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Understanding Basic Logic: Statements, Arguments, and Proofs

This overview introduces essential concepts in basic logic: statements, arguments, and proofs. A statement claims something about the world, which can be true or false. Arguments consist of premises aimed at supporting a conclusion. A strong argument requires a proof relationship between these premises and the conclusion, with all premises being true. Examples illustrate the difference between good and bad arguments, emphasizing the importance of logical coherence. This foundational logic framework is crucial for critical thinking and reasoning skills.

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Understanding Basic Logic: Statements, Arguments, and Proofs

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  1. Basic Logic Definitions Statement: A sentence that makes some claim about the world. True Statement: A statement in which the claim does correspond to the way the world actually is. (E. g.: The sky is blue.)

  2. False Statement: A statement in which the claim does not correspond to the way the world actually is. (E. g.: The sky is pink.) Argument: Group of statements in which the truth of several (the premises) is supposed to prove that another (the conclusion) is true.

  3. Proof: Proof exists when the premises’ being true gives you a good reason to believe that the conclusion is true. For example: S. Wright is in Mr. Jones’ class. Most of the students in Mr. Jones’ class are boys. Therefore, S. Wright is probably a boy.

  4. An example of a lack of proof: The director needs a singing, brown haired actress for his play. Most of the actresses at the audition are brown haired. Therefore, the director will probably find the actress he needs for his play at the audition.

  5. What’s Needed for an Argument to Be Good • There must be a proof relationship between the premises and the conclusion. • All the premises must actually be true.

  6. Two Arguments Most boys love to play sports. Britney Spears is a boy. Therefore, Britney Spears probably loves to play sports. Most popular singers have talent. Britney Spears is a popular singer. Therefore, Britney Spears probably has talent. The first argument is bad. The second argument is good.

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