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Notes # 1: Deductive Arguments

1. An argument is a set of statements that consists of a conclusion and the statements said by the arguer to lead to that conclusion.
   
   
2. Premises are the statements that lead to the conclusion.
   
   
3. A deductive argument is an argument in which the arguer is maintaining that the premises show that the conclusion is necessarily true.
   
   
4. A deductive argument is said to be valid if the premises logically lead to the conclusion.
   
   
5. A deductive argument is said to be sound if it is valid and has true premises.  The conclusion of a sound deductive argument is necessarily true.
   
   
6. A syllogism is a deductive argument with two premises.  Here is one example of a syllogism that is valid and sound:
                   All human beings are mortal.
                   Socrates is a human being.
                   Thus, Socrates is mortal.
   
   
7. Now consider this syllogism:
                   All dogs are cats.
                   All cats are birds.
                   Thus, all dogs are birds.
   This argument is valid, because the conclusions follows from the premises, but it is clearly not sound since the premises are false.
   
   
8. Of course, more complex deductive arguments may have more than two premises.
   
   
9. In many cases arguments are linked together.  The conclusion of one argument becomes a premise for the next argument.  In analyzing complex arguments, it is often important to break the argument down into its component parts.
   
   
10. In many cases parts of deductive arguments are missing.  In order to critique an argument, it may be important to uncover the missing premises.