Logic

1. What is logic? Logic is a way of thinking that helps us figure out if an argument makes sense. It’s about understanding how to connect different ideas to reach a conclusion that’s correct. Logic gives us rules to tell the difference between good arguments and bad ones.

2. What is a statement? In logic, a statement is a sentence that can only be true or false, not both. It’s like a fact you can agree or disagree with. For example, “The sky is blue” is a statement. We can combine simple statements to make more complex ones using words like “and,” “or,” and “not.”

3. What is an argument? An argument in logic is not like a disagreement between people. Instead, it’s a set of statements where some (called premises) are used to support another statement (called the conclusion). The premises are like the reasons, and the conclusion is what you’re trying to prove based on those reasons.

4. Validity and soundness: When we talk about arguments in logic, we look at two things:
   • Validity: Validity is about the structure of the argument. If an argument is valid, it means that if the premises are true, the conclusion must be true too.
   • Soundness: An argument is sound if it’s valid AND all its premises are actually true in real life.
5. Types of logic: There are different ways of using logic:
   • Deductive logic: Deductive logic starts with general ideas and moves to specific conclusions. If you start with true statements, you’ll always end up with a true conclusion.
   • Inductive logic: Inductive logic starts with specific observations and tries to make general conclusions. It’s not as certain as deductive logic, but it’s useful for making predictions.
   • Abductive logic: Abductive logic is about finding the most likely explanation for something when you don’t have all the information.
6. Logical connectives: Logical connectives are words or symbols we use to join statements together:
   • AND: True only if both statements are true.
   • OR: True if at least one statement is true.
   • NOT: Changes a true statement to false, or a false statement to true.
   • IMPLIES: True unless the first statement is true and the second is false.

7. Truth tables and logical equivalence: A truth table is a tool that shows all the possible true/false combinations for a logical statement. It helps us understand complex statements better. Two statements are logically equivalent if they’re true and false in all the same situations.

8. Laws of logic: Laws of logic are basic rules that form the foundation of logical thinking:
   • Law of identity: A thing is always equal to itself.
   • Law of non-contradiction: Something can’t be true and false at the same time.
   • Law of the excluded middle: Something must be either true or false, with no in-between.
9. How logic works - logical reasoning: Using logic involves these steps:
   1. Figure out what statements are involved.
   2. Look at how these statements are connected.
   3. Check if the conclusion makes sense based on the other statements.
   4. See if the statements you started with are actually true in real life.

In summary, logic is a way of thinking that helps us figure out how to reach correct conclusions from the information we start with. Logic gives us tools to check if an argument makes sense by looking closely at how it’s put together and what it’s saying.