Philosophy 251 Critical Thinking

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Philosophy 251Critical Thinking

• Review Syllabus
• What is Philosophy?
• 4 main branches
• Metaphysics
• Ethics
• Epistemology
• Logic

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Logic

• Different Branches
• Formal logic
• Concerned with the general forms of deductive
  reasoning
• Studied using a symbolic notation
• Informal logic
• In general this is concerned with nondeductive
  reasoning
• Typically uses very little symbolic notation

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Inference

• Logic, both formal and informal, is the study of
  inference.
• Inference (defn) is a relationship between
  thoughts or statements. We infer statement B
  from statement A iff A supports, justifies, or
  makes it reasonable to believe B.

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Examples (p. 18)

• Alan is broke and he is unhappy.
• Alan is broke therefore he is unhappy.
• Anne was in a car accident last week, and she
  deserves an extension on her essay.
• Anne was in a car accident last week, so she
  deserves an extension on her essay.
• The triangle has equal sides and equal angles.
• The triangle has equal sides hence it has equal
  angles

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Inference Indicators
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What is a statement?

• A statement (defn) is a sentence that is used to
  make a claim that is capable of being true or
  false.
• Statements are sentences that are in the
  declarative mood (this is to be contrasted with
  other moods of sentences e.g., sentences in the
  interrogative mood (questions), sentences in the
  imperative mood (commands), etc.)

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Examples

• Shut the door! (imperative)
• Is the door shut? (interrogative)
• The door is shut. (declarative)
• Only sentences in the declarative mood are
  capable of being true or false.

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Arguments

• An argument (defn) is a set of statements that
  claims that one or more of those statements,
  called the premises, support another of them,
  called the conclusion.
• A argument is not mere disagreement or
  contradiction.

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Logical Strength

• (Defn) An argument has logical strength when its
  premises, if true, actually provide support for
  its conclusion.
• Two points
• 1. the logical strength of an argument is
  independent of the truth of the premises.

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Example
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Logical Strength

• Two points
• 1. the logical strength of an argument is
  independent of the truth of the premises.
• 2. the logical strength of an argument is often
  a matter of degree.

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Logical Strength

• Deductive arguments these are arguments that
  have the highest degree of logical strength.
• In deductive arguments the conclusion follows
  necessarily from the premises.
• That is, if the premises are true, then it is
  impossible for the conclusion to be false.
• Deductive arguments are nonampliative.

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Examples

• All men are mortal
• All Greeks are men
• All Greeks are mortal
• Since Antigonish is the largest city in Nova
  Scotia, and Moncton is a city in Nova Scotia, it
  follows that Antigonish is larger that Moncton.

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Logical Strength

• Inductive Arguments these are arguments that are
  not deductive.
• In inductive arguments the conclusion does not
  follow necessarily from the premises.
• That is, if the premises are true, it is possible
  that the conclusion is or could be false.
• Some inductive arguments will be stronger than
  others.
• Inductive arguments are ampliative.

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Examples

• Arthur has been a moderate social drinker for
  twenty years and no one has ever known him to get
  drunk. Therefore, he wont get drunk at the
  party tonight.
• Every swan I have ever seen is white, hence it
  follows that all swans are white.

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Truth, Logical Strength and Soundness

• Truth is a property of sentences.
• Logical Strength is a property of arguments or
  inferences.
• These concepts are independent of each other.
  The truth or falsity of a sentence has nothing to
  do with the logical strength of an argument, and
  the logical strength of an argument does not
  contribute to the truth or falsity of the
  sentences that make it up.

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Truth, Logical Strength and Soundness

• If we want to use arguments (and our critical
  thinking skills) to arrive at the truth (and
  isnt this what we want?!), then we are going to
  be concerned with both truth and logical
  strength. That is, arguments that have true
  premises and are logically strong are going to
  have conclusions which are likely to be true.
• Arguments/inferences that have true premises and
  are logically strong are sound.

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Truth, Logical Strength and Soundness

• Instead of asking Is X a good argument?
• Ask these two questions instead
• 1. Are the premises true?
• 2. Is it logically strong?

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Exceptions

• Counterfactual arguments
• E.g. If Hitler had invaded Britain in 1940 he
  would have succeeded, because at that time the
  Germans had military superiority.
• Reductio ad absurdum (reducing to absurdity)
• In these sorts of arguments we assume the
  opposite (negation) of what we are trying to
  prove and show that it leads to a contradiction.

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Critical Thinking Skills

• The primary focus of critical thinking is to
  develop skills to determine if arguments are
  sound.
• Requires three types of skills
• Interpretative skills (meaning, definition, etc.)
• Verification skills (assessing truth, adequacy,
  etc.)
• Reasoning skills (inductive and deductive
  principles)