statements

A statement whose truth value depends on evidence or information from outside itself.
1. authority
2. experience or observation
3. deduction

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The Four Relationships Between Statements

1. Consistency - both T at the same time
2. Implication - truth of one requires the truth of the other
3. Logical Equivalence - Two statements that imply one another
4. Independence - if T/F of one has nothing to do with T/F of the other

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The Three Types of Disagreements

1. Real Disagreement - both cannot be T at the same time
2. Apparent Disagreement - differences of opinion or perception
3. Verbal Disagreement - different definitions used for the same word

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How to Translate a Statement Into Standard Categorical Form

1. Identify the entire subject and write it down
2. Choose the proper "to be" verb (am, is, are, was, were, be, being, been)
3. Rewrite the entire predicate as a predicate nominative (i.e., a noun) - throws rocks becomes a rock-thrower

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The Subject and Predicate of a Statement

Subject - Who or What the sentence is about
Predicate - Describes or asserts something about the subject

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The Square of Opposition

A diagram of basic relations between categorical statements with the same subject and predicate
A, E, I and O statements
A - All S are P
E - No S are P
I - Some S are P
O - Some S are not P

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The Relationship Demonstrated by the Square of Opposition:
Contradiction
Contrariety
Sub-Contrariety
Subimplication
Superimplication

Contradiction - Always have opposite truth values
A and O, E and I
Contrariety - Both false, but can't both be true
A and E
Sub-Contrariety - If both true, but both cannot be false
I and O
Subimplication - Only exists between pairs of A and I statements and E and O statements
Superimplication - Only exists between pairs of I and A statements and O and E statements

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Argument

Set of statements that appear to implied or supported by the others

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Conclusion

A statement that appears to be implied by the premises

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Premise

Statements that support and imply the conclusion

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Syllogism

A deductive argument with two premises and three terms

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Categorical Syllogism

Consists of three statements in categorical form

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Major, Minor, and Middle Term

Major Term - predicate of the conclusion
Minor Term - subject of the conclusion
Middle Term - Found once in each premise

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Schema

A representation of a syllogism
Statements are in standard order with standard abbreviations
Example:
Some M are P
All S are M
. ' . Some S are P

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Mood

A three-letter description of the types of categorical statements when arranged in standard order.
Example:
IAI