Logical Reasoning in Philosophy

Introduction to Logical Reasoning

• Logical reasoning is a method used by philosophers and scientists to draw conclusions from facts or statements.
• Involves following a set of premises to arrive at a specific conclusion.

Sound Arguments

• Definition: A sound argument has all true premises and a valid conclusion.
• Example of a Sound Argument:
  • Premise 1: London is in England.
  • Premise 2: Tom is in London.
  • Conclusion: Tom is in England.

Invalid and Unsound Arguments

• Example of an Unsound but Valid Argument:

  • Premise 1: London is in Denmark.
  • Premise 2: Holly is in London.
  • Conclusion: Holly is in Denmark.
  • Explanation:
    • Valid, as the conclusion follows the premises logically.
    • Not sound because Premise 1 is false.

• Example of a Valid Argument that is Not Sound:

  • Premise 1: Fred is human.
  • Premise 2: Humans are in London.
  • Conclusion: Fred is in London.
  • Explanation:
    • Both premises are true, but the conclusion does not logically follow.
    • There are many humans worldwide, not all in London.

Types of Logical Reasoning

1. Deductive Reasoning

• Definition: An argument intended to be completely true and certain.
• Examples:

  • Premise 1: All men are mortal.

  • Premise 2: I am a man.

  • Conclusion: I am mortal.

  • Alternative Example:

  • Premise 1: All humans have brains.

  • Premise 2: I am human.

  • Conclusion: I have a brain.

2. Inductive Reasoning

• Definition: Arguments that lead to conclusions that are highly probable rather than certain.
• Examples:

  • Premise 1: For the past ten years, the neighbor's dog hasn't bitten me.

  • Premise 2: I will be walking past the neighbor's dog today.

  • Conclusion: The neighbor's dog will not bite me today.

  • Alternative Example:

  • Premise 1: All known living organisms need water to survive.

  • Premise 2: Every new living organism found needs water.

  • Conclusion: If we find a new living organism, it would need water to survive.

3. Abductive Reasoning

• Definition: Similar to inductive reasoning but the conclusions are even less probable; it involves making inferences based on observations.
• Example:
  • Premise 1: Fred has been stabbed.
  • Premise 2: A knife matching the stab wound has Tom's fingerprints.
  • Conclusion: Tom stabbed Fred.
  • Explanation:
    • This conclusion is likely but not certain; other explanations could exist.

Conclusion

• Logical reasoning is essential for formulating sound arguments in philosophy and science.
• Encouragement to apply these concepts in creating logically sound arguments.