Classifying & Comparing: Statements

Gig Φ Philosophy
(at-a-glance overviews of philosophical concepts)

Published October, 2022

Truth Tables: Statements : PREVIOUS

NEXT : Truth Tables: Arguments

Classifying Statements

Constructing a truth table for compound statements not only helps us to determine the possible truth values of that statement, but can also tell us something about the statement's logical structure.

What is more, a truth table for compound statements reveals whether the truth of the statement depends on the specific truth values of its components or the logical form or structure of the entire statement.

We can classify even the most complex compound statements in the following ways (Notice in the examples below that the determination of classification depends solely upon the truth values under the main logical operator):

TAUTOLOGY

All TRUE

SELF-CONTRADICTORY

All FALSE

CONTINGENT

≥1 TRUE & ≥1 FALSE

Comparing Statements

Similarly, truth tables may also be used to determine the relationship between multiple statements.

This is valuable when considering the strength of an argument and how well various parts of the argument work to support one another.

We can compare statements to one another in the following ways:

LOGICAL EQUIVALENCE

SAME values on each line

CONTRADICTION

OPPOSITE values on each line

CONSISTENT

≥1 line both TRUE

INCONSISTENT

0 lines both TRUE

Truth Tables: Statements : PREVIOUS

NEXT : Truth Tables: Arguments

Classifying & Comparing: Statements

Gig Φ Philosophy(at-a-glance overviews of philosophical concepts)

Published October, 2022

Classifying Statements

Constructing a truth table for compound statements not only helps us to determine the possible truth values of that statement, but can also tell us something about the statement's logical structure.

What is more, a truth table for compound statements reveals whether the truth of the statement depends on the specific truth values of its components or the logical form or structure of the entire statement.

We can classify even the most complex compound statements in the following ways (Notice in the examples below that the determination of classification depends solely upon the truth values under the main logical operator):

TAUTOLOGY

All TRUE

SELF-CONTRADICTORY

All FALSE

CONTINGENT

≥1 TRUE & ≥1 FALSE

Comparing Statements

Similarly, truth tables may also be used to determine the relationship between multiple statements.

This is valuable when considering the strength of an argument and how well various parts of the argument work to support one another.

We can compare statements to one another in the following ways:

LOGICAL EQUIVALENCE

SAME values on each line

CONTRADICTION

OPPOSITE values on each line

CONSISTENT

≥1 line both TRUE

INCONSISTENT

0 lines both TRUE

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Gig Φ Philosophy
(at-a-glance overviews of philosophical concepts)