Critical thinking mid-term

 Argument

  -  Logic 

  - Argument 

    - A group of statement

    - Composed of premises and conclusion

    - The premises are supposed to support the conclusion

  - Deductive argument and inductive argument

    - The premises of deductive argument are intended to provide complete and unfailing support for the conclusion

    - Whereas the premises of inductive arguments are only meant to provide probable evidence that the conclusion is true.

    - Example 

      Ex1) Every raven that has been observed so far was black. So, all ravens are black.

      > Inductive

      Ex2) All men are mortal and Socrates is a man. Hence, Socrates is mortal.

      > Deductive

      Ex3) Jon W. has been clutching his head, and he just took some aspirin. He must have a headache.

      > Deductive? Inductive?

        - Reason for inductive : the premises don't actually guarantee the conclusion.

        - Reason for deductive : the premises are being put forward ad if they guarantee the conclusion

 Validity

  - Validity : the criterion used to evaluate the inferential claim of deductive arguments

    - Valid Argument : a deductive argument in which it is impossible for the premises to be true and the conclusion false. 

    - Invalid Argument : a deductive argument in which it is possible for the premises to be true and the conclusion false.

 Soundness 

  - Evaluation of the factual claim of an argument is also important.

    - A sound argument is valid and has all true premises. 

    - An unsound argument is either invalid, or has at least one false premise.

 Strength

  - An inductive argument is strong when the conclusion is probably true, given the truth of the premises.

  - If the conclusion is not likely to be true (or probably false) despite the truth of the premises, then it is weak.

 Cogency 

  - An inductive argument is cogent when it is strong and has actually true premises.

  - An inductive argument that is weak or has false premises is uncogent.

 *Exercises 

  - All sound argument are valid. -> True

  - All unsound argument are invalid. -> False

  - No cogent is a weak argument. -> True

  - Every uncogent argument has at least one false premise. -> False

  - All sound arguments have true premises and true conclusion. ->True.

 Forms of an Argument
  - Form and Contents
    - We can't always determine whether a given argument is valid or not merely from the truth values of the premises. This is because, validity is essentially a matter of form and not content.
    - Form: Underlying logical structure of an argument
    - Content: (roughly) what the argument is about
    - Examples
     Ex1) Either Jones or Smith is a murderer. Smith is a murderer. Therefore, Jones is not a murderer.
     - Content : What is this argument about?
     - Form : Either A or B.
                              B.
                    Therefore, not-A.
  - Valid Forms
    - Valid form: the truth of the premises guarantees the truth of the conclusion.
    - If a deductive argument has a valid form, then it is valid, regardless of its content.
  - Invalid Forms
    - If a deductive argument does not have a valid form, then it has an invalid form.
    - If a deductive argument has invalid form, then it is invalid, regardless of its content
  - Substitution Instances
    - Substitution instances: the result of the procedure where you uniformly replace the variable letters with specific statements in a given argument form

 How to Construct Counterexamples
  - Any invalid argument has an invalid argument form underlying it. To show an argument is invalid, we isolate its form and give it new content, such that the premises are obviously true, and the conclusion is clearly false. This is called the counterexample method.

 Counterexample Exercises
  - Counterexample Method
    - Procedure:
      1. Identify the form of the argument.
      2. Replace the substitution letters with well-known truths as the premises and a well-known falsity as the conclusion.

 Diagramming Argument
  - Diagramming Arguments
    - A. Since we often encounter sufficiently complex arguement, it is useful to be able to pictorially represent an argument.
    - B. Procedure ;
      - i. Assign a number to each statement.
      - ii. Identify the premises and the conclusion.
        a. General tip
          1) Start from the conclusion.
          2) Use indicators, if applicable.
      - iii. Clarify the patterns of inferential support.
        a. Specify missing premise(s), if necessary.
        b. Eliminate fillers.
  - Diagramming Various Argument Patterns
    - A. Vertical Pattern
      - i. Sometimes we are led to a conclusion by a single premise which itself can be the conclusion of another argument.
    - B. Horizontal Pattern
      - i. Sometimes many premises can each provide independent support for a given conclusion.
    - C. Conjoint premises
      - i. Sometimes a conclusion is supported by more than one premise neither of which provides independent support for it.
    - D. Sub-Arguments
    - E. Filer-Statements
      - i. Some statements play no actual role in the argument structure. Such a statement is simply filler material.
      - ii. Filler statements are numbered, but will not appear in the diagram.
    - F. Missing Premises
      - i. Some arguments contain missing premises.

 Fallacies
  - What's A Fallacy?
    - A. Fallacies are errors in reasoning.
    - B. Some fallacies are common and can be psychologically persuasive.
    - C. Two categories:
      i. Formal fallacies
      ii. Informal fallacies
  Fallacies Involving Irrelevant Premises
    - Fallacies Involving Irrelevant Premises
      - A. Argument against the person (ad hominem)
      - B. Circumstantial Ad Hominem
      - C. Ad Hominem Tu Quoque
      - D. Straw Man
      - E. Appeal to the Force
      - F. Appeal to the People
      - G. Appeal to Pity
      - H. Appeal to Ignorance

 Fallacies Involving Ambiguity
  - Equivocation
    - i. Premises : contain an ambiguous word
    - ii. Conclusion : is reached by trading on the ambiguity
  - Amphiboly
    - i. Premises : contain a sentence with an ambiguous structure
    - ii. Conclusion : is reached by trading on the ambiguity
  - Composition
    - i. Premises : the parts (or members) have attribute X
    - ii. Conclusion : the whole (or group) has attribute X
  - Division
    - i. Premises : the whole (or group) has attribute X
    - ii. Conclusion : the parts (or members) have attribute X