What is a Statement?
In logic, a statement is a declarative sentence that asserts something to be the case. Crucially, it must have a truth value – it can be either true or false, but not both or neither.
Key Characteristics
- Asserts a proposition.
- Has a definite truth value (true or false).
- Forms the basis of logical arguments.
Distinguishing Statements
Not all sentences are statements. Questions, commands, and exclamations do not assert a truth value and are therefore not statements.
For example, “The sky is blue” is a statement, while “What is your name?” is not.
Types of Statements
Statements can be simple or compound. Compound statements are formed by connecting simple statements using logical connectives like ‘and’, ‘or’, and ‘not’.
Simple Statement: 'It is raining.'
Compound Statement: 'It is raining AND the wind is blowing.'
Importance in Logic
Statements are the fundamental units of propositional logic. Analyzing the truth values and relationships between statements allows us to construct and evaluate valid arguments.
Applications
The concept of statements is vital in computer science (programming logic), mathematics (proofs), and everyday reasoning to ensure clarity and accuracy in communication.
Challenges and Misconceptions
A common misconception is that statements must be factually true in the real world. In logic, a statement only needs to be capable of being true or false, regardless of its empirical truth.