What is a Proposition?

Mathematical Logic · Axiom Academy

Discover the building blocks of logical reasoning through interactive exploration. Let's start with a simple question: Can you tell if the following statement is true or false? Step 2: What Makes a Proposition? Not all statements are propositions. For each statement below, decide: Can you definitively say it's either true or false? Drag each statement to the correct category. Which are propositions and which are not? Step 4: Simple vs Compound Propositions Some propositions are built from simpler ones. Click on a proposition to see its structure. A declarative statement that is either true or false , but not both. Declarative: Makes a claim (not a question, command, or assignment) Has Truth Value: Can be definitely verified as true or false Simple: One single claim Compound: Multiple claims connected by logical operators (AND, OR, NOT, etc.) Propositions are the fundamental units of logical reasoning. Just as numbers are the foundation of arithmetic, propositions are the foundation of logic. By understanding what makes a valid proposition, you can build complex logical arguments, write mathematical proofs, and reason precisely about the world.

This is the written version of the interactive lesson above. See the full Mathematical Logic course.