Midterm Review Flashcards
Logic
The science and art of reasoning well.
3 Laws of Thought
- Law of Excluded Middle - T or F
- Law of Identity - If T, then T
- Law of Noncontradiction - Not both T and F
Formal Logic
Deals with proper modes of reasoning
Informal Logic
Deals with operation of thinking that are indirectly related to reasoning
Induction
Reasoning with probability from examples or experience to general rules
Deduction
Reasoning with certainty from premises to conclusions
Term
A concept expressed precisely in words
Definition
A statement that gives the meaning of a term
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
Genus and Species
Genus - more broad or general
Species - more specific
Extension and Intension
Increasing Extension - becomes more broad
Decreasing Extension - becomes more specific
Increasing Intension - becomes more specific
Decreasing Intension - becomes more broad
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
The Rules for Defining by Genus and Difference
A definition should…
- state the essential attributes of the term
- not be circular
- not be too broad or too narrow
- not be unclear or figurative
- be stated positively, if possible
- be of the same part of speech as the term
Statement
A sentence that is either true of false
Self-Supporting Statements
A statement whose truth value can be determined from the statement itself.
- Self -reports
- T of F by logical structure
- T or F by definition
Supported Statements
A statement whose truth value depends on evidence or information from outside itself.
- authority
- experience or observation
- deduction
The Four Relationships Between Statements
- Consistency - both T at the same time
- Implication - truth of one requires the truth of the other
- Logical Equivalence - Two statements that imply one another
- Independence - if T/F of one has nothing to do with T/F of the other
The Three Types of Disagreements
- Real Disagreement - both cannot be T at the same time
- Apparent Disagreement - differences of opinion or perception
- Verbal Disagreement - different definitions used for the same word
How to Translate a Statement Into Standard Categorical Form
- Identify the entire subject and write it down
- Choose the proper “to be” verb (am, is, are, was, were, be, being, been)
- Rewrite the entire predicate as a predicate nominative (i.e., a noun) - throws rocks becomes a rock-thrower
The Subject and Predicate of a Statement
Subject - Who or What the sentence is about
Predicate - Describes or asserts something about the subject
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
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
Argument
Set of statements that appear to implied or supported by the others
Conclusion
A statement that appears to be implied by the premises
Premise
Statements that support and imply the conclusion
Syllogism
A deductive argument with two premises and three terms
Categorical Syllogism
Consists of three statements in categorical form
Major, Minor, and Middle Term
Major Term - predicate of the conclusion
Minor Term - subject of the conclusion
Middle Term - Found once in each premise
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
Mood
A three-letter description of the types of categorical statements when arranged in standard order.
Example:
IAI
Figure
A number from 1 to 4 identifying the placement of the middle term
Validity
Valid statement if and only if the premise implies the conclusion
Soundness
Valid syllogism that has true premises
Counterexamples
Syllogism that has a false conclusion to show the original syllogism to be invalid
Distribution
A term that refers to all members of it’s categories
Rules for Validity
Rules
- In at least on premise the term must be distributed
- If a term is distributed in its conclusion it must also be distributed in its premise
- It cannot have two negative premises
- It cannot have a negative premise and affirmative conclusion
- It cannot have two affirmative premises and a negative conclusion
How to Tell if a Term is Distributed in a Statement
S P A D U E D D I U U O U D
Immediate Inferences
A statement that can be directly inferred from another statement
The Complement of a Term
A set of all terms not included in the given term.
Thus, the term P is non-P
Enthymemes
An argument in which a statement is unstated and assumed. It is a syllogism with one assumed statement.
Hypothetical Syllogisms
A statement that affirms an outcome based on a condition. It has the form If P then Q.
Modus Ponens
P >Q
P
. ‘ . Q
Modus Tollens
P > Q
~Q
. ‘ . ~P
Affirming the Consequent
P > Q
Q
. ‘ . P
Denying the Antecedent
P > Q
~P
. ‘ . ~Q
