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3.4 Fallacies in Logic

3.4 Fallacies in Logic
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  • 1. Weapons in Iraq

    Outline the invalid syllogism and identify the logical fallacy. (See Example 1 and Example 2.)

    A politician states, "If something is not there, you will not find it. We did not find weapons of mass destruction in Iraq. So, there are no such weapons in Iraq."

    • Worked-Out Solution

      Here is one possible invalid syllogism.

      Premise: If something is not there, you will not find it.
      Premise: We did not find any weapons of mass destruction in Iraq.
      Conclusion: Therefore, there are no such weapons in Iraq.

      This type of fallacy is called affirming the consequent.

      Premise: If P, then Q.
      Premise: Q.
      Conclusion: Therefore, P.

      In the first premise, Q is called the consequent. The name affirming the consequent comes from the fact that the second premise states that Q is true.

      Note about Fallacies

      Stating that a syllogism is a fallacy simply means that the conclusion was not obtained by logical deduction. It does not mean that the conclusion of the syllogism is false.

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     __   __    _____     ______    ______   _    _   
     \ \\/ //  |  ___||  /_   _//  /_   _// | |  | || 
      \   //   | ||__      | ||     -| ||-  | |/\| || 
      / . \\   | ||__     _| ||     _| ||_  |  /\  || 
     /_//\_\\  |_____||  /__//     /_____// |_// \_|| 
     `-`  --`  `-----`   `--`      `-----`  `-`   `-` 
                                                      
    
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  • 2. Weapons in Iraq

    Outline the invalid syllogism and identify the logical fallacy. (See Example 1 and Example 2.)

    A representative states, "If Saddam had shipped his weapons out of Iraq, we would not have found them. We didn't find Saddam's weapons, so he must have shipped them out of Iraq."

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     _____     __   __    ______     ___              
    |  __ \\   \ \\/ //  /_____//   / _ \\      ___   
    | |  \ ||   \ ` //   `____ `   / //\ \\    /   || 
    | |__/ ||    | ||    /___//   |  ___  ||  | [] || 
    |_____//     |_||    `__ `    |_||  |_||   \__ || 
     -----`      `-`'    /_//     `-`   `-`     -|_|| 
                         `-`                     `-`  
    
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  • 3. Weapons of Mass Destruction

    Outline the invalid syllogism and identify the logical fallacy. (See Example 1 and Example 2.)

    A radio show host says, "If we found weapons of mass destruction in Iraq, it would prove that Iraq had such weapons. We haven't found weapons of mass destruction in Iraq, and this proves that Iraq did not have such weapons."

    • Worked-Out Solution

      Here is one possible invalid syllogism.

      Premise: If we found weapons of mass destruction in Iraq, then it would prove that Iraq had such weapons.
      Premise: We haven't found weapons of mass destruction in Iraq.
      Conclusion: Therefore, Iraq did not have such weapons.

      This type of fallacy is called denying the antecedent.

      Premise: If P, then Q.
      Premise: P is not true.
      Conclusion: Therefore, Q is not true.

      In the first premise, P is called the antecedent. The name denying the antecedent comes from the fact that the second premise states that P is not true.

      Note about Fallacies

      Stating that a syllogism is a fallacy simply means that the conclusion was not obtained by logical deduction. It does not mean that the conclusion of the syllogism is false.

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     _    _      ___      ______     ___              
    | |  | ||   / _ \\   /_   _//   / _ \\    ____    
    | |/\| ||  | / \ ||  `-| |,-   / //\ \\  |    \\  
    |  /\  ||  | \_/ ||    | ||   |  ___  || | [] ||  
    |_// \_||   \___//     |_||   |_||  |_|| |  __//  
    `-`   `-`   `---`      `-`'   `-`   `-`  |_|`-`   
                                             `-`      
    
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  • 4. A Safer America

    Outline the invalid syllogism and identify the logical fallacy. (See Example 1 and Example 2.)

    A political pundit states, "If the war in Iraq made America safer, there will have been no major terrorist attack since we invaded. There hasn't been any such attack. So, the war made America safer."

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     _____       ___      ______    ______   __   __  
    |  __ \\    / _ \\   /_   _//  /_   _//  \ \\/ // 
    | |  \ ||  / //\ \\  `-| |,-    -| ||-    \   //  
    | |__/ || |  ___  ||   | ||     _| ||_    / . \\  
    |_____//  |_||  |_||   |_||    /_____//  /_//\_\\ 
     -----`   `-`   `-`    `-`'    `-----`   `-`  --` 
                                                      
    
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  • 5. Supporting the War

    Outline the invalid syllogism and identify the logical fallacy. (See Example 1 and Example 2.)

