TOPIC SIX- THE ART OF REASONING

• Statements


  A specific type of sentence that has truth value, meaning they can be either true or false
• Statements are a kind of sentence
• Statements


  • Have truth value - they can be either true or false
• Statements


  • "Washington D.C. is the capital of the United States" (true statement)
  • "The moon is a satellite of the earth" (true statement)
  • "Two plus two is four" (true statement)
• Argument


  A group or set of statements which are intended to prove one other statement
• Premises


  The statements being used to prove the one other statement
• Conclusion


  The statement that is being proven
• Every argument only has one conclusion
• Logical arguments


  • All humans are mortal. Socrates is human. Therefore, Socrates is mortal.
  • I have gone to work five times a week for the last ten years. During this time, it has always taken me 30 minutes to get to work. Tomorrow, I will drive to work. Therefore, tomorrow it will take me 30 minutes to get to work.
• Premise indicator


  Words that indicate a premise is about to follow, e.g. "since", "because", "given that"
• Propositions


  The technical name for statements in logic
• Conclusion indicator


  Words that indicate a conclusion is about to follow, e.g. "therefore", "thus", "consequently", "it follows that"
• It is better to understand the logic behind the argument rather than just focusing on the conclusion/premise indicator words
• Non-statements


  • "What time is it?" (question)
  • "Bring me my car keys" (command)
• Questions and commands are sentences but do not have truth value
• Inductive argument


  The truth of the conclusion depends on chance and contingency
• Deductive argument


  The truth of the conclusion does not depend on chance or contingency, but on necessity
• In inductive arguments, the conclusion could be true or false depending on what happens
• In deductive arguments, if the premises are true, the conclusion must be true</b>
• In a well-reasoned deductive argument, if the premises are true, it is impossible for the conclusion to be false
• Inductive argument example


  • For the last 10 years I have driven to work in 30 minutes, so tomorrow I will drive to work in 30 minutes
• Deductive argument example


  • The Statue of Liberty is in New York City, New York City is in the United States, therefore the Statue of Liberty is in the United States
• Even if the premises in a deductive argument are false, the conclusion must follow if the argument is well-reasoned
• If a deductive argument has true premises but a false conclusion, it is just a poorly reasoned deductive argument
• Poorly reasoned deductive argument example

  • All banks are financial institutions, Merrill Lynch is a financial institution, therefore Merrill Lynch is a bank
• Practical reasons for distinguishing inductive and deductive arguments

  To assess the strength of claims and conclusions - inductive arguments have more room for doubt, deductive arguments must follow necessarily from the premises
• Philosophical reasons for distinguishing inductive and deductive arguments

  Deductive reasoning allows for a priori knowledge, knowledge that is not based on experience - this relates to the possibility of metaphysical knowledge
• Deductive argument


  Arguments where the conclusion is not a matter of probability or chance, but must necessarily follow if the premises are true
• Inductive argument


  Arguments where the conclusion is a matter of probability or likelihood
• Deductive argument


  1. Premises are true

  2. Conclusion must necessarily follow
• Deductive arguments


  • Idea of necessity - given true premises, conclusion must be true
• Inductive argument


  Conclusion is a matter of chance, contingency or probability, unlike deductive arguments where the conclusion must follow if the premises are true
• Deductive argument forms/types


  • Arguments based on mathematics
  • Arguments from definition
  • Categorical syllogisms
  • Hypothetical syllogisms
  • Disjunctive syllogisms
• Inductive arguments


  • Conclusion doesn't necessarily have to follow, it could follow, it might follow, it all depends on chance and/or contingency
• Arguments based on mathematics

  Arguments based on mathematical calculation, computation or measurement
• Types of inductive arguments

  • Predictions
  • Arguments from analogy
  • Generalizations
  • Arguments from authority
  • Arguments based on signs
  • Causal inferences
• Arguments based on mathematics


  • The area of a triangle is the product of the base and the height divided by two. Triangle A has base of 4. Triangle A has height of 8. Therefore, the area of triangle A is sixteen.
• Validity


  A concept that only applies to deductive arguments, meaning a well-reasoned deductive argument
• Prediction


  Conclusion drawn based on knowledge of the past
• Arguments from definition


  Conclusions rely on the definition of a word or phrase