Square of Opposition
Make sure you know how to draw the square of opposition:)
Terms in this set (69)
The relationship between a universal and a particular statement of the same quality, in which the falsity of the particular necessitates the falsity of the universal.
I to A
O to E
truth value implied by superimplication
falsity only (falsity flows upward)
The relationship between a universal and a particular statement of the same quality, in which the truth of the universal necessitates the truth of the particular.
A to I
E to O
truth value implied by subimplication
truth only (truth flows downward)
Two statements are subcontraries if and only if they can both be true but cannot both be false.
I and O
subcontrariety is the opposite of
Two statements are contrary if and only if they can both be false but cannot both be true.
A to E
In any argument that involves contrary claims, it may be possible for both claims to be false-there may be a third option.
A to O and
E to I
square of opposition
a diagram of the basic relationships between categorical statements with the same subject and predicate
Universal affirmative statements (All S are P)
Universal negative statements (No S are P)
Particular affirmative statements (Some S are P)
Particular negative statements (Some S are not P)
A statement that either affirms or denies something about a given subject
The four basic forms for categorical statements
1. All S are P
2. No S are P
3. Some S are P
4. Some S are not P
All categorical statements have what two parts?
Subject and predicate
subject of statement
term being described, or about which something is asserted
predicate of statement
term that describes or asserts something about the subject
quantity of statement
Scope of its claim about the extension; how much of the subject is the statement talking about. Some? None? All?
Two options for quantity of a statement
universal or particular
A statement is universal when it makes a claim about the entire (all and no) extension of the subject.
A statement is particular when it makes a claim about the part (some and some...not) of the extension of the subject.
quality of a statement
the positive or negative nature of its claim about the subject; identifies whether the statement is affirmative (all and some) or negative (no or some...not)
affirmative quality keywords
all or some
negative quality keywords
no or some...not
All S are P
No S are P
Some S are P
Some S are not P
a statement in standard form must begin with the words _, _, or _
all, no, some
the verb in a statement in standard form must be the ___
verb of being
the predicate and subject in a statement in standard form must be a _ or __
noun, noun phrase
To analyze statements using categorical logic, translate them into a form that uses what verb?
verb of being
What are the verbs of being?
am, is, are, was, were, be, being, been
What should be maintained when translating?
tense of verbs
What is the first step in putting statement into standard form?
identify and write down the entire subject
What is the second step in putting statement into standard form?
choose the proper 'to be' verb
What is the third step in putting statement into standard form?
rewrite the entire predicate as a predicate nominative
When there appears to be inconsistency between statements
Three common types of disagreements
Real, Apparent, Verbal
An actual inconsistency between two statements: they cannot both be true at the same time.
A difference of opinion or perception. (These statements are self-reports, and so both can be true.)
A misunderstanding due to differing definitions for one or more words. (Precising or lexical definitions help remove verbal disagreements.)
Four basic relationships between statements
Consistency, implication, logical equivalence, and independence
Two statements can both be true at the same time.; there is no conflict between them.
Two statements cannot be true at the same time; there is a conflict between them.
One statement implies the other. Two statements are related by implication if the truth of one requires the truth of the other; both statements have to be consistent
Two statements are logically equivalent if they imply one another. This means that both statements must be true or both statements must be false.
the truth or falsity of one has no effect on the truth or falsity of the other; neither statement can imply the other; the statements must be consistent
A sentence that is either true or false, i.e. has a truth value.
What are the possible truth values of a statement?
True truth value and false truth value (no truth value=not a statement at all)
Three kinds of sentences that have no truth value
Questions, commands, and nonsense
Two types of statements
Self-supporting statements and Supported statements
A statement whose truth value can be determined from the statement itself.
Three types of self-supporting statements
~Statements that are true or false by logical structure
~Statements that are true or false by definition
A statement by a person concerning his or her own desires, beliefs, or feelings. (ex, "I believe, I think, I want)
Are self-reports normally taken as true or false?
Statements that are true or false by logical structure
A statement that can be seen to be true or false by how the sentence is put together.
A statement which is true by logical structure.
A statement that is false by logical structure.
Statements that are true or false by definition
These statements are necessarily true or false because of the definitions of the words in the sentence.
A statement whose truth value depends on evidence or information from outside itself.
Name three sources of information for supported statements. Do others exist?
Authority, experience/observation, and deduction; yes
All s are p
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