    A talk show host says, "If you support the war in Iraq, you support America. The senator doesn't support the war, so he obviously doesn't support America."

    • Worked-Out Solution

      Here is one possible invalid syllogism.

      Premise: If you support the war in Iraq, then you support America.
      Premise: The senator doesn't support the war in Iraq.
      Conclusion: Therefore, the senator doesn't support America.

      This type of fallacy is called denying the antecedent.

      Premise: If P, then Q.
      Premise: P is not true.
      Conclusion: Therefore, Q is not true.

      In the first premise, P is called the antecedent. The name denying the antecedent comes from the fact that the second premise states that P is not true.

      Note about Fallacies

      Stating that a syllogism is a fallacy simply means that the conclusion was not obtained by logical deduction. It does not mean that the conclusion of the syllogism is false.

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      ______   _    _     ______     ___    __    __  
     /_   _// | || | ||  /_   _//   / _ \\  \ \\ / // 
     `-| |,-  | || | ||  `-| |,-   | / \ ||  \ \/ //  
       | ||   | \\_/ ||    | ||    | \_/ ||   \  //   
       |_||    \____//     |_||     \___//     \//    
       `-`'     `---`      `-`'     `---`       `     
                                                      
    
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  • 6. George W. Bush

    Outline the invalid syllogism and identify the logical fallacy. (See Example 1 and Example 2.)

    An opinion columnist writes, "If a person is a great leader, then that person will do what he or she believes is right. George W. Bush did what he believed was right. He was a great leader."

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      _  _    _    _     ____      ______  __    __  
     | \| || | || | ||  |  _ \\   /_   _// \ \\ / // 
     |  ' || | || | ||  | |_| ||   -| ||-   \ \/ //  
     | .  || | \\_/ ||  | .  //    _| ||_    \  //   
     |_|\_||  \____//   |_|\_\\   /_____//    \//    
     `-` -`    `---`    `-` --`   `-----`      `     
                                                     
    
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  • 7. Fighting in Iraq

    Outline the invalid syllogism and identify the logical fallacy. (See Example 1 and Example 2.)

    A political science professor says, "If we had overthrown Saddam in the first Gulf War, we would not be fighting in Iraq today. It is clear that we are fighting in Iraq as a consequence of our decision not to end Saddam's regime in 1991."

    • Worked-Out Solution

      Here is one possible invalid syllogism.

      Premise: If we had overthrown Saddam's regime in 1991, then we would not be fighting in Iraq today.
      Premise: We did not overthrow Saddam's regime in 1991.
      Conclusion: Therefore, we are still fighting in Iraq today.

      This type of fallacy is called denying the antecedent.

      Premise: If P, then Q.
      Premise: P is not true.
      Conclusion: Therefore, Q is not true.

      In the first premise, P is called the antecedent. The name denying the antecedent comes from the fact that the second premise states that P is not true.

      Note about Fallacies

      Stating that a syllogism is a fallacy simply means that the conclusion was not obtained by logical deduction. It does not mean that the conclusion of the syllogism is false.

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     _    _     ______   __   _      ___      ______  
    | || | ||  /_   _// | || | ||   / _ \\   /_   _// 
    | || | ||   -| ||-  | '--' ||  / //\ \\    | ||   
    | \\_/ ||   _| ||_  | .--. || |  ___  ||  _| ||   
     \____//   /_____// |_|| |_|| |_||  |_|| /__//    
      `---`    `-----`  `-`  `-`  `-`   `-`  `--`     
                                                      
    
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  • 8. Invading Iraq

    Outline the invalid syllogism and identify the logical fallacy. (See Example 1 and Example 2.)

    A senator states, "The United States invaded Iraq on the premise that Saddam Hussein had weapons of mass destruction. Saddam did not have weapons of mass destruction, so the United States should not have invaded Iraq."

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     _    _      ___      _____     ______    ____    
    | \  / ||   / _ \\   /  ___||  /_   _//  |  _ \\  
    |  \/  ||  / //\ \\ | // __     -| ||-   | |_| || 
    | .  . || |  ___  ||| \\_\ ||   _| ||_   | .  //  
    |_|\/|_|| |_||  |_|| \____//   /_____//  |_|\_\\  
    `-`  `-`  `-`   `-`   `---`    `-----`   `-` --`  
                                                      
    
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