Introductory Logic Unit 1
Terms in this set (55)
a sentence which is either true or false
Sentences which have no truth value are not statements, including:
questions, commands, and nonsense
Self Supporting statement
a statement whose truth value can be determined from the statement itself.
Three categories of Self-Supporting statements
Statements which are true or false by logical structure
Statements which are true or false by definitions
is a statement which is always true because of its logical structure
a statement which is false by logical structure
a statement whose truth value depends on evidence or information from outside itself
What information must be gathered before declaring a statement either true or false?
authority, experience, deduction
What are the four major relationships with which we are concerned between statements?
Consistency, Implication, Logical equivalence, Independence
when two statements can be true at the same time
Two statements are related by implications if the truth of one requires the truth of the other
Two statements are logically equivalent if they imply one another.
If the truth or falsity of one statement has no effect on the truth or falsity of the other.
What two indications can we use to help determine if statements are independent?
Neither statement can imply the other, and the statements must be consistent.
When there appears to be inconsistency.
What are the three kinds of disagreements that concern us?
Real disagreements, Apparent disagreement, verbal disagreement
an actual inconsistency between two statements: they cannot both be true at the same time.
a difference of opinion or perception.
a misunderstanding due to differing definitions for one or more words.
Why is it important to define terms in the first part of any debate?
because of the possibility of verbal disagreements.
In order to help analyse statements in arguments, the statements must be translated so they use only the verb of _____________
being (is, are, was, were, will be)
To translate a statement to use only verb of being
1. identify the entire subject
2. choose the "to be" verb that matched the subject and predicate
3. rewrite the entire predicate as a predicate nominative.
Sample: John eats turnips
John is a turnip-eater
Sample: Paul resisted Peter and Barnabas.
Paul was a Peter-and-Barnabas resister.
Sample: The donkey rebuked the prophet
The donkey was a prophet rebuker.
statements which affirm or deny something about a given subject.
Four types of categorical statements
universal affirmative, universal negative, particular affirmative, and particular negative.
Categorical statements can be translated into one of four forms:
1. All S are P 2. No S are P
3. Some S are P 4. Some S are not P
Statements have 2 parts
subject & predicate
Subject of a statement
the term being described, or about which something is asserted.
Predicate of a statement
is the term that describes or asserts something about the subject.
Each statement also has
quantity & quality
Quantity of a statement
the scope of its claim about the extension of the subject: universal (all and no) or particular (some and some ...not)
Quality of a statement
the positive or negative nature of its claim about the subject: affirmative (all and some) or negative (no and some ...not).
Rules for translating categorical statements into standard categorical form:
1. The statements must begin with the words all, no, or some.
2. The verb must be the verb of being: is, are, was, were, will be, etc.
3. Both the subject and the predicate must be a noun or a noun phrase.
The four categorical statements can be abbreviated
A, E, I and O
The Square of opposition
a diagram of the basic relationships between statements with the same subject and predicate. Allows us to analyze the relationship between the statements.
Universal affirmative statements
Universal negative statements
Particular affirmative statements
Particular negative statements
The 4 types of categorical statements are related to one another --
they are not independent
The statements in the opposite corner of the square of opposition are
If one is true, the other must be false. (A&O and I&E) Both statements cannot be true.
exists between the universal statements A & E only.
two statements are contrary if and only if they can both be false but cannot both be true.
the relationship which exists between I & O statements
when both statements can be true but both cannot be false.
The relationship of crontrariety is the opposite of
the relationship between a universal and particular statement of the same quality, in which the truth of the universal necessitates the truth of the particular.
Subimplication can only exist between pairs of
A & I statements and pairs of E & O statements
If an A statement is true, then its corresponding I statement must be true. If an E statement is true, then its corresponding O statement must be true.
the relationship between a universal and particular statement of the same quality, in which the falsity of the particulary necessitate the falsity of the universal.
Superimplication is the implication of
Superimplication can only exist between
pairs of I & A statements and pairs of O & E statements.
In a relationship of superimplication, if a particular statement is false, then
the universal statement of the same quality is false